# Patent

## Title
Control device for legged mobile body

## Abstract

A desired motion determiner of a control unit of a legged mobile robot determines a leg motion parameter specifying the motion trajectory of a distal end of a leg of the robot on the basis of the information on a floor geometry of an environment in which the robot travels and a requirement related to a travel route of the robot, thereby sequentially determining the desired motion of the robot. A floor geometry information output unit which outputs floor geometry information to the desired motion determiner outputs floor geometry information in which a rising surface of a stepped portion of a predetermined type, the contact thereof with a leg of the robot should be avoided, has been shaped into a surface having a gentler slope than an actual rising surface. The desired motion determiner determines the leg motion parameter such that the leg will not come in contact with the stepped portion having the shaped rising surface.

## Background
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a control device for a legged mobile robot, such as a bipedal robot.
2. Description of the Related Art
For a legged mobile robot which moves by the motions of a plurality of legs provided such that the legs extend from a base body, a control technique that allows a desired gait including a desired motion of the robot to be sequentially generated in real time and to control the motion of the robot so as to make the actual gait of the robot follow the desired gait has been proposed by the applicant of the present application in, for example, Japanese Patent No. 3269852, Japanese Patent No. 4246638, and Published PCT International Application WO2002/040224.
To sequentially generate desired motions of the robot in real time while controlling the motion of the robot as described above, it is necessary to supply the information on a floor geometry, which indicates the floor geometry of the environment in which the robot travels, to a device which generates the desired motions. The device which generates the desired motions determines the desired motion by reflecting the information on the floor geometry on the desired motion of the robot.
For example, a desired motion generator determines the motion trajectory of the distal portion of each leg, including an expected landing position or the like of each leg, in a desired motion of the robot on the basis of the supplied floor geometry information.
Basically, the desired motion of the robot should be determined to assure a smooth motion of the robot on an actual floor surface. Hence, it is considered to be desirable that the floor geometry indicated by the floor geometry information used for generating the desired motion always agrees with an actual floor geometry.
In this case, however, the study by the inventor of the present application has revealed that the following inconvenience may occur.
It is assumed that, for example, there is a stepped portion, including a locally projecting portion, around an expected robot travel route, and that the contact between the stepped portion and the distal end of a leg of the robot is not originally expected. In this case, the desired motion generator will determine the motion trajectory of the distal end of the leg of a free leg such that the distal end of the free leg of the robot will not come in contact with the stepped portion. However, there is also a case where the motion trajectory may be a trajectory that passes a position relatively near the stepped portion.
In such a situation, if the actual robot moves completely in accordance with the desired motion, then there will be no contact between the leg of the robot and the stepped portion. However, there is a case where the motion trajectory of the distal end of the free leg relative to the actual floor deviates from the trajectory expected in the desired motion due to a slippage or the like of a supporting leg of the actual robot. In this case, a leg of the robot may come in contact with the stepped portion if the current motion trajectory of the distal end of the leg is maintained as it is.
Further, in this case, the original motion trajectory of the distal end of a leg of the robot is determined on the assumption that there will be no stepped portion on the trajectory. For this reason, if a possibility of contact between the distal end of a free leg and the stepped portion arises due to a slippage of a supporting leg of the actual robot, then changing the motion trajectory of the distal end of the free leg to obviate the possibility of the contact may require a significant change in the motion trajectory. Further, in such a case, it may be inconveniently impossible to actually change the motion trajectory because of restrictions on the dynamics of the robot or the capabilities of actuators.
The present invention has been made with a view toward overcoming the above drawbacks of the prior art, and it is an object of the invention to provide a control device capable of controlling the motions of a robot while generating desired motions that make it possible to properly avoid a predetermined type of stepped portion existing around a travel route of the robot.
SUMMARY OF THE INVENTION
To this end, a control device for a legged mobile robot in accordance with the present invention is a control device which determines a desired motion of a legged mobile robot which travels by moving a plurality of legs extended from a base body, thereby controlling the motions of the robot so as to cause an actual motion of the robot to follow the determined desired motion, including:
a desired motion determiner which determines a leg motion parameter specifying the motion trajectory of a distal end of a leg of the robot on the basis of at least the information on a floor geometry of an environment in which the robot travels and a requirement related to a travel route of the robot, thereby sequentially determining the desired motion having the motion of the distal end of the leg specified by the leg motion parameter;
a motion controller which controls the motion of the robot so as to cause the actual motion of the robot to follow the determined desired motion; and
a floor geometry information output unit which outputs the floor geometry information to the desired motion determiner,
wherein, in the floor geometry information output by the floor geometry information output unit to the desired motion determiner, at least the floor geometry information on a stepped portion, the contact with which a leg of the robot should be avoided and which is a predetermined type of stepped portion existing around the travel route of the robot is the information on a floor geometry in which the rising surface between a lower step surface and an upper step surface of the stepped portion indicated by the floor geometry information has been shaped to be a gentler slope surface than an actual rising surface (a first aspect of the invention).
In the present description, the term “floor” will be used to also include an outdoor ground surface or a road surface rather than meaning only a floor, such as an indoor floor, in a normal sense.
The term “stepped portion” does not have to be integral with a floor, and it may be formed by, for example, an object placed on a floor surface. Further, the “stepped portion” may be, for example, a locally projecting portion.
According to the first aspect of the invention, the desired motion determiner determines the leg motion parameter on the basis of at least the floor geometry information output from the floor geometry information output unit and the requirement related to the travel route of the robot. In this case, the floor geometry information on the predetermined type of stepped portion in the floor geometry information output from the floor geometry information output unit to the desired motion determiner is the information on a floor geometry in which the rising surface of the stepped portion has been shaped to be a gentler slope surface than an actual rising surface.
Therefore, the desired motion determiner recognizes the predetermined type of stepped portion as a stepped portion having the gentle surface as the rising surface, and determines the leg motion parameter such that the contact between the stepped portion, including the gentle slope surface, and a leg of the robot will be avoided.
Thus, the leg trajectory parameter will be determined such that the landing position of the distal end of the leg will not come excessively close to the stepped portion, deviating from the stepped portion including the gentle slope surface (the rising surface) in the motion trajectory of the distal end of a free leg of the robot. Further, the leg motion parameter will be determined such that, even if the trajectory of the distal end of the free leg in the air passes near the stepped portion, the trajectory rides over the gentle slope surface of the stepped portion. Consequently, the leg motion parameter will be determined such that the contact with the predetermined type of stepped portion will be avoided with an allowance.
As a result, the possibility of the contact between the predetermined type of stepped portion and a leg of the robot will be minimized even if the actual trajectory of the distal end of a free leg deviates from the trajectory expected by a desired motion of the robot relative to an actual floor due to a slippage or the like of the distal end of a supporting leg of the robot.
Moreover, the leg motion parameter is determined such That, in the case where the trajectory of the distal end of a free leg in the air passes near a stepped portion, the trajectory will ride over the gentle slope surface of the stepped portion. Thus, even if a possibility of the contact with the stepped portion arises due to the deviation of the trajectory of the distal end of a free leg of the robot, the contact can be avoided by making a small revision of the trajectory. This makes it possible to reduce dynamic restrictions or the restrictions or the like on the capabilities of the actuators of the robot in revising the trajectory, allowing the trajectory to be smoothly corrected in many cases.
Thus, according to the first aspect of the invention, the motion of the robot can be controlled while generating a desired motion that makes it possible to properly avoid a predetermined type of stepped portion existing around the travel route of the robot.
Supplementally, according to the first aspect of the invention, in the aforesaid floor geometry information, regarding, for example, a stepped portion on which the distal end of a leg is expected to be rested during a travel of the robot (e.g., a stepped portion that is not to be avoided, such as each step of a staircase), the rising surface may be shaped into a gentle slope surface or may have the same shape as that of an actual stepped portion.
Further, the floor geometry information output unit may store and retain floor geometry information prepared beforehand and output the stored and retained floor geometry information to the desired motion determiner. Alternatively, however, the floor geometry information output unit may be a device that acquires actual floor geometry information indicative of an actual floor geometry in an environment in which the robot travels and then generates floor geometry information, which is to be output to the desired motion determiner, by processing the acquired actual floor geometry information. In this case, the processing may be any type of processing as long as at least a portion of the rising surface of the predetermined type of stepped portion that exists around the travel route in the actual floor geometry indicated by the actual floor geometry information is shaped into the aforesaid gentle slope surface.
The requirement related to the travel route means a requirement for determining which travel route the robot should take to travel. The requirement may be, for example, a desired travel route itself for the robot or a desired direction in which the robot should travel, or a parameter that can indirectly specify the desired travel route or the traveling direction.
In the first aspect of the invention, the stepped portion of the predetermined type is preferably, for example, a stepped portion in which the tilt angle of at least the actual rising surface thereof on the acute angle side relative to a horizontal surface is an angle closer to 90° than a predetermined angle (a second aspect of the invention).
According to the second aspect of the invention, the floor geometry information on the stepped portion, at least the actual rising surface of which is a vertical surface (a surface parallel to the vertical direction) or a surface close thereto is output from the floor geometry information output unit to the desired motion determiner as the information on a stepped portion formed by shaping the rising surface into a gentle slope surface. This arrangement makes it easy to determine a desired motion of the robot that permits the avoidance of contact between the stepped portion whose actual rising surface is a vertical surface (a surface parallel to the vertical direction) or a surface close thereto and the distal end of a leg of the robot.
In the second aspect of the invention, in the floor geometry information output from the floor geometry information output unit to the desired motion determiner, regarding a stepped portion in which the tilt angle of an actual rising surface thereof on the acute angle side relative to the horizontal surface is smaller than a predetermined angle, the rising surface may not be shaped into a gentle slope surface.
In the first aspect or the second aspect of the invention described above, as a more specific embodiment of the aforesaid desired motion determiner, the following embodiment, for example, may be adopted. The desired motion determiner includes a proper leg motion determiner which sequentially determines whether there will be contact between the distal end of a free leg and a stepped portion of the predetermined type by the time a free leg lands on the basis of the floor geometry information output from the floor geometry information output unit and the latest leg motion parameter that has been determined in the case where it is assumed that the actual motion of the distal end of the free leg of the robot were continued after the current time according to at least a motion trajectory specified by the determined latest leg motion parameter; and a leg motion parameter updater which updates the leg motion parameter such that the contact will be avoided in the case where the determination result is affirmative (a third aspect of the invention).
According to the third aspect of the invention, the determination result given by the proper leg motion) determiner will be affirmative if a current motion trajectory (the motion trajectory specified by a determined latest leg motion parameter) of the distal end of a free leg will inconveniently lead to the contact between the distal end and the stepped portion of the predetermined type in the future due to, for example, a slippage or the like of a supporting leg while the robot is traveling. In this case, the leg motion parameter is updated such that the contact will be avoided.
With this arrangement, the motion trajectory of the distal end of the free leg of the robot can be appropriately adjusted to avoid the contact while moving the robot. Here, the deviation of the motion trajectory of the distal end of the free leg attributable to the slippage or the like of the supporting leg while the robot is traveling is usually relatively small. Further, the stepped portion of the predetermined type recognized by the desired motion determiner on the basis of the floor geometry information is a stepped portion whose rising surface has been shaped into a gentle slope surface. Hence, the sectional shape of the stepped portion in a plane that includes the motion trajectory will not develop a sudden change even if a relatively small deviation takes place as described above in the motion trajectory of the distal end of the free leg. Thus, the leg motion parameter can be generally updated simply by slightly changing the motion trajectory of the distal end of the free leg. This allows the motion of the robot to be smoothly continued.
In the third aspect of the invention described above, the leg motion parameter updater preferably updates the leg motion parameter such that the landing position of the distal end of the free leg in the future is closer to the landing position immediately before the distal end of the free leg leaves a floor than the landing position of the distal end of the free leg in the future specified by the leg motion parameter before updating in the case where the height of the distal end of the free leg in the motion trajectory is set to be greater than the height specified by the leg motion parameter before updating in order to avoid the contact (a fourth aspect of the invention).
According to the fourth aspect of the invention, when increasing the height of distal end of the free leg in a motion trajectory by updating the leg motion parameter, the leg motion parameter is updated such that the landing position of the distal end of the free leg in the future is closer to the landing position immediately before the free leg leaves a floor than the landing position of the distal end of the free leg in the future specified by the leg motion parameter before updating. This arrangement makes it possible to prevent the path length of the motion trajectory of the distal end of the free leg from being extended by updating the leg motion parameter. As a result, a leg of the robot can be moved while restraining the moving velocity (angular velocity or the like) of a joint of a leg of the robot from becoming excessive while at the same time maintaining the traveling velocity of the robot approximately at a constant level before and after updating the leg motion parameter.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a perspective view illustrating the schematic construction of a bipedal mobile robot as a mobile body in an embodiment of the present invention;
FIG. 2 is a block diagram illustrating the hardware configuration of a control unit provided in the robot of FIG. 1;
FIG. 3 is a block diagram illustrating the functional construction of the control unit;
FIG. 4 is a block diagram illustrating the processing by a compensating total floor reaction force moment distributor shown in FIG. 3;
FIG. 5(a) is a diagram illustrating an example of a floor geometry for explaining the processing by a floor geometry shaper 114 shown in FIG. 3, and FIG. 5(b) is a sectional diagram at V-V line in FIG. 5(a);
FIG. 6 is a diagram illustrating a running gait of the robot of FIG. 1;
FIG. 7 is a graph illustrating an example of a desired floor reaction force vertical component trajectory generated by a gait generator shown in FIG. 3;
FIGS. 8(a) and 8(b) are graphs illustrating an example of the desired floor reaction vertical component trajectory (a component in an X-axis direction and a component in a Y-axis direction) generated by the gait generator shown in FIG. 3;
FIG. 9 is a diagram visually illustrating a dynamic model of a robot used in the processing by the gait generator and a posture stabilization control calculator shown in FIG. 3;
FIG. 10 is a flowchart illustrating main routine processing carried out by the gait generator shown in FIG. 3;
FIG. 11 is a diagram visually showing a divergent state of a posture of the robot shown in FIG. 1;
FIG. 12 is a flowchart illustrating subroutine processing in S022 of FIG. 10;
FIG. 13 is a diagram illustrating the modes of motions of feet of the robot shown in FIG. 1 and supporting leg coordinate systems;
FIGS. 14(a) and 14(b) are diagrams for explaining determination processing in S101 of FIG. 12 and processing in S020 of FIG. 10, which is carried out according to a determination result;
FIG. 15 is a graph illustrating a desired floor reaction force vertical component trajectory in a normal turning gait of the robot shown in FIG. 1;
FIG. 16 is a graph illustrating a desired ZMP trajectory (a component in the X-axis direction) in the normal turning gait of the robot shown in FIG. 1;
FIG. 17 is a flowchart illustrating the subroutine processing in S024 of FIG. 10;
FIG. 18 is a flowchart illustrating the subroutine processing in S208 of FIG. 17;
FIG. 19 is a flowchart illustrating the subroutine processing in S026 of FIG. 10;
FIG. 20 is a flowchart illustrating the subroutine processing in S028 of FIG. 10;
FIG. 21 is a flowchart illustrating the subroutine processing in S702 of FIG. 20;
FIG. 22 is a graph for explaining the processing in S710 of FIG. 20;
FIG. 23 is a diagram for explaining the processing in S030 of FIG. 10;
FIG. 24 is a flowchart illustrating the subroutine processing in S032 of FIG. 10; and
FIG. 25 is a graph illustrating a desired floor reaction force vertical component trajectory in a walking gait of the robot shown in FIG. 1.



DESCRIPTION OF THE PREFERRED EMBODIMENTS
The following will describe an embodiment of the present invention by taking a bipedal mobile robot as an example of a legged mobile robot.
As illustrated in FIG. 1, a bipedal mobile robot 1 (hereinafter referred to simply as the robot 1) according to the present embodiment has a body 24 as a base body and a pair of right and left legs (leg links) 2, 2 extended from the body 24 as a moving mechanism for moving the body 24 above a floor surface.
The body 24 is connected to the proximal end portions (upper end portions) of the two legs 2, 2 through the intermediary of a waist joint (hip joint), which will be discussed later, and is supported above the floor surface by one or both of the legs 2, 2 that are in contact with the ground.
The two legs 2, 2 share the same construction and each thereof has six joints. The six joints are a joint 10R or 10L for turning a waist (hip) (for the rotation in the yaw direction relative to the body 24), a joint 12R or 12L for turning the waist (hip) in a roll direction (about an X-axis), a joint 14R or 14L for rotating the waist (hip) in a pitch direction (about a Y-axis), a joint 16R or 16L for rotating a knee in the pitch direction, a joint 18R or 18L for rotating an ankle in the pitch direction, and a joint 20R or 20L for rotating an ankle in the roll direction, which are arranged in this order from the body 24.
In the description of the present embodiment, reference characters R and L mean the correspondence to the right leg and the left leg. Further, the X-axis, a Y-axis, and a Z-axis mean three coordinate axes of a supporting leg coordinate system, which will be discussed later. The X-axis direction and the Y-axis direction of the supporting leg coordinate system are the directions of two axes that are orthogonal to each other on a horizontal plane, the X-axis axis direction corresponding to the longitudinal direction (the direction of the roll axis) of the robot 1 and the Y-axis direction corresponding to the lateral direction (the direction of the pitch axis) of the robot 1. The Z-axis direction is the vertical direction (the gravitational direction) and corresponds to the up-and-down direction (the direction of a yaw axis) of the robot 1.
The joints 10R(L), 12R(L) and 14R(L) of each leg 2 constitute a waist joint (hip joint) having 3 degrees of freedom, the joint 16R(L) constitutes a knee joint having 1 degree of freedom, and the joints 18R(L) and 20R(L) constitute an ankle joint having 2 degrees of freedom.
Further, the waist joint (hip joint) 10R(L), 12R(L), and 14R(L) and the knee joint 16R(L) are connected by a thigh link 32R(L), while the knee joint 16R(L) and the ankle joint 18R(L) and 20R(L) are connected by a crush link 34R(L). A foot 22R(L) constituting a distal portion (lower end portion) of each leg 2 is attached under the ankle joints 18R(L) and 20R(L) of each leg 2. Further, the upper end portion (the proximal end portion) of each leg 2 is connected to the body 24 through the intermediary of the waist joints (hip joints) 10R(L), 12R(L), and 14R(L).
Each of the aforesaid joints may have a publicly known structure proposed in, for example, Japanese Patent Publication Laid-Open No. 3-184782 by the applicant of the present application. In this case, an actuator rotatively driving each joint is constructed of an electric motor 42 (refer to FIG. 2) provided with a speed reducer.
The construction of each leg 2 described above provides the foot 22R(L) of each leg 2 with 6 degrees of freedom relative to the body 24. When the robot 1 travels, desired motions of the two feet 22R and 22L can be accomplished by driving 6*2=12 joints of the two legs 2, 2 together (“*” in the present description denotes multiplication for scalar calculation, while it denotes an outer product in vector calculation) at appropriate angles. This arrangement enables the robot 1 to implement motions for traveling in a three-dimensional space, such as a walking motion or a running motion.
In this case, both legs 2, 2 function as the moving mechanism for moving the body 24, which serves as the base body, on the floor surface. The body 24 serving as the base body is supported by the legs 2, 2 such that the body 24 is enabled to perform relative motions in relation to the legs 2, 2 through the intermediary of the waist joint (hip joint). Further, the motions of the body 24 relative to the floor surface can be controlled by controlling the drive of each joint of both legs. The motions of the body 24 include motions in an up-and-down direction (the vertical direction, a direction perpendicular to the floor surface, and the like) and motions for changing the posture of the body 24 in addition to motions in the horizontal direction (or a direction parallel to the floor surface) of the body 24.
In the present embodiment, a pair of right and left arms is attached to both sides of an upper portion of the body 24 and a head is mounted on the upper end of the body 24, although not shown. Further, each arm is capable of performing motions, such as swinging the arm to the front and the rear relative to the body 24, by a plurality of joints (a shoulder joint, an elbow joint, a wrist joint, and toe like) provided therein. However, these arms and the head may be omitted.
The body 24 includes therein a control unit 26 which controls the operation of the robot 1. In FIG. 1, however, the control unit 26 is shown outside the body 24 for the convenience of illustration.
A six-axis force sensor 36 is interposed between the ankle joints 18R(L), 20R(L) and the foot 22R(L) of each leg 2. The six-axis force sensor 36 detects the translational force components in the directions of three axes of a floor reaction force and the moment components about the three axes, which are transmitted to each of the legs 2 from a floor through the intermediary of the foot 22R(L), then outputs the detection signals to the control unit 26.
The body 24 has an inclination sensor 40 for measuring the inclination angles (the inclination angles in the roll direction and the pitch direction) of the body 24 relative to the vertical direction (the gravitational direction) and the changing velocities (angular velocities) thereof. More specifically, the inclination sensor 40 is constructed of an acceleration sensor and a rate sensor (angular velocity sensor), such as a gyro sensor, and outputs the detection signals of these sensors to the control unit 26. Then, the control unit 26 measures the inclination angle and the angular velocity of the body 24 relative to the vertical direction by a publicly known technique on the basis of the outputs of the inclination sensor 40.
Further, the electric motor 42 (refer to FIG. 2), which rotatively drives each joint is provided with an encoder (rotary encoder) 44 (refer to FIG. 2) for detecting the rotational angle of each joint, and a detection signal of the encoder 44 is output to the control unit 26.
Referring to FIG. 2, the control unit 26 is constructed of an electronic circuit unit having a microcomputer including a first arithmetic unit 50 and a second arithmetic unit 52 composed of CPUs, an A/D converter 54, a counter 56, a D/A converter 58, a RAM 60, a ROM 62, and a bus line 64 which transfers data among these constituent elements.
In the control unit 26, the outputs of the six-axis force sensor 36 and the inclination sensor 40 are converted into digital values by the A/D converter 54, and then input to the RAM 60 through the bus line 64. An output of the encoder (rotary encoder) 44 of each joint of the robot 1 is input to the RAM 60 through the counter 56.
The first arithmetic unit 50 generates a desired gait, which will be discussed later, calculates a joint displacement command (the desired value of the rotational angle of each joint), and sends out the calculated joint displacement command to the RAM 60. The second arithmetic unit 52 reads out a joint displacement command from the RAM 60 and an actual joint displacement (the actually measured value of the rotational angle of each joint) measured through the counter 56 from an output of the encoder 44, and calculates a drive command of the electric motor 42 of each joint necessary to cause the actual joint displacement to follow the joint displacement command (a command value that specifies the output torque of the electric motor 42).
Further, the second arithmetic unit 52 outputs the calculated drive command to a servo amplifier 46 for driving the electric motor 42 through the intermediary of the D/A converter 58. At this time, the servo amplifier 46 drives the electric motor 42 (energizes the electric motor 42) of the basis of the input drive command. Thus, the actual joint displacement of each joint is controlled to follow a joint displacement command.
Referring now to FIG. 3, the operation of the control device of the robot 1 in the present embodiment will be outlined. The sections except for the actual robot in FIG. 3 indicate the functions implemented by the processing carried out by the control unit 26 (the processing carried out primarily by the first arithmetic unit 60 and the second arithmetic unit 62).
In FIG. 3, for the sake of convenience, it is assumed that the actually measured values (actual joint displacements and the like) recognized by the control unit 26 from the outputs of the aforesaid sensors mounted on the robot 1 are output from the actual robot 1. In the following description, the aforesaid reference characters R and L will be omitted unless it is necessary to particularly distinguish the right leg 2 and the left leg 2.
The control unit 26 has a gait generator 100 that generates a desired gait, which is a target of the motion (gait) of the robot 1, by using a dynamic model expressing the dynamics of the robot 1 (the relationship between a motion of the robot 1 and an external force acting on the robot 1) and outputs the generated desired gait. The desired gait generated and output by the gait generator 100 is composed of a target related to the motion of the robot 1 and a target related to the external force acting on the robot 1.
In the present embodiment, a desired gait is composed of a desired body position/posture trajectory, which is the trajectory of a desired position and a desired posture of the body 24, a desired foot position/posture trajectory, which is the trajectory of a desired position and a desired posture of each foot 22, a desired arm posture trajectory, which is the trajectory of a desired posture of each arm, a desired ZMP trajectory, which is the trajectory of a desired position of the ZMP (Zero Moment Point) of the robot 1, and a desired total floor reaction force trajectory, which is a desired trajectory of the total floor reaction force as an external force acting on the robot 1. Of these constituent elements, the desired body position/posture trajectory, the desired foot position/posture trajectory, and the desired arm posture trajectory correspond to the targets related to the motion of the robot 1, while the desired ZMP trajectory and the desired total floor reaction force trajectory correspond to the targets of the external force. If any other part that can be moved in relation to the body 24 in addition to the legs 2 and the arms are provided, then a desired position/posture trajectory of the movable part will be added to the desired gait as a part of the targets related to the motion of the robot 1.
Here, the term “trajectory” in the aforesaid desired gait means a temporal change pattern (time series patter) and is formed of the time series of instantaneous values calculated for each control cycle (arithmetic processing cycle) of the gait generator 100. In the following description, the term “trajectory” may be replaced by the term “pattern.” In the following description, the term “desired” will be frequently omitted unless there is a possibility of misunderstanding.
The position and the velocity of the body 24 will mean the position and its moving speed of a predetermined representative point of the body 24 (e.g., the central point between the right and left hip joints). Similarly, the position and the speed of each foot 22 will mean the position and its moving velocity of a predetermined representative point of each foot 22. In the present embodiment, the representative point of each foot 22 is set at a point on the bottom surface of each foot 22, such as a point at which a perpendicular line from the center of the ankle joint of each of the legs 2 to the bottom surface of each root 22 intersects with the bottom surface.
The term “posture” means a spatial orientation. For example, the posture of the body is expressed by the inclination angle (posture angle) of the body 24 in the roll direction relative to the vertical direction (about the X-axis) and the inclination angle (posture angle) of the body 24 in the pitch direction (about the Y-axis). The posture of a foot is expressed by the spatial azimuths of two axes fixedly set on each foot 22. In the present description, a body posture may be referred to as a body posture angle. The body posture may include the rotational angle of the body 24 in the yaw direction (about the Z-axis).
Further, constituent elements in a gait other than the elements related to an external force acting on the robot 1 (a desired ZMP and a desired total floor reaction force), namely, foot position/posture, body position/posture and the like, which relate to the motion of each portion of the robot 1 are generically referred to as “motions.”
The floor reaction force acting on each foot 22 (a floor reaction force composed of a translational force and a moment) is referred to as “each foot floor reaction force” and the resultant force of “each foot floor reaction force” of all (two) feet 22R and 22L of the robot 1 is referred to as “total floor reaction force.” The following description, however, will hardly refer to each foot floor reaction force. Hence, the term “floor reaction force” will be regarded to have the same meaning as the term “total floor reaction force.”
The ZMP means a point on a floor surface at which the horizontal component of a moment (a moment component about the horizontal axis) acting about the point due to the resultant force of an inertial force generated by a motion of the robot 1 and the gravitational force acting on the robot 1 becomes zero. In a gait that satisfies a dynamic balance condition, the ZMP and the central point of a floor reaction force agree with each other. In this case, imparting a desired ZMP is equal to imparting the central point of a desired floor reaction force.
A desired floor reaction force is generally expressed by a point of action and a translational force and moment acting on the point. The point of action may be set anywhere, and in the present embodiment, a desired ZMP is used as the point of action of a desired floor reaction force. In a gait that satisfies the dynamic balance condition, the ZMP and the central point of a floor reaction force agree with each other, as described above, so that the moment component of the desired floor reaction force having the desired ZMP as the point of action will be zero, excluding a vertical component (a moment component about the Z-axis).
A desired body position/posture trajectory and a desired arm posture trajectory of a desired gait generated by the gait generator 100 are input to a robot geometric model (kinematics calculator) 102.
Further, a desired foot position/posture trajectory, a desired ZMP trajectory (a desired floor reaction force central point trajectory), and a desired total floor reaction force trajectory (more specifically, a desired translational floor reaction force vertical component trajectory, a desired translational floor reaction force horizontal component trajectory, and the trajectory of a desired floor reaction force moment about a desired ZMP) are input to a composite-compliance operation determiner 104 and a desired floor reaction force distributor 106.
Then, the desired floor reaction force distributor 106 distributes the desired floor reaction force to the respective feet 22R and 22L to determine the desired foot floor reaction force central point (the desired position of the floor reaction force central point of each of the feet 22R and 22L) and the desired foot floor reaction force (the desired floor reaction force to be applied to the floor reaction force central point of each of the feet 22R and 22L). The trajectories of desired foot floor reaction force central points and the desired foot floor reaction forces, which have been determined, are input to the composite-compliance operation determiner 104. Regarding a desired floor reaction force output from the gait generator 100, only a component necessary for the compliance control by the composite-compliance operation determiner 104 may be output. For example, the output of a desired translational floor reaction force horizontal component from the gait generator 100 may be omitted.
The composite-compliance operation determiner 104 determines a corrected desired foot position/posture with mechanism deformation compensation obtained by correcting a desired foot position/posture. The trajectory of the corrected desired foot position/posture is input to the robot geometric model 102.
The robot geometric model 102 calculates the joint displacement commands of the joints of the two legs 2, 2 that satisfy the desired body position/posture and the corrected desired foot position/posture with mechanism deformation compensation, which have been received, by inverse-kinematics calculation on the basis of a kinematics model (rigid link model) of the robot 1, and then outputs the calculated joint displacement commands to a joint displacement controller 108. Further, the robot geometric model 102 calculates the joint displacement commands of the joints of the arms that satisfy a desired arm posture, and outputs the calculated joint displacement commands to the joint displacement controller 108.
Then, the joint displacement controller 108 uses the joint displacement commands calculated by the robot geometric model 102 as the desired values to carry out follow-up control of the rotational angles of the joints (actual joint displacements) of both legs 2, 2 and both arms of the robot 1 through the intermediary of the servo amplifier 46. More specifically, the joint displacement controller 108 adjusts the output torque of the electric motor 42 as an actuator driving force such that the actual joint displacements (actually measured values) measured on the basis of the outputs of the encoder 44 agree with the joint displacement commands.
An actual foot floor reaction force, which is the floor reaction force actually acting on each foot 22 of the robot 1 by an actual motion of the robot 1 subjected to the follow-up control described above is measured from an output of the six-axis force sensor 36, and the actually measured value of the actual foot floor reaction force is input to the composite-compliance operation determiner 104.
Further, the actual body posture angle, which is the real posture angle (an inclination angle relative to the vertical direction) of the body 24 of the robot 1, is measured on the basis of an output of the inclination sensor 40, and the actually measured value of the actual body posture angle is input to a posture stabilization control calculator 112. The posture stabilization control calculator 112 also receives, for example, a desired body posture angle (the desired value of the posture angle of the body 24 relative to the vertical direction) of a desired body position/posture generated by the gait generator 100. The desired body posture angle takes a constant value (fixed value) in the present embodiment, and it is, for example, the posture angle of the body 24 when the body trunk axis of the body 24 of the robot 1 is set in the vertical direction (the posture angle=0). If the desired body posture angle takes a constant value (fixed value) as described above, then the step for supplying the desired body posture angle to the posture stabilization control calculator 112 may be omitted.
Then, the posture stabilization control calculator 112 calculates a body posture angle deviation Δθ, which is a difference between an input actual body posture angle (actually measured value) and a desired body posture angle. Further, the posture stabilization control calculator 112 calculates a compensating total floor reaction force moment Mdmd, which is the required value of a floor reaction force moment to be additionally applied to the robot 1 about a desired ZMP, on the basis of the calculated body posture angle error Δθ by the feedback control law as a required manipulated variable (required feedback manipulated variable) for converging the body posture angle error Δθ to zero.
In this case, a PD law, for example, is used as the feedback control law. Based on the body posture angle error Δθ and the temporal change rate thereof (differential value Δω, the compensating total floor reaction force moment Mdmd is calculated according to the following expression 50.

Mdmd=K1*Δθ+K2*Δω  Expression 50

K1 and K2 in this expression 50 denote a proportional gain and a differential gain, respectively. The values of these K1 and K2 are predetermined values set beforehand in the present embodiment.
In this case, more specifically, the compensating total floor reaction force moment Mdmd is composed of a component in the roll direction (about the X-axis) Mdmdx and a component in the pitch direction (about the Y-axis) Mdmdy. The reference characters Mdmdx and Mdmdy mean required moments about a desired ZMP (more specifically, the required value of a perturbation of a floor reaction force moment about a desired ZMP) necessary for converging the component in the roll direction (about the X-axis) and the component in the pitch direction (about the Y-axis), respectively, of the body posture angle error Δθ to zero.
Further, the component about the X-axis Mdmdx is calculated according to expression 50 on the basis of the components of the X-axis of Δθ and Δω. Similarly, the component about the Y-axis Mdmdy is calculated according to expression 50 on the basis of the components of the Y-axis of Δθ and Δω.
The values of the gains K1 and K2 in expression 50 may be variably set as necessary according to the motional state of the robot 1. For example, the value or values of one of both of K1 and K2 may be variably determined according to the entire center of gravity of the robot 1 or the vertical inertial force of the body 24. This makes it possible to compensate for the influence of the vertical inertial force attributable to a motion of the robot 1 and calculate the value of Mdmd that allows the body posture angle error Δθ to smoothly converge to zero.
Further, the Δθ may be converted to the positional error of the mass point of an inverted pendulum model, which will be discussed later, (specifically, the Δθ is multiplied by a height h of a body mass point 24b, which will be discussed later), and the Mdmd may be calculated according to the PD law on the basis of the positional error and the temporal change rate thereof.
The compensating total floor reaction force moment Mdmd determined by the posture stabilization control calculator 112 is divided into a desired floor reaction force moment for compliance control and a model manipulation floor reaction force moment through the intermediary of a compensating total floor reaction force moment distributor 110.
The desired floor reaction force moment for compliance control is a perturbation floor reaction force moment about a desired ZMP to be additionally applied to the actual robot 1 in order to bring the aforesaid body posture angle error Δθ close to zero. The model manipulation floor reaction force moment is a perturbation floor reaction force moment about a desired ZMP additionally generated in a dynamic model for generating a gait, which will be discussed later, for the same purpose as that of the desired floor reaction force moment for compliance control. The model manipulation floor reaction force moment is, in other words, a perturbation floor reaction force moment generated about a desired ZMP by a motion of a finally determined desired gait by the gait generator 100 (a desired gait output by the gait generator 100).
These floor reaction force moments are determined as described below for each component in the roll direction (about the X-axis) and the pitch direction (about the Y-axis). First, the model manipulation floor reaction force moment is determined according to expression 52 given below. Incidentally, Mdmd in expression 52 means each component (Mdmdx or Mdmdy) in the roll direction (about the X-axis) and the pitch direction (about the Y-axis). Similarly, a floor reaction force moment permissible range means the permissible range of the floor reaction force moment of each component in the roll direction (about the X-axis) and the pitch direction (about the Y-axis). The floor reaction force moment permissible range is determined in the gait generator 100 (in S1008 of FIG. 24), as will be described Later.
In the case where Mdmd>Upper limit value of the floor reaction force moment permissible range;

Model manipulation floor reaction force moment=−(Mdmd−Upper limit value of floor reaction force moment permissible range)

In the case where Mdmd<Lower limit value of the floor reaction force moment permissible range;

Model manipulation floor reaction force moment=−(Mdmd−Lower limit value of floor reaction force moment permissible range)

In the case where Lower limit value of the floor reaction force moment permissible range Mdmd Upper limit value of the floor reaction force moment permissible range;

Model manipulation floor reaction force moment=0   Expression 52

In expression 52 given above, the compensating total floor reaction force moment Mdmd (more specifically, Mdmdx or Mdmdy) itself is compared with the floor reaction force moment permissible range. Basically, however, the object to be compared with the floor reaction force moment permissible range in the above expression 52 is the moment obtained by adding Mdmd to a reference instantaneous value of a floor reaction force moment about a desired ZMP. The reference instantaneous value indicates the moment about the desired ZMP in a desired total floor reaction force generated by the gait generator 100 when it is assumed that the aforesaid body posture angle error Δθ is steadily maintained at zero.
In this case, according to the present embodiment, the reference instantaneous value of the moment about a desired ZMP is steadily zero for the components in both roll direction (about the X-axis) and pitch direction (about Y-axis). Hence, the result obtained by adding Mdmd to the reference instantaneous value is equal to Mdmd. For this reason, in the above expression 52, Mdmd (more specifically, Mdmdx or Mdmdy) is directly compared with the floor reaction force moment permissible range.
Subsequently, the desired floor reaction force moment for compliance control is determined according to expression 54 given below for each component in the roll direction (about the X-axis) and the pitch direction (about the Y-axis). As with the case of expression 52, Mdmd in expression 54 means each component (Mdmdx or Mdmdy) in the roll direction (about the X-axis) and the pitch direction (about the Y-axis).

Desired floor reaction force moment for compliance control=Mdmd+Model manipulation floor reaction force moment   Expression 54

Hence, the floor reaction force moments are determined such that the difference between the desired floor reaction force moment for compliance control and the model manipulation floor reaction force moment is equal to Mdmd.
The block diagram of the compensating total floor reaction force moment distributor 110 performing the computation described above is shown in FIG. 4. The arithmetic processing is carried out on each component in the roll direction (about the X-axis) and the pitch direction (about the Y-axis). If the compensating total floor reaction force moment Mdmd (Mdmdx or Mdmdy) stays within a floor reaction force moment permissible range, then Mdmd is immediately determined as the desired floor reaction force moment for compliance control and the model manipulation floor reaction force moment is determined to be zero.
For each component in the roll direction (about the X-axis) and the pitch direction (about the Y-axis), if the compensating total floor reaction force moment Mdmd (Mdmdx or Mdmdy) deviates from a floor reaction force moment permissible range, then the boundary value of either the upper limit value or the lower limit value of the floor reaction force moment permissible range, whichever is closes to Mdmd, is determined as the desired floor reaction force moment for compliance control, and a moment obtained by reversing the sign of a deviation of Mdmd from the floor reaction force moment permissible range (=Mdmd−Boundary value of the floor reaction force moment permissible range) is determined as the model manipulation floor reaction force moment.
Referring back to FIG. 3, the gait generator 100 receives the model manipulation floor reaction force moment determined as described above. The gait generator 100 also receives the floor geometry information for generating gaits output from the floor geometry shaper 114 and required parameters, which will be discussed later.
Here, the floor geometry shaper 114 receives actual floor geometry information indicating an actual floor geometry around the robot 1 (including a front area in a direction in which the robot 1 travels). The actual floor geometry information is generated by the control unit 26 on the basis of, for example, an image taken by an imaging camera (not shown) mounted on the head or the like of the robot 1.
The aforesaid actual floor geometry information may be input, as needed, to the control unit 26 from, for example, a server or the like outside the robot 1 by wireless communication with the robot 1. Alternatively, the robot 1 may be provided with a self position recognizing function (a function for recognizing its own position and orientation of the robot 1 in a global coordinate system) and map information including the actual floor geometry information on an environment in which the robot 1 travels may be stored beforehand in a memory of the robot 1. Then, the actual floor geometry information around the robot 1 recognized from its own position and orientation of the robot 1 may be acquired from the map information and the acquired information may be input to the floor geometry shaper 114. The actual floor geometry information may include information on properties, such as the frictional coefficient and the hardness, of an actual floor.
Although it will be discussed in more detail hereinafter, after receiving the actual floor geometry information as described above, the floor geometry shaper 114 processes the geometry information on a predetermined object to be processed, i.e., an object to be shaped, in the input actual floor geometry information by differentiating the information from that on an actual floor geometry. Thus, the floor geometry information for generating gaits is generated and output.
Although it will be discussed in more detail hereinafter, after receiving the model manipulation floor reaction force moment and the floor geometry information for generating gaits, the gait generator 100 determines a desired ZMP trajectory and generates the motion of a desired gait (a desired motion) by using a dynamic model such that the horizontal component of the floor reaction force moment about the determined desired ZMP will provide the model manipulation floor reaction force moment. In this case, the motion trajectory of the foot 22 of a free leg (the foot position/posture trajectory) is determined by incorporating the aforesaid floor geometry information for generating gaits.
The desired total floor reaction force output from the gait generator 100 to the composite-compliance operation determiner 104 is output, aiming at setting the horizontal component of the floor reaction force moment about the desired ZMP to zero.
Further, the desired floor reaction force moment for compliance control, which has been determined as described above by the compensating total floor reaction force moment distributor 110, is input to the composite-compliance operation determiner 104. Then, the composite-compliance operation determiner 104 determines the corrected desired foot position/posture with mechanism deformation compensation (trajectory) obtained by correcting a desired foot position/posture such that the actual floor reaction force moment about the desired ZMP approaches the desired floor reaction force moment for compliance control, while causing the motion of the robot 1 to follow the motion of the desired gait generated by the gait generator 100.
In this case, it is virtually impossible to make the foot position/posture of the robot 1 and all floor reaction force states agree with desired states, so that tradeoff is adopted to achieve maximum possible agreement in a compromising manner. More specifically, the composite-compliance operation determiner 104 imparts a weight to the control error relative to each desired value when determining the corrected desired foot position/posture with mechanism deformation compensation (trajectory) therapy to minimize the weighted average of the control error or the squared control error).
In other words, the corrected desired foot position/posture with mechanism deformation compensation (trajectory) is determined such that the actual floor reaction force moment about the desired ZMP and the actual foot position/posture of the robot 1 approach the desired floor reaction force moment for compliance control and the desired foot position/posture, respectively, as much as possible. Then, the composite-compliance operation determiner 104 outputs the corrected desired foot position/posture as the final desired values of the foot position/posture to the robot geometric model 102, thereby controlling the operation of the robot 1.
In the present embodiment, the operation control means in the present invention is implemented by the processing carried out by the composite-compliance) operation determiner 104 described above. More specifically, the composite-compliance operation determiner 104 controls the operation of the actual robot 1 to additionally apply the desired floor reaction force moment for compliance control as an additional external force to the robot 1 while causing the actual motion of the robot 1 to follow the motion of the desired gait.
The construction and the operation of the composite-compliance operation determiner 104 or the like described above are described in detail in, for example, Japanese Patent Application Laid-Open No. 10-277969 filed by the present applicant. Therefore, no further detail of the composite-compliance operation determiner 104 will be given in the present description.
Thus, the operation of the robot 1 is controlled such that no model manipulation floor reaction force moment will cc added to the floor reaction force of the actual robot 1 while generating the motion of the desired gait such that a model manipulation floor reaction force moment as the model manipulation external force on the dynamic model of the robot 1 is additionally generated about the desired ZMP. Hence, there will be an imbalance (unbalance) between the motion of the desired gait and the floor reaction force by the model manipulation floor reaction force moment, which is the difference. This is equivalent to applying a floor reaction force moment, which has a sign reversed from the sign of the model manipulation floor reaction force moment, to the actual robot 1 from the viewpoint of the effect for converging the body posture angle error Δθ to zero.
In other words, determining an appropriate model manipulation floor reaction force moment makes it possible to converge the actual posture of the body 24 of the actual robot 1 to a desired posture and consequently stabilize the entire posture of the actual robot 1.
In this case, the sum of the model manipulation floor reaction force moment with a reversed sign and the desired floor reaction force moment for compliance control will be a total restoring force (floor reaction force moment) for converging the body posture angle error Δθ to zero. In other words, the difference between the desired floor reaction force moment for compliance control and the model manipulation floor reaction force moment will be the total restoring force.
The model manipulation floor reaction force moment can take any value independently of a range in which ZMP can exist, thus enabling an extremely high posture restoring force to be generated.
The following will described in more detail the processing by the floor geometry shaper 114 and the processing by the gait generator 100.
First, the floor geometry shaper 114 defines, as the object to be processed, the information on the geometry of a stepped portion of a predetermined type existing in the area around a travel route (the travel route expected at the present time) of the robot 1 in the received actual floor geometry information, and then shapes the geometry of the rising surface (more specifically, the tilt of the rising surface) between an upper step surface and a lower step surface of the stepped portion to be processed.
In this case, to be more specific, the stepped portion to be processed is a stepped portion, the contact with which the foot 22 of the robot 1 should avoid (in other words, the stepped portion not to be contacted). A stepped portion on which one or both of the feet 22 of the robot 1 are expected to be placed according to a traveling schedule of the robot 1 or a travel command issued by a maneuvering device or the like is excluded from the object to be processed. Further, the stepped portion to be processed is a stepped portion in which the angle of the rising surface between the upper step surface and the lower step surface relative to a horizontal surface is larger than a predetermined angle, e.g., 45° (a stepped portion whose rising surface is perpendicular or approximately perpendicular to a horizontal surface).
The stepped portion to be processed may be the one like a staircase (a stepped portion having a plurality of steps). Further, the stepped portion to be processed does not have to have a flat upper step surface, and may be a protrusion locally positioned on a flat floor surface. Furthermore, the stepped portion to be processed does not have to be integral with an actual floor surface, and may be an installed object on the actual floor surface.
Here, an example of the stepped portion to be processed is illustrated in FIGS. 5(a) and 5(b). In this example, as illustrated in FIG. 5(a), it is assumed that the robot 1 travels along the travel route indicated by the chain line in the drawing by alternately landing the feet 22R and 22L of the robot 1 on an actual floor surface (a real floor surface). In this case, the actual floor surface has a stepped portion DF as illustrated, and the robot 1 is supposed to travel on the actual floor surface, which is the lower step surface of the stepped portion DF. Incidentally, the stepped portion DF of the actual floor surface in the illustrated example has a rising surface DFs1 between the upper step surface and the lower step surface, and the rising surface DFs1 is substantially perpendicular to the horizontal surface.
If the actual floor surface indicated by the input actual floor geometry information has the stepped portion DF as described above and the stepped portion DF exists in the surrounding area of the travel route of the robot 1 (the area between the two dashed lines shown in FIG. 5(a)), as illustrated in FIG. 5(a), then the floor geometry shaper 114 determines the stepped portion DF as the stepped portion to be processed. In the illustrated example, the corner of the stepped portion DF partly projects into the aforesaid surrounding area.
The surrounding area of the travel route of the robot 1 includes, for example, an area through which the robot 1 passes within the width thereof (within the width in the transverse direction of the travel route) and has a width that is larger than the passing area by a certain extent. The surrounding area may be set on the basis of, for example, the expected landing position/posture of the foot 22 of a free leg of the robot 1, which will be discussed later. Alternatively, if the desired travel route of the robot 1 is determined in advance, then the aforesaid surrounding area may be set on the basis of the desired travel route.
The floor geometry shaper 114 shapes, as described below, the rising surface of the stepped portion to be processed, which has been determined as described above. The floor geometry shaper 114 shapes the rising surface of the stepped portion of the actual floor surface to be processed, which is indicated by the input actual floor geometry information into a gentle slope surface having a slope that is gentler than the actual rising surface (a slope whose angle on the acute angle side relative to a horizontal surface is smaller). In other words, the rising surface is changed into a gentle slope surface. Then, the floor geometry shaper 114 outputs the geometry information on the shaped floor surface as the floor geometry information for generating gaits. Hence, the floor geometry information for generating gaits is the floor geometry information in which the geometry of the rising surface of the stepped portion to be process has been changed from the geometry of the actual floor surface indicated by the information on the actual floor geometry.
For instance, in the example illustrated in FIGS. 5(a) and 5(b), the rising surface DFs1 of the stepped portion DF of the actual floor surface is shaped (or changed) into a gentle slope surface DFs2 indicated by the virtual line. Then, the geometry information on the floor surface having the gentle slope surface DFs2 after the shaping is output as the floor geometry information for generating gaits.
In the example of the present embodiment, the gentle slope surface after the shaping is a flat surface having a certain tilt angle; however, the gentle slope surface may have a tilt angle that changes continuously or stepwise.
Basically, the shaping of the rising surface of a stepped portion to be processed may be implemented only on a portion that exists in the surrounding area of the travel route of the robot 1. Further, shaping a portion deviating from :he surrounding area (a portion that is unlikely to influence the traveling motion of the robot 1) may be omitted.
The above has described in detail the processing carried out by the floor geometry shaper 114.
Taking the running gait illustrated in FIG. 6 as an example, a desired gait generated by the gait generator 100 will now be outlined.
In the following description, the terms “floor reaction force vertical component” and “floor reaction force horizontal component” will mean “translational floor reaction force vertical component” and “translational floor reaction force horizontal component,” respectively, unless otherwise particularly specified.
Further, the term “two-leg supporting period” in a gait will refer to a period during which the robot 1 supports its own weight by its both legs 2, 2, the term “one-leg supporting period” will refer to a period during which the robot 1 supports its own weight by either one of the legs 2, 2, and the term “floating period” will refer to a period during which both legs 2, 2 are off a floor (floating in the air). Further, the leg 2 supporting the self weight of the robot 1 during the one-leg supporting period will be referred to as “the supporting leg,” while the leg 2 not supporting the self eight will be referred to as “the free leg.” The running gait, which will be mainly described in the present embodiment, does not include the two-leg supporting period. Instead, the running gait repeats the one-leg supporting period (landing phase) and the floating period alternately. In this case, neither of the legs 2, 2 supports the self weight of the robot 1; however, the leg 2 which was a free leg and the leg 2 which was a supporting leg in the one-leg supporting period immediately preceding the floating period will be still called the free leg and the supporting leg, respectively, in the floating period.
First, referring to FIG. 6, which illustrates the running gait, this running gait is the same gait as that of a normal running gait of a human. This running gait alternately repeats the one-leg supporting period during which the foot 22 of only one of the right and left legs 2 (supporting leg) of the robot 1 lands (comes in contact with the ground) and the floating period during which both legs 2, 2 float in the air.
The circled numerals in FIG. 6 indicate the time-series sequence in the running gait. In this case, the first state in FIG. 7 indicates the state at the beginning (initial state) of the one-leg supporting period, the second state indicates the state at a midpoint of the one-leg supporting period, the third state indicates the state at the beginning of the floating period (the end of the one-leg supporting period) following the one-leg supporting period, the fourth state indicates the state at a midpoint in the floating period, and the fifth state indicates the state at the end of the floating period (the beginning of the next one-leg supporting period). The blank arrows in FIG. 6 indicate the direction in which the robot 1 advances.
In this running gait, the robot 1 lands at the heel of the foot 22 of the supporting leg (the leg 2 on the front side in the running direction of the robot 1) at the beginning of the one-leg supporting period, as illustrated in the first state of FIG. 6.
Subsequently, after landing with substantially the entire bottom surface of the landed foot 22 (the foot 22 of the supporting leg) in contact with the floor, as illustrated by the second state in FIG. 6, the robot 1 jumps into the air by kicking the floor with the tiptoe of the foot 22 of the supporting leg (the foot 22 of the leg 2 on the rear side relative to the advancing direction of the robot 1 in the third state of FIG. 6), as illustrated by the third state in FIG. 6. This ends the one-leg supporting period and starts the floating period at the same time. The free leg in the one-leg supporting period exists at the rear of the supporting leg at the beginning of the one-leg supporting period, as illustrated by the first state in FIG. 6. Thereafter, the free leg is swung to the front of the supporting leg toward the next intended landing position, as illustrated by the second and the third states in FIG. 6.
Subsequently, after the floating period illustrated by the fourth state in FIG. 6, the robot 1 lands at the heel of the foot 22 of the free leg (the leg 2 that was the free leg in the one-leg supporting period immediately before the start of the floating period), starting the next one-leg supporting period.
Assuming the running gait illustrated in FIG. 6, the basic general outline of a desired gait generated by the gait generator 100 will be given.
When the gait generator 100 generates a desired gait, a required parameter representing basic requirements related to a motion mode of the robot 1 is input to the gait generator 100 through radio communication or the like from a control device, a server or the like, which are outside the robot 1 and which are not shown.
The required parameter is composed of, for example, the type of motion (walking, running, or the like) of the robot 1, desired landing position/posture (intended landing position/posture) of the foot 22 of the free leg, targeted landing time (expected landing time) or a parameter necessary to determine the above factors (e.g., the mean traveling speed or traveling direction or the travel route or the like of the robot 1). The required parameter may be stored and retained beforehand in a memory device, not shown, of the robot 1 and may be read by the gait generator 100 according to a predetermined schedule. The gait generator 100 also receives the floor geometry information for generating gaits output by the floor geometry shaper 114.
The gait generator 100 generates a desired gait according to a predetermined algorithm by using the aforesaid required parameter and the floor geometry information for generating gaits. To be more specific, according to the present embodiment, the gait generator 100 determines the gait parameters as the parameters that define some constituent elements of the desired gait, such as the desired foot position/posture trajectory of the desired gait and a desired floor reaction force vertical component trajectory, on the basis of the required parameter and the floor geometry information for generating gaits, and then sequentially determines the instantaneous values of the desired gait by using the aforesaid gait parameters and the dynamic model of the robot 1. Thus, the gait generator 100 generates the time series pattern (trajectory) of the desired gait.
In this case, the desired foot position/posture trajectory is generated for each foot 22 by using a finite-duration setting filter proposed in, for example, U.S. Pat. No. 3,233,450 by the applicant of the present application. The finite-duration setting filter is constituted of a plurality of stages (three stages or more in the present embodiment) of variable time constant first-order lag filters, i.e., filters whose transfer functions are expressed in the form of 1/(1+τs) (“τ” denotes a variable time constant; the filters will be hereinafter referred to as the unit filters), the stages being connected in series. The finite-duration setting filter is capable of generating and outputting a trajectory in which a specified value is reached at desired specified time. In this case, the time constant τ of the unit filters in each stage is set in a sequentially variable manner according to the remaining time from a start of the output/generation through the finite-duration setting filter to the aforesaid specified time.
More specifically, the time constant τ is set such that the value of τ reduces from a predetermined initial value (>0) as the remaining time becomes shorter until finally the value of τ reaches zero at the specified time when the remaining time reaches zero. Further, a step input having a height based on the specified value (more specifically, a change amount from the initial value to the specified value of the output of the finite-duration setting filter) is supplied to the finite-duration setting filter.
The finite-duration setting filter is capable of not only generating an output that reaches a specified value at specified time but also setting a changing velocity of an output of the finite-duration setting filter at specified time to zero or approximately zero. Especially when three or more stages (three stages are fine) of the unit filters are connected, even the changing acceleration (the differential value of the changing speed) of an output of the finite-duration setting filter can be set to zero or approximately zero.
The foot position/posture trajectory (the position/posture trajectory from the instant the foot 22 lands to the instant the foot 22 lands next) is generated, for example, as described below by using the aforesaid finite-duration setting filter. The desired foot position trajectory in, for example, the X-axis direction (longitudinal direction) is generated as follows.
The height of the step input to the finite-duration setting filter is determined on the basis of the position in the X-axis direction of the next expected landing position of each foot 22 defined by the aforesaid required parameter (more specifically, a change amount (movement amount) in the X-axis direction relative to the landing position preceding the next expected landing position, which corresponds to the aforesaid specified value). Further, the time constant τ is initialized to a predetermined initial value and then the determined step input is supplied to the finite-duration setting filter, starting the generation of the trajectory of the position of the foot 22 in the X-axis direction. At the time of generating the trajectory, the time constant τ is sequentially and variably set such that the time constant τ reduces from the initial value to zero by the expected landing time (corresponding to the aforesaid specified time) of the foot 22. Thus, the trajectory of the position of the foot 22 in the X-axis direction, by which the expected landing position is reached at the expected landing time, is generated.
Further, the desired foot position trajectory in the Z-axis direction (the vertical direction) is generated, for example, as described below. First, the position of the foot 22 in the Z-axis direction at which the height (the vertical position) of the foot 22 becomes maximum (hereinafter referred to as the highest-point position) and the time at which the highest-point position is reached are determined on the basis of the next expected landing position and the expected landing time of the foot 22 and floor geometry information (the information on a floor geometry on a longitudinal plane that includes the current landing position and the next expected landing position of the foot 22). Then, the height of the step input to the finite-duration setting filter is determined on the basis of the highest-point position (corresponding to the aforesaid specified value). Further, the time constant τ is initialized, and thereafter, the determined step input is supplied to the finite-duration setting filter and the foot position trajectory in the Z-axis direction to the highest-point position is sequentially generated. At this time, the time constant τ is sequentially and variably set such that the time constant τ reduces from the initial value to zero until the time at which the highest-point position is reached (corresponding to the aforesaid specified time).
Further, when the generation of the trajectory of the position in the Z-axis direction up to the highest-point position is completed, the time constant τ is initialized, and a step input having a polarity opposite from that of the previous step input (more specifically, a step input with an opposite polarity that has a height based on the change amount in the Z-axis direction from the highest-point position to the next expected landing position (corresponding to the aforesaid specified value)) is input to the finite-duration setting filter, and the trajectory of the foot position in the Z-axis direction from the highest-point position to the expected landing position is sequentially generated. At this time, the time constant τ is sequentially and variably set such that the time constant τ reduces from the initial value to zero by the expected landing time of the foot 22.
In the generation of the foot position trajectory in the Z-axis direction, the time constant τ may alternatively be variably set such that it continuously reduces from its initial value to zero from the time at which the trajectory generation is started to the time at which the foot 22 is expected to land. At the same time, the polarity of a step input may be switched to an opposite polarity at or in the vicinity of the time when the highest-point position is reached, thereby generating the foot position trajectory in the Z-axis direction. This arrangement enables the foot 22 to reach an expected landing position at expected landing time with no problem although it does not enable the foot 22 to accurately reach a desired highest-point position.
A foot posture trajectory can be also generated by using the finite-duration setting filter in the same manner as with the foot position trajectory described above. In this case, among spatial components of a foot posture, for a component involved in a posture angle that monotonously changes (monotonously increases or monotonously decreases), the foot posture trajectory may be generated in the same manner as the generation of the foot position trajectory in the X-axis direction described above. Further, for a component involved in a posture angle change of an extremely large value or an extremely small value, the foot posture trajectory may be generated in the same manner as the generation of the foot position trajectory in the Z-axis direction described above.
The desired foot position/posture trajectory generated by the finite-duration setting filter as described above is the desired position/posture trajectory of each foot 22 in a supporting leg coordinate system, which will be discussed later.
The desired foot position/posture trajectory to be generated as described above is generated such that the position of each foot 22 starts moving while gradually accelerating from an initial ground contacting state (the state at the starting time of a desired gait) to an expected landing position. Then, the desired foot position/posture trajectory gradually reduces the changing velocity of the position to zero or approximately zero until finally the expected landing time is reached, and the foot stops at the expected landing position at the expected landing time. Accordingly, the ground speed at the instant each foot 22 lands the changing velocity of the position of each foot 22 in the supporting leg coordinate system fixed to a floor) becomes zero or approximately zero. Therefore, the landing impact will be small even when both legs 2, 2 simultaneously land from the state in which both legs 2, 2 are in the air (the state in the floating period) in the running gait.
In the aforesaid running gait, the vertical velocity of the body 24 is directed downward from the latter part of the floating period due to the gravitational force acting on the robot 1, and remains downward at the time of landing. Hence, the relative velocity of the foot 22 of the free leg in relation to the body 24 is directed upward immediately before landing when the desired foot position/posture trajectory is generated such that the ground speed becomes zero or approximately zero at the instant the foot 22 lands, as described above, and the desired position/posture trajectory of the body 24 is generated such that the dynamic balance condition is satisfied, as will be described later.
This means that, at the landing instant in the running gait, the desired gait of the robot 1 is a gait in which the leg 2 of the free leg side is drawn in toward the body 24 at the time of landing. In other words, according to the desired gait in the present embodiment, the robot 1 lands with the foot 22 of the free leg pulled up, as observed from the body 24, such that the ground speed of the foot 22 becomes zero or approximately zero at the instant of landing. This reduces a landing impact, thus preventing an excessive landing impact.
In the present embodiment, since the finite-duration setting filter is formed of three stages or more (e.g., three stages) of the unit filters connected in series, the velocity of each foot 22 (the changing velocity of the foot position) reaches zero or approximately zero by the expected landing time and also each foot 22 stops with the acceleration thereof reaching zero or approximately zero at the expected landing time. This means that the ground speed at the landing instant also becomes zero or approximately zero. Hence, the landing impact will be further smaller. In particular, even if the landing time of the actual robot 1 deviates from desired landing time, the impact will not increase much. Supplementally, in order to set the ground speed of each foot 22 to zero or approximately zero at expected landing time, the number of stages of the unit filters of the finite-duration setting filter may be two. However, in this case, the acceleration of each foot 22 at the expected landing time will not generally become zero.
Regarding the foot posture, after each foot 22 lands at the heel thereof at the expected landing time, the foot 22 continues to move until substantially the entire bottom surface of the foot 22 comes in contact with the floor. For this reason, the time at which substantially the entire bottom surface of the foot 22 comes in contact with the floor is set to the aforesaid specified time when generating the foot posture trajectory by the finite-duration setting filter.
In the present embodiment, the foot position trajectory has been generated by using the finite-duration setting filter. Alternatively, however, a desired foot position trajectory may be generated by using a function of, for example, a polynomial expression, which is set such that the changing velocity of the foot position at expected landing time becomes zero or approximately zero (the temporal differential value of the foot position becomes zero) and further the changing acceleration (the temporal differential value of the changing velocity) of the foot position at the expected landing time becomes zero or approximately zero. This applies also to the generation of a desired foot posture trajectory. However, regarding the generation of the desired foot posture trajectory, a function of a polynomial expression or the like is set such that the changing velocity of the posture of each foot 22 and further the changing acceleration thereof becomes zero or approximately zero at the time when substantially entire bottom surface of each foot 22 comes in contact with the floor, as described above.
The gait generator 100 explicitly sets a desired floor reaction force vertical component. The desired floor reaction force vertical component trajectory is set, for example, as illustrated in FIG. 7. In the present embodiment, the shape of a desired floor reaction force vertical component trajectory (specifically, the shape in a one-leg supporting period) in a running gait is fixed to a trapezoidal shape (a shape bulging toward an increasing side of the floor reaction force vertical component). Further, the height of the trapezoid and the time of breakpoints are determined as the gait parameters (floor reaction force vertical component trajectory parameters) that define the desired floor reaction force vertical component trajectory.
In the floating period of a running gait, the desired floor reaction force vertical component is constantly set to zero. The desired floor reaction force vertical component trajectory is preferably set to be substantially continuous (such that values are not discontinuous) as with this example. This is for ensuring smooth operations of joints of the robot 1 when controlling a floor reaction force. Here, the phrase “substantially continuous” means that skipped values which inevitably result when a trajectory that is continuous in an analog manner (continuous trajectory in a true sense) is expressed in a digital manner by a discrete-time system do not cause loss of the continuity of the trajectory.
Supplementally, in the present embodiment, a floor reaction force is taken as an overall external force acting on the robot 1, so that a desired floor reaction force vertical component defines the inertial force in the vertical direction of the entire robot 1 (of the overall center of gravity of the robot 1). In other words, the result obtained by subtracting a component balancing the gravitational force acting on the entire robot 1 from the desired floor reaction force vertical component will balance the inertial force in the vertical direction of the entire robot 1. Accordingly, determining the desired floor reaction force vertical component eventually determines the inertial force in the vertical direction of the entire robot 1.
The desired ZMP trajectory is set as illustrated in, for example, FIGS. 8(a) and 8(b). In the running gait illustrated in FIG. 6, the robot 1 lands at its heel of the foot 22 of the supporting leg, as described above, then jumps into the air by kicking at the tiptoe of the foot 22 of the supporting leg, and lastly lands at the heel of the foot 22 of a free leg.
Hence, the position in the X-axis direction (longitudinal position) of the desired ZMP trajectory in the one-leg supporting period is set such that the position starts from the heel of the foot 22 of the supporting leg as its initial position, moves to the center in the longitudinal direction of the foot 22 in the period during which substantially the entire bottom surface of the foot 22 of the supporting leg comes in contact with the ground, and then moves to the tiptoe of the foot 22 of the supporting leg by the time of leaving the floor, as illustrated in FIG. 8(a). The position in the Y-axis direction (lateral position) of the desired ZMP trajectory in the one-leg supporting period is set at the same position as the position in the Y-axis direction of the center of the ankle joint of the leg 2 on the supporting leg side, as illustrated in FIG. 8(b).
As illustrated in FIG. 8(a), the position of the desired ZMP trajectory in the X-axis direction during the floating period is set to continuously move from the tiptoe of the foot 22 of the supporting leg to the landing position of the heel of the foot 22 of the free leg until the floating period ends (until the leg 2 of the free leg side lands).
Further, as illustrated in FIG. 8(b), the position of the desired ZMP trajectory in the Y-axis direction during the floating period is set to continuously move from the position in the Y-axis direction at the center of the ankle joint of the leg 2 on the supporting leg side to the position in the Y-axis direction at the center of the ankle joint of the leg 2 on the free leg side until the floating period ends (until the leg 2 of the free leg side lands). In other words, the desired ZMP trajectory is set to be a trajectory that is continuous (substantially continuous) throughout the entire period of the gait. Here, the meaning of the phrase “substantially continuous” ZMP trajectory mentioned above is the same as that in the case of the aforesaid floor reaction force vertical component trajectory.
In the present embodiment, the positions and time of the breakpoints of the desired ZMP trajectories illustrated in FIGS. 8(a) and 8(b) are set as the ZMP trajectory parameters (the parameters that define the desired ZMP trajectory).
The ZMP trajectory parameters are determined to have a high stability allowance and not to develop a sudden change. Here, a state in which a desired ZMP exists around the center of a smallest convex polygon (so-called supporting polygon) that includes a ground contact surface of the robot 1 indicates a high stability allowance (for more detail, refer to Japanese Patent Application Laid-Open No. 10-86081). The desired ZMP trajectories illustrated in FIGS. 8(a) and 8(b) are set such that the aforesaid conditions are satisfied.
Further, a desired arm posture is expressed in terms of a relative posture in relation to the body 24.
Further, desired body position/posture and desired foot position/posture are described using a global coordinate system. The global coordinate system is a coordinate system fixed to a floor. More specifically, the supporting leg coordinate system described below is used.
The supporting leg coordinate system is a coordinate system fixed to a floor, in which the origin thereof is a point at which the normal extended from the center of the ankle of the leg 2 on the supporting leg side to a floor surface intersects with the floor surface (this point agrees with the representative point of the foot 22 in a state wherein the substantially entire bottom surface of the foot 22 of the supporting leg is in contact with the floor surface in an example of the present embodiment) in a state wherein the foot 22 of the supporting leg is in a posture parallel to the floor surface and substantially the entire bottom surface of the foot 22 of the supporting leg is in contact (close contact) with the floor surface. The horizontal plane passing the origin is defined as an XY plane. In this case, the X-axis direction and the Y-axis direction are the longitudinal direction and the lateral direction, respectively, of the foot 22 of the supporting leg.
The origin of the supporting leg coordinate system does not necessarily coincide with the representative point of the foot 22 (the point that represents the position of the foot 22) in the state wherein substantially the entire bottom surface of the foot 22 of the supporting leg is in contact with the floor surface. Alternatively, the origin may be set at a point on the floor surface that is different from the aforesaid representative point.
Referring now to FIG. 9, the dynamic model of the robot 1 used for generating a gait in the present embodiment will be described.
The dynamic model of the robot 1 used in the present embodiment is a model formed of an inverted pendulum provided with a rod 24a, which can be swung with a desired ZMP as its supporting point and which has a variable length, and a mass point 24b supported by the upper end of the rod 24a, as illustrated in FIG. 9 (hereinafter referred to as the inverted pendulum model in some cases). The rod 24a is not supposed to have a mass.
In this dynamic model, a motion of the mass point 24b of the inverted pendulum corresponds to a motion of the body 24 of the robot 1, and the relationship between a motion of the body 24 and a floor reaction force acting on the robot 1 is expressed in terms of the relationship between a motion of the mass point 24b (hereinafter referred to as the body mass point 24b) and a floor reaction force acting on the inverted pendulum.
Further, in the dynamic model, the masses of the legs 2, 2 of the robot 1 are regarded to be sufficiently smaller than that of the body 24 (or the mass of the combination of the body 24, the arms and the head), and the mass of the body mass point 24b is to agree with the mass of the entire robot 1. The position of the body mass point 24b is set to a position uniquely determined from the body position/posture of the robot 1.
The behavior of the dynamic model (the dynamics of The robot on the dynamic model) is mathematized as shown below. However, for the purpose of simplifying the description, only a dynamic equation on a sagittal plane (a plane that includes the X-axis and the Z-axis of the supporting leg coordinate system) will be described, omitting a dynamic equation on a lateral plane (a plane That includes the Y-axis and the Z-axis of the supporting Leg coordinate system).
For the convenience of description, the variables and parameters related to the dynamic model are defined as follows.

    Zb: Vertical position of the body mass point (Position in the Z-axis direction)
    Xb: Horizontal position of the body mass point (Position in the X-axis direction)
    mb: Mass of the body mass point
    Xzmp: Horizontal position of a desired ZMP (Position in the X-axis direction)
    Zzmp: Vertical position of a desired ZMP (Position in the Z-axis direction)
    Fx: Horizontal component of a floor reaction force (more specifically, a component in the X-axis direction of a translational floor reaction force)
    Fz: Vertical component of a floor reaction force (more specifically, a component in the Z-axis direction of a translational floor reaction force)
    Mzmp_y: Floor reaction force moment about a desired ZMP (more specifically, a component about the Y-axis of the floor reaction force moment)
    Mb_y: Floor reaction force moment about the origin of the supporting leg coordinate system (more specifically, a component about the Y-axis of the floor reaction force) moment)


On an arbitrary variable A, dA/dt denotes a first-order differential value of A, and d2A/dt2 denotes a second-order differential value of A. Accordingly, if the variable A denotes a displacement (position), then dA/dt denotes a velocity, and d2A/dt2 denotes acceleration. Reference character “g” denotes a gravitational acceleration constant. Here, “g” takes a positive value.
The dynamic equations of the dynamic model are given by expressions 01 to 04.

Fz=mb*(g+d2Zb/dt2)  Expression 01

Fx=mb*d2Xb/dt2  Expression 02

Mb—y=−mb*Xb*(g+d2Zb/dt2)+mb*Zb*(d2Xb/dt2)  Expression 03

Mzmp—y=−mb*(Xb−Xzmp)*(g+d2Zb/dt2)+mb*(Zb−Zzmp)*(d2Xb/dt2)  Expression 04

In this case, the relationship between Mb_y and Mzmp_y is represented by the following expression 05.

Mb—y=Mzmp—y−mb*Xzmp*(g+d2Zb/dt2)+mb*Zzmp*(d2Xb/dt2)=Mzmp—y−Xzmp*Fz+Zzmp*Fx   Expression 05

The positional difference between a desired ZMP and the origin of the supporting leg coordinate system in the vertical direction (Z-axis direction) is usually zero or approximately zero, so that Zzmp may be regarded as zero (Zzmp=0).
Further, a relative variation amount of height of the body 24 (the position in the vertical direction) relative to a mean height, that is, the divergence of the vertical position of the body 24, when the robot 1 travels is generally sufficiently small. Therefore, Zb≠h is applicable (h: Constant value indicating a mean height of the body mass point 24b corresponding to a mean height of the body 24). Accordingly, Zb in the second term of the right side of expression 03 given above and the second term of the right side of expression 04 given above may be replaced by the constant value h.
The gait generator 100 in the present embodiment generates a desired gait for one step in order, the desired gait for one step being defined by a period from the instant one of the legs 2 of the robot 1 lands to the instant the other leg 2 lands. Thus, in the running gait which is generated in the present embodiment and which is illustrated in FIG. 6, the desired gait from the instant the one-leg supporting period begins to the instant the floating period following the one-leg supporting period ends (the instant the next one-leg supporting period begins) is generated in order.
Here, in the present description, the term “one step” of a desired gait is used to mean the period from the instant one of the legs 2 of the robot 1 lands to the instant the other leg 2 lands. Further, a desired gait which is about to be generated anew is referred to as “a current time gait,” the next desired gait is referred to as “a next time gait,” and the further next desired gait is referred to as “a next but one time gait.” A desired gait generated immediately preceding a current time gait is referred to as “a last time gait.”
Further, when the gait generator 100 generates a current time gait, the required parameters that define the expected landing position/posture and the expected landing time of the foot 22 of a free leg for the next two steps of the robot 1 are input to the gait generator 100 (or the gait generator 100 reads the required parameters from a memory device). Then, the gait generator 100 uses the required parameters to generate a desired body position/posture trajectory, a desired foot position/posture trajectory, a desired ZMP trajectory, a desired floor reaction force vertical component trajectory, a desired arm posture trajectory and the like.
At this time, in order to generate a current time gait that enables the continuity of the motion of the robot 1 to be secured, the gait generator 100 determines a normal turning gait as a virtual cyclic gait following the current time gait (a gait in which the same pattern of motion of the robot 1 is continuously repeated at a certain cycle) on the basis of the required parameters. Then, the gait generator 100 generates the current time gait such that the current time gait will be converged to a normal turning gait the future.
Taking the generation of a running gait illustrated In FIG. 6 as a major example, the following will explain the processing for generating a gait carried out by the gait generator 100 with reference to detailed diagrams of
FIG. 10 to FIG. 24. The gait generator 100 generates a desired gait by carrying out the gait generating processing (main routine processing) illustrated by the flowchart (structured flowchart) of FIG. 10.
First, in S010, various initializing operations, such as initializing time t to zero, are performed. This processing is carried out at the time of a startup or the like of the gait generator 100.
Subsequently, the gait generator 100 proceeds via S012 to S014 wherein the gait generator 100 waits for a timer interrupt at each control cycle (the arithmetic processing cycle in the flowchart of FIG. 10). The control cycle is denoted by Δt.
Subsequently, the gait generator 100 proceeds to S016 determine whether a gait changeover has taken place. At this time, if the gait has changed, then the gait generator 100 proceeds to S020 via the processing in S018. In this case, the gait generator 100 initializes time t to zero in S018. If it is determined in S016 that the gait has not changed, then the gait generator 100 proceeds to S020.
Here, the phrase “the gait changeover” means the timing at which the generation of a last time gait is completed and the generation of a current time gait is about to begin. For example, a control cycle that follows the control cycle at which the generation of the last time gait has been completed provides the gait changeover.
Subsequently, in S020, the gait generator 100 determines a next time's gait supporting leg coordinate system, a next but one time's gait supporting leg coordinate system, a current time gait cycle, and a next time gait next time gait cycle. Determining a supporting leg coordinate system means to determine the position of the origin thereof and the posture of the supporting leg coordinate system (the orientation of each coordinate system axis).
These supporting leg coordinate system and gait cycle are basically determined on the basis of the aforesaid required parameters. More specifically, in the present embodiment, the required parameters input to the gait generator 100 include required values that define the expected landing positions/postures of the foot 22 of a free leg for the following two steps (the foot position/posture in a state wherein the foot 22 is rotated without a slippage such that substantially the entire sole comes contact with a floor surface after the foot 22 lands) and expected landing time. The required values for the first step and the required values for the second step are considered to correspond to the current time gait and the next time gait, respectively, and supplied to the gait generator 100 before the generation of the current time gait is started (before the gait changeover in S016 mentioned above). An arrangement may be made so that these required values can be changed in the middle of generating the current time gait.
Then, at the control cycle of a gait changeover (the control cycle at which t=0), the next time gait's supporting leg coordinate system is determined on the basis of the required value of the expected landing position/posture of the foot 22 of the free leg of the first step (the foot 22 of the free leg in the current time gait) in the aforesaid required parameters.
For example, referring to FIG. 13, it is assumed that the required values of the expected landing position/posture of the foot 22 of the free leg (22L in the figure) involved in the current time gait (the first step) specify the position/posture obtained by moving, from the landing position/posture of the foot 22 (22R in the figure) of the supporting leg of the current time gait, in the X-axis direction (in the longitudinal direction of the foot 22R of the supporting leg in the current time gait) and in the Y-axis direction (in the lateral direction of the foot 22R of the supporting leg in the current time gait) of the current time's gait supporting leg coordinate system by xnext and ynext, respectively, and rotating about the Z-axis (about the vertical axis) by θznext.
At this time, the next time gait's supporting leg coordinate system is determined to be a coordinate system in which the origin thereof is the representative point of a foot 22L (more specifically, a point on the floor that coincides with the representative point) in the case where the foot 22L is landed according to the required values of the expected landing position/posture of the foot 22L of the free leg in the current time gait (in the case where the representative point of the foot 22 coincides with the required value of the expected landing position and the posture (orientation) of the foot 22 coincides with the required value of the expected landing posture), and the longitudinal direction and the lateral direction of the foot 22L in the horizontal plane passing the origin are defined as an X′-axis direction and a Y′-axis direction, as illustrated.
In the same manner as that described above, at the control cycle of a gait changeover (the control cycle at which t=0), the next but one time's gait supporting leg coordinate system (refer to the X′′ Y′′ coordinate in FIG. 13) is determined on the basis of the required values of the expected landing position/posture of the foot 22 of the free leg of the second step. The current time gait cycle is determined to be the time from the expected landing time (required value) of the foot 22 of the supporting leg of the current time gait to the expected landing time (required value) of the foot 22 of the free leg of the first step (current time gait). The next time gait next time gait cycle is determined to be the time from the expected landing time (required value) of the foot 22 of the free leg of the first step to the expected landing time (required value) of the foot 22 of the free leg of the second step.
At a control cycle after the gait changeover (a control cycle at which t>0), the next time's gait supporting leg coordinate system, the next but one time's gait supporting leg coordinate system, the current time gait cycle, and the next time gait next time gait cycle are basically set to be the same as those determined in a previous control cycle.
The required parameters are input to the gait generator 100 from, for example, a maneuvering device or a server or the like outside the robot 1. Alternatively, the required parameters may be stored and retained beforehand in a memory device of the robot 1 as a moving schedule of the robot 1. Further alternatively, the next and the next but one time's gait supporting leg coordinate systems and the current and the next time gait next time gait cycles may be determined on the basis of a command (request) from the controlling device and a movement history of the robot 1 up to the moment. The required parameters may be parameters that directly specify the positions and postures of the next and the next but one time's gait supporting leg coordinate systems and the current and the next time gait next time gait cycles.
Supplementally, in the present embodiment, the expected landing position/posture of the foot 22 of a free leg of the robot 1 in one or both of the current time gait and the next time gait (i.e., the position/posture of at least one of the next time's gait supporting leg coordinate system and the next but one time's gait supporting leg coordinate system), or the gait cycle of the current time gait or the next time gait is revised from the one initially determined in S020 in some cases. In other words, at each control cycle, the processing in S020 is carried out more than once in some cases.
Subsequently, the gait generator 100 proceeds to S022 to determine the gait parameters of a normal turning gait as a virtual cyclic gait following the current time gait (a virtual cyclic gait to which the current time gait aims to converge). The gait parameters in the present embodiment include a foot trajectory parameter that defines a desired foot position/posture trajectory in a normal turning gait, a body posture trajectory parameter that defines a desired body posture trajectory, an arm trajectory parameter that defines a desired arm posture trajectory, a ZMP trajectory parameter that defines a desired ZMP trajectory, and a floor reaction force vertical component trajectory parameter that defines a desired floor reaction force vertical component trajectory.
Here, “the normal turning gait” means a cyclic gait in which no discontinuity takes place in the motional states (motional states, such as foot position/posture and body position/posture) of the robot 1 at the boundary of a gait (a gait boundary of each cycle) when the gait is repeated. Further, “the normal turning gait” is a cyclic gait, which repeats the same pattern of gait at a certain cycle, meaning that it is a gait that permits continuous motions of the robot 1. In other words, “the normal turning gait” is a cyclic gait that enables repeated motions of the same pattern without developing discontinuity in a gait trajectory (a gait which, in principle, does not develop “divergence,” which will be discussed later, when repeated an infinite number of times).
In the present embodiment, the normal turning gait, which is a cyclic gait, repeats a gait for one cycle at certain intervals, the gait for one cycle being formed of a gait for two steps of the robot 1, i.e., the gait composed of the first turning gait following the current time gait and the second turning gait following the first turning gait. Here, the term “turning” is used, because a zero turning rate means traveling straight, so that traveling straight ran be also included in the term “turning” in a broad sense.
If a desired gait to be generated is a running gait illustrated in FIG. 6, then the first turning gait and the second turning gait of a normal gait are both gaits having the one-leg supporting period and the floating period as with a desired gait. In other words, the basic gait pattern of the first turning gait and the second turning gait are the same as that of the current time gait.
To supplement the description of the normal turning gait (hereinafter referred to simply as the normal gait in some cases), the gait for one cycle of a normal gait of a bipedal robot need to include a gait for at least two steps. In this case, it is possible to set a complicated normal gait in which the gait for one cycle has three steps for more. However, the normal gait is used merely to determine The value of a desired (proper) divergent component at the end (ending time) of the current time gait, as will be discussed later. Therefore, using a normal gait formed of a gait having three steps or more as one cycle provides little effect despite the complicated processing for generating the gait. For this reason, the gait for one cycle of the normal gait in the present embodiment is formed of a gait of two steps (a set of the first turning gait and the second turning gait). In the case of a legged mobile having three feet or more, the number of gaits defining the normal gait will increase accordingly.
Here, “divergence” means that the position of the body 24 of the robot 1 deviates to a position far apart from the positions of both feet 22, 22, as illustrated in FIG. 11. The value of a divergent component is a numerical value indicating the degree of the deviation of the position of the body 24 of the robot 1 from the positions of both feet 22, 22 (more specifically, the origin of the supporting leg coordinate system set on the ground contact surface of the foot 22 of the supporting leg).
The normal gait is a virtual gait prepared by the gait generator 100 to determine a desired motional state of the robot 1 at the end of the current time gait. Hence, the normal turning gait is not directly output from the gait generator 100.
In the present embodiment, a divergent component is used as an indicator in generating gaits so as to continuously generate desired gaits without developing the aforesaid divergence. In this case, even for a normal gait, which is a typical example of a continuous gait, the initial divergent component of the normal gait (the divergent component at the starting time of the normal gait) changes if the gait parameters of the normal gait change. More specifically, a proper divergent component changes according to the type of gait, such as walking, running and a traveling speed.
In the present embodiment, therefore, when generating a current time gait, the gait generator 100 first determines, on the basis of the required parameters related to the current time gait (or the supporting leg coordinate system and the gait cycle determined in S020), a normal gait as a virtual cyclic gait in the future ideally suited as the gait following the current time gait to be generated (a gait targeted also at convergence in the future) and as a virtual cyclic gait in the future that enables stable travel of the robot 1 to be continued, then determines an initial divergent component of the normal gait. Then, the gait generator 100 generates the current time gait such that the terminal divergent component of the current time gait coincides with the initial divergent component of the determined normal gait (more generally, the current time gait is continued or gradually approximated to the normal gait). The basic guideline of the gait generation described above is the same as that disclosed in Patent No. 3726081 previously proposed by the present applicant.
However, in the present embodiment, the divergent component of a gait is defined on the basis of a state equation of the aforesaid dynamic model (the inverted pendulum model) illustrated in FIG. 9, as will be discussed later. The definition of the divergent component will be discussed in detail hereinafter.
Referring back to the main subject, the gait generator 100 carries out in S022 the subroutine processing illustrated by the flowchart of FIG. 12.
First, in S100, the gait generator 100 determines a foot trajectory parameter of the gait parameters of the normal gait such that a foot position/posture trajectory continues in the order of a current time gait, a first turning gait, and a second turning gait. The following will describe a specific setting method with reference to FIG. 3. In the following description, the foot 22 of the leg 2 on the supporting leg side will be referred to as the supporting leg foot 22, while the foot 22 of the leg 2 on the free Leg side will be referred to as the free leg foot 22. The “initial” gait and the “terminal” gait will mean the starting time and the ending time, respectively, of each gait or instantaneous gaits at the starting time and the ending time.
The foot trajectory parameter is constituted of the positions/postures of the supporting leg foot 22 and the free leg foot 22, respectively, at the beginning and the end of the first turning gait and the second turning gait, respectively, and the gait cycle of each turning gait (the rime from the beginning to the end of each turning gait). In the foot trajectory parameter, the free leg foot position/posture at the beginning of the first turning gait are defined as the supporting leg foot position/posture at the end of the current time gait observed from a next time gait's supporting leg coordinate system.
In this case, in a running gait, the supporting leg foot 22 at the end of the current time gait is moving in the air. Further, the supporting leg foot position/posture at the end of the current time gait is determined by generating a foot position/posture trajectory (more specifically, a trajectory observed from the next time gait's supporting leg coordinate system) from the supporting leg foot position/posture at the beginning of the current time gait (=the free leg foot position/posture at the end of a last time gait) to a free leg foot position/posture at the end of the next time gait, which is determined on the basis of the required value of the expected landing position/posture of the free leg foot 22 of the second step in the aforesaid required parameter (the required values of the expected landing position/posture in the next time gait of the supporting leg foot 22 of the current time gait) or a next but one time's gait supporting leg coordinate system corresponding to the required value, to the end of the current time gait by using the aforesaid finite-duration setting filter.
The free leg foot position/posture at the end of the next time gait is determined such that the position/posture of the foot 22 obtained by turning the foot 22 in the pitch direction with the toes down while keeping the foot 22 in contact with the ground from the position/posture to a horizontal posture coincide with the position/posture of the next but one time's gait supporting leg coordinate system. In other words, the free leg foot position/posture at the end of the next time gait are the position/posture of the foot 22 in a state wherein the foot has been rotated by a predetermined angle in the pitch direction with the toes lifted while the foot 22 is kept in contact with the ground without a slippage from the required values of the expected landing position/posture of the free leg foot 22 of the second step in the required parameter (a state wherein the heel has been landed with the toes up).
Further, the supporting leg foot position/posture at the beginning of the first turning gait are the free leg foot position/posture at the end of the current time gait observed from the next time gait's supporting leg coordinate system. In this case, the free leg foot position/posture at the end of the current time gait are determined on the basis of the aforesaid next time gait's supporting leg coordinate system or the required values of the expected free leg landing position/posture of the first step (the current time gait) of the aforesaid required parameter corresponding thereto, as with the case of the free leg foot position/posture at the end of the next time gait. More specifically, the free leg foot position/posture at the end of the current time gait are determined such that the representative point of the foot 22 when the foot 22 has been rotated, from the position/posture, with the toes down while keeping the foot 22 in contact with the ground until substantially the entire bottom surface of the foot 22 comes in contact with a floor surface coincides with the origin of next time gait's supporting leg coordinate system.
The free leg foot position/posture at the end of the first turning gait is determined on the basis of the position/posture of the next but one gait supporting leg coordinate system observed from the next time gait's supporting leg coordinate system, as with the technique for determining the free leg foot position/posture at the end of the current time gait or the free leg foot position/posture at the end of the next time gait. To be more specific, the free leg foot position/posture at the end of the first turning gait are determined such that the position/posture of the foot 22 when the foot 22 has been rotated in the pitch direction without a slippage while keeping the foot 22 in contact with the ground from the position/posture to the horizontal posture coincide with the position/posture of the next but one time's gait supporting leg coordinate system observed from the next time gait's supporting leg coordinate system.
At the end of the first turning gait, the supporting leg foot 22 is off the floor and in the air. In order to determine the trajectory after the supporting leg foot 22 leaves the floor, the expected landing position/posture of the supporting leg foot of the first turning gait are set. The expected landing position/posture of the supporting leg foot of the first turning gait are determined on the basis of the position/posture of the next but two time's gait supporting leg coordinate system observed from the next time gait's supporting leg coordinate system. To be more specific, the expected landing position/posture of the supporting leg foot of the first turning gait are the position/posture of the next but two time's gait supporting leg coordinate system observed from the next time gait's supporting leg coordinate system. The next but two time's gait supporting leg coordinate system is determined such that the relative position/posture relationship between the next out one time's gait supporting leg coordinate system and the next but two time's gait supporting leg coordinate system coincides with the relative position/posture relationship between the current time's gait supporting leg coordinate system and the next time gait's supporting leg coordinate system.
The supporting leg foot position/posture at the end of the first turning gait are determined by generating a foot position/posture trajectory from the supporting leg foot position/posture at the beginning of the first turning gait to the expected landing position/posture of the supporting leg foot of the first turning gait (more specifically, the trajectory observed from the next time gait's supporting leg coordinate system) until the end of the first turning gait by using the aforesaid finite-duration setting filter, as with the case where the supporting leg foot position/posture at the beginning of the first turning gait have been determined.
The free leg foot position/posture at the beginning of the second turning gait are the supporting leg foot position/posture at the end of the first turning gait observed from the next but one time's gait supporting leg) coordinate system. The supporting leg foot position/posture at the beginning of the second turning gait are the free leg foot position/posture at the end of the first turning gait observed from the next but one time's gait supporting leg coordinate system.
The free leg foot position/posture at the end of the second turning gait are the free leg foot position/posture at the end of the current time gait observed from the current time's gait supporting leg coordinate system. The supporting leg foot position/posture at the end of the second turning gait are the supporting leg foot position/posture at the end of the current time gait observed from the current time's gait supporting leg coordinate system.
The gait cycles of the first turning gait and the second turning gait are set to be the same as the next time gait next time gait cycle. The gait cycles of the first turning gait and the second turning gait do not necessarily have to be the same; however, both cycles are preferably determined on the basis of at least the next time gait next time gait cycle.
Next, the gait generator 100 proceeds to S101 to determine whether the foot position/posture trajectory of each foot 22 of the first turning gait and the second turning gait in a current time gait and a normal gait would be appropriate if the foot position/posture trajectories were generated on the basis of the expected landing position/posture and expected landing time of the foot 22 of the free leg of the current time gait respectively specified by the next time's gait supporting leg coordinate system and the current time gait cycle previously determined in S020 and the normal gait parameters determined in S100.
To be more specific, the gait generator 100 tentatively generates, by using the finite-duration setting filter, toe foot position/posture trajectory of each foot 22 of the first turning gait and the second turning gait in a current time gait and a normal gait on the basis of the expected landing position/posture and expected landing time of the foot 22 of the free leg of the current time gait respectively specified by the next time's gait supporting leg coordinate system and the current time gait cycle previously determined in S020 and the normal gait parameters determined in S100. Then, the gait generator 100 compares the foot position/posture trajectory generated as described above with the floor geometry indicated by the floor geometry information for generating gaits (more specifically, the floor sectional geometry on a longitudinal plane including a foot position trajectory) input from the floor geometry shaper 114 as previously described to determine whether the foot 22 will come in contact with a stepped portion shaped as described above (including a gentle slope surface after the shaping). Thus, the gait generator 100 determines whether the foot position/posture trajectories of the current time gait and the normal gait are appropriate.
If the determination result in S101 is negative, then the gait generator 100 terminates the subroutine processing in FIG. 12 and carries out the processing from S020 in FIG. 10 again. In this case, if the foot 22 of a free leg would come in contact with the stepped portion (including the gentle slope surface) during any one of the current time gait, the first running gait, and the second turning gait, then the gait generator 100 changes in S020 at least one of the expected landing position/posture of the foot 22 of the free leg in the current time gait (consequently, the position/posture in the next time's gait supporting leg coordinate system) and the expected landing position/posture of the foot 22 of the free leg in the next time gait (consequently, the position/posture in the next but one time's gait supporting leg coordinate system) to position/posture different from the current values (the expected landing position/posture determined by immediately preceding processing in S020 in the current control cycle) in order to avoid the contact. In this case, according to the present embodiment, the current state is maintained at the current time gait cycle and the next time gait next time gait cycle.
An example will be described below with reference to FIGS. 14(a) and 14(b). This example will discuss a motion the left foot 22L in FIG. 5(a) as the free leg foot in a current time gait in the example of the floor geometry illustrated in FIGS. 5(a) and 5(b). Further, it is assumed that a foot position/posture trajectory of the free leg foot 22L has been tentatively generated on the basis of the expected landing position/posture of the free leg foot 22 of the current time gait (consequently, the positron/posture of the next time's gait supporting leg coordinate system) and the current time gait cycle determined at the current stage, causing the free leg foot 22L to take the path illustrated in FIG. 14(a). In this case, the free leg foot 22L will come in contact, in the middle of the current time gait, with the gentle slope surface DFs2 of the stepped portion DF in the floor geometry information for generating gaits. In such a case, the determination result in S101 will be negative.
In such a case, the height of the maximum height point of the trajectory of the free leg foot 22L and the expected landing position (consequently, the position of the next time's gait supporting leg coordinate system) in the current time gait are changed in the processing in S020 carried out by the gait generator 100 again such that the path (the positional trajectory) of the free leg foot 22L will be a trajectory that will not cause the contact between the free leg foot 22L and the stepped portion DF (or will cause the free leg foot 22L to ride over the gentle slope surface DFs2 of the stepped portion DF), as illustrated in, for example, FIG. 14(b). In other words, the height of the maximum height point of the trajectory of the free leg foot 22L of the current time gait is changed to be greater than the current height and the expected landing position of the free leg foot 22L of the current time gait is changed to be closer to an immediately preceding landing position of the free leg foot 22 (the landing position immediately before the foot leaves a floor) than the current one.
Changing the height of the maximum height point of the trajectory of the free leg foot 22L and the expected landing position in the current time gait as described above will cause the path length of the free leg foot 22L in the current time gait to remain the same or hardly change before and after changing the aforesaid maximum height point and expected landing position. In the present embodiment, the current time gait cycle and the expected landing time of the free leg foot 22L in the current time gait are not changed. This arrangement makes it possible to restrain the moving velocity (rotational angular velocity) of a joint of the free leg 2 from becoming excessively high.
If the free leg foot 22 of the next time gait comes in contact with the stepped portion in the floor geometry information for generating gaits, then the height of the maximum height point of the path and the expected landing position of the free leg foot 22 of the next time gait will be changed in the same manner as that described above.
Supplementally, in the present embodiment, the gait cycles of the current time gait and the next time gait have not been changed. Alternatively, however, the gait cycle of the current time gait or the next time gait may be also changed in addition to changing the expected landing position or the like of the free leg foot 22, as necessary.
Returning to the description with reference to FIG. 12, if the determination result in S101 is affirmative, then the gait generator 100 proceeds to S102 to determine the body posture trajectory parameters that specify the desired body posture trajectory in a normal gait.
In this case, according to the present embodiment, the body posture trajectory parameters of the normal gait are determined such that the desired body posture trajectory specified thereby agrees with the trajectory of a reference body posture in a predetermined pattern established beforehand. The reference body posture in the present embodiment is set to a constant posture (fixed posture) free of temporal changes. The reference body posture is such that, for example, the body trunk axis of the body 24 is steadily set in the vertical direction (a body posture in a state wherein the robot 1 is standing in an upright posture), i.e., a posture in which the body posture angle relative to the vertical direction is steadily maintained at zero. The parameters (e.g., the value of a certain body posture angle of the reference body posture) that define the trajectory of the reference body posture are determined as the body posture trajectory parameters. If the body posture is set at the constant posture, then the angular velocity and the angular acceleration of the body posture angle will automatically be maintained at zero at all times.
Supplementally, the body posture of a normal gait does riot have to be a constant posture as long as the body posture is set such that the body posture connects at the beginning of the normal gait (the beginning of a first turning gait) and the end thereof (the end of a second turning gait), i.e., as long as the body posture angle and the angular velocity thereof respectively agree at the beginning and the end of the normal gait. In the present embodiment, the reference body posture has been set to the constant posture as described above in order to ensure easy understanding of the present embodiment.
Subsequently, the gait generator 100 proceeds to S104 no determine arm posture trajectory parameters, more specifically, arm posture trajectory parameters other than those related to the angular momentum changes of both arms about the vertical axis (or the body trunk axis of the body 24). For example, the parameters defining the relative height of the hand distal end of an arm in relation to the body 24 and the relative center-of-gravity position of the entire arm are determined as the arm posture trajectory parameters. In this case, according to the present embodiment, the relative center-of-gravity position of the entire arm is set to be maintained at a constant position relative to the body 24.
Subsequently, the gait generator 100 proceeds to S106 to determine floor reaction force vertical component trajectory parameters. In this case, the floor reaction force vertical component trajectory parameters are determined such that the floor reaction force vertical component trajectory defined by the parameters will be substantially continuous in both the first turning gait and the second turning gait.
To be more specific, a desired floor reaction force vertical component trajectory of a normal gait is set according to a pattern illustrated in, for example, FIG. 15. According to the pattern, in both the first turning gait and the second turning gait, the floor reaction force vertical component changes in a trapezoidal shape in a one-leg supporting period, and the floor reaction force vertical component is maintained at zero in a floating period. The time of a breakpoint of the pattern and the height (peak value) of the trapezoidal portion are determined as the floor reaction force vertical component trajectory parameters.
The floor reaction force vertical component trajectory parameters are determined such that the mean value of the floor reaction force vertical components in the period equivalent to one cycle of the normal gait (the period combining the period of the first turning gait and the period of the second turning gait) agrees with the self weight of the robot 1. In other words, the floor reaction force vertical component trajectory parameters are determined such that the mean value of the floor reaction force vertical components during the period equivalent to one cycle of the normal gait has the same magnitude as that of the gravitational force acting on the entire robot 1 and is in the opposite direction.
Determining the floor reaction force vertical component trajectory parameters (and subsequently the floor reaction force vertical component trajectory) is necessary to satisfy a condition of a normal gait. The condition of the normal gait is that an initial state (the initial state of a first turning gait observed from the supporting leg coordinate system of the first turning gait of the normal gait) and a terminal state (the terminal state of a second turning gait observed from the supporting leg coordinate system of the first turning gait following the second turning gait of the normal gait) on every state amount of the normal gait (motional state amounts, including the position, the posture and the velocity of each portion of the robot 1) coincide with each other (hereinafter, the condition will be referred to as the boundary condition of a normal gait in some cases).
Hence, the difference between the overall center-of-gravity vertical velocity of the robot 1 at the end of the normal gait and the overall center-of-gravity vertical velocity at the beginning of the normal gait (more specifically, the difference between the overall center-of-gravity vertical velocity at the end of the second turning gait and the overall center-of-gravity vertical velocity at the beginning of the first turning gait) must be also zero. The aforesaid difference is the integral value of the difference between the floor reaction force vertical component and the gravitational force (the first-order integral value in the period equivalent to one cycle from the beginning to the end of the normal gait). Therefore, in order to bring the difference to zero, the floor reaction force vertical component trajectory must be determined such that the mean value of the floor reaction force vertical components in the period equivalent to one cycle of the normal gait agrees with the self weight of the robot I, as described above.
In the present embodiment, the mean value of the floor reaction force vertical components in the period of the first turning gait and the period of the second turning gait, respectively, is made to agree with the self weight of the robot 1. To be more specific, for example, the time of each of the breakpoint of the trapezoidal portion of the floor reaction force vertical component trajectory in each turning gait is set according to the gait cycles of the first turning gait and the second turning gait, and then the height of the trapezoidal portion (the peak value of the floor reaction force vertical component) is determined such that the mean value of the floor reaction force vertical components in each of the periods of the first turning gait and the second turning gait agrees with the self weight of the robot 1. In this case, the height of the trapezoidal portion can be determined by solving an equation which indicates a condition that the mean value and the self weight coincide with each other, taking the height as an unknown value.
Thus, the difference between the overall center-of-gravity vertical velocity at the end of the first turning gait and the overall center-of-gravity vertical velocity at the beginning of the first turning gait becomes zero, and the difference between the overall center-of-gravity vertical velocity at the end of the second turning gait and the overall center-of-gravity vertical velocity at the beginning of the second turning gait also becomes zero. This, however, is not a must. For example, if there is a possibility that the body vertical position becomes excessively high or low in the vicinity of the boundary between the first turning gait and the second turning gait, then the height or the like of the trapezoidal shape of the floor reaction force vertical component trajectory of each turning gait may be corrected from the state wherein the mean value and the self weight coincide with each other in each turning gait.
Subsequently, the gait generator 100 proceeds to S108 to determine ZMP trajectory parameters which define a desired ZMP trajectory of a normal gait composed of the combination of the first turning gait and the second turning gait. In this case, the desired ZMP trajectory is determined such that the stability allowance is high and no sudden change occurs, as previously described.
More specifically, in the running gait illustrated in FIG. 6, the heel of the supporting leg foot 22 (the free leg foot 22 in the floating period) lands, and after a while, substantially the entire bottom surface of the supporting leg foot 22 comes in contact with the ground, then after a while, only the tiptoe of the supporting leg foot 22 comes in contact with the ground. Next, the robot 1 kicks the floor at the tiptoe of the supporting leg foot 22 and jumps into the air, and lastly, lands at the heel of the free leg foot 22. The desired ZMP must exist in a ground contact plane.
In the present embodiment, therefore, the position of the desired ZMP of each of the first turning gait and the second turning gait of a normal gait in the X-axis direction is determined such that the desired ZMP remains at that position until substantially the entire bottom surface of the foot 22 comes in contact with the ground, taking the heel of the supporting leg foot 22 as the initial position, as illustrated in FIG. 8(a).
Subsequently, the desired ZMP is determined such that the desired ZMP moves to the center of the supporting leg foot 22 and further moves to the tiptoe by the time when the tiptoe of the foot 22 comes in contact with the ground, and thereafter remains at the tiptoe of the supporting leg foot 22 until leaving the floor. After that, as previously described, the desired ZMP is determined such that the desired ZMP continuously moves from the tiptoe of the supporting leg foot 22 to the landing position of the heel of the free leg foot 22 by the time of the next landing of the free leg foot 22.
Thus, the desired ZMP trajectory (the trajectory of the position in the X-axis direction) of the normal gait formed of the first turning gait and the second turning gait is determined as illustrated in FIG. 16. The time and position of each of the breakpoints of the desired ZMP trajectory are determined as the ZMP trajectory parameters of the normal gait. In this case, the time of the breakpoints is determined according to the gait cycles of the first turning gait and the second turning gait determined on the basis of the aforesaid required parameters. Further, the positions of the breakpoints are determined on the basis of the positions/postures of the next time gait's supporting leg coordinate system and the next out one time's gait supporting leg coordinate system or the required values of the expected free leg foot landing positions/postures of the first step and the second step that define the positions/postures of these coordinate systems.
The position in the Y-axis direction of the desired ZMP trajectory is determined in the same manner as that illustrated in FIG. 8(b). To be more specific, the trajectory of the position of the desired ZMP in the Y-axis direction in the first turning gait is determined according to the same pattern illustrated in FIG. 8(b). Further, the trajectory of the position of the desired ZMP in the Y-axis direction in the second turning gait is determined to be a trajectory which has the same configuration as the trajectory of the first turning gait and continues to the end of the trajectory.
This completes the detailed description of the processing in S022 of FIG. 10.
Referring back to FIG. 10, after carrying out the processing in S022 as described above, the gait generator 100 proceeds to S024 wherein the gait generator 100 calculates the initial state of the normal gait. The initial state calculated here specifically includes the initial body posture velocity (the initial body position and the initial body velocity) and the initial divergent component of the normal gait. The initial state is exploratorily calculated by the processing illustrated by the flowchart of FIG. 17.
First, in S200, the gait generator 100 determines the initial states of the desired foot position/posture, the desired arm posture, and the desired body posture angle of the normal gait (the state at the starting time of the normal gait (=the ending time of the current time gait)) on the basis of the normal gait parameters (the gait parameters determined in S022 of FIG. 10). Here, the term “state” means the pair of a position or posture and the temporal change rate thereof (the changing velocity of a position or posture). For example, the initial state of the desired foot position/posture means the pair of the foot position/posture at the starting time of the normal gait and the temporal change rate thereof (i.e., the moving velocity and the changing velocity of the posture of the foot 22). The same applies to the initial state of the desired arm posture and the initial state of the desired body posture angle.
In this case, the initial state of the position/posture of the supporting leg foot and the initial state of the position/posture of the free leg foot are determined on the basis of the foot trajectory parameters determined in S100 of FIG. 12.
To be more specific, among the foot trajectory parameters, the supporting leg foot position/posture at the beginning of the first turning gait and the free leg foot position/posture at the beginning of the first turning gait are determined as the supporting leg foot position/posture and the free leg foot position/posture, respectively, at the starting time of the normal gait.
Further, the temporal change rate of the supporting leg foot position/posture at the starting time of the normal gait is calculated as the temporal change rate of the foot position/posture at the starting time (the starting time of the normal gait) of a foot position/posture trajectory from the supporting leg foot position/posture at the beginning of the first turning gait to the free leg foot position/posture at the end of the second turning gait (the trajectory observed from the next time gait's supporting leg coordinate system), the trajectory being generated by a finite-duration setting filter. In this case, the temporal change rate of the supporting leg foot position/posture at the starting time of the normal gait can be calculated on the basis of the trajectory from the normal gait beginning time to the time immediately thereafter in the foot position/posture trajectory from the supporting leg foot position/posture at the beginning of the first turning gait to the free leg foot position/posture at the end of the second turning gait.
Further, the temporal change rate of the free leg foot position/posture at the starting time of the normal gait is calculated as the temporal change rate of the foot position/posture at the starting time (the starting time of the normal gait) of a foot position/posture trajectory from the supporting leg foot position/posture at the beginning of the current time gait to the free leg foot position/posture at the end of the first turning gait (the trajectory observed from the next time gait's supporting leg coordinate system), the trajectory being generated by a finite-duration setting filter. In this case, in the foot position/posture trajectory from the supporting leg foot position/posture at the beginning of the current time gait to the free leg foot position/posture at the end of the first turning gait, generating a trajectory from the starting time of the current time gait to the starting time (or time immediately thereafter) of the normal gait makes it possible to calculate the temporal change rate of the free leg foot position/posture at the starting time of the normal gait from the trajectory (the trajectory in the vicinity of the starting time of the normal gait).
The initial state of an arm posture is determined by determining the arm posture (including the overall center-of-gravity positions of both arms relative to the body 24) at the starting time of the normal gait and the change amounts of the arm postures in a period immediately following the starting time of the normal gait on the basis of the arm posture trajectory parameters determined in S104 of FIG. 12.
Further, the initial state of the body posture angle is determined by determining the body posture angle at the starting time of the normal gait and the change amount of the body posture angle in a period immediately following the starting time on the basis of the body posture trajectory parameters determined in S102 of FIG. 12. In the present embodiment, the body posture defined by the body posture trajectory parameters is a posture in which the body trunk axis of the body 24 is steadily oriented in the vertical direction. Therefore, the body posture angle and the angular velocity thereof are both zero at the starting time of the normal gait.
Subsequently, the gait generator 100 proceeds to S202 provisionally determine (Xs, Vxs) (Xs: horizontal position; Vxs: horizontal velocity), which are the candidates of the initial body horizontal position/velocity (the candidates of the horizontal position and the horizontal velocity of the body 24 at the starting time of the normal gait). The candidates (Xs, Vxs) provisionally determined here may be arbitrary and may be provisionally determined as, for example, the candidates (Xs, Vxs) of the body horizontal position/velocity at the initial state of the normal gait determined when the last time gait was generated.
To simplify the description, an example will be taken in which the initial state (the initial body horizontal position/velocity) of a normal gait in the X-axis direction (the roll-axis direction) on a sagittal plane is explored. However, in effect, the initial state of the normal gait (the initial state that satisfies the aforesaid boundary condition of the normal gait) must be explored separately or simultaneously in the X-axis direction (the roll-axis direction) and the Y-axis direction (the pitch-axis direction) on both the position and the velocity.
As an exploratory determining technique, a method in which a pseudo Jacobian (sensitivity matrix) is determined and a next candidate is determined by a steepest descent method or the like, or a simplex method may be used. In the present embodiment, for example, the steepest descent method is used.
Subsequently, the gait generator 100 proceeds to S206 via S204 to determine initial body vertical position/velocity (Zs, Vzs), which is a pair of the vertical position (the position in the Z-axis direction) Zs and the vertical velocity (the velocity in the Z-axis direction) Vzs of the body 24 at the starting time of the normal gait.
In the present embodiment, the initial body vertical velocity Vzs is determined, for example, as described below.
The following expression applies to the kinetic relationship for the robot 1.

Terminal overall center-of-gravity vertical position−Initial overall center-of-gravity vertical position=Second-order integration of (Floor reaction force vertical component/Overall mass of the robot)+Second-order integration of gravitational acceleration+Initial overall center-of-gravity vertical velocity*Duration of one step  Expression 13

(where the gravitational acceleration takes a negative value)

In the normal gait, a terminal overall center-of-gravity vertical position and an initial overall center-of-gravity vertical position coincide with each other, so that the right side of the above expression 13 must be zero. Thus, the initial overall center-of-gravity vertical velocity can be determined from the relationship. To be more specific, first, the value obtained by dividing the floor reaction force vertical component calculated on the basis of the floor reaction force vertical component trajectory parameters determined in S104 of FIG. 12 described above is divided by the overall mass of the robot 1 and the obtained result is subjected to the second-order integration in the period from the beginning to the end of the normal gait, thereby determining the overall center-of-gravity movement amount (the first term of the right side of expression 13) based on the floor reaction force vertical component.
Further, the gravitational velocity is subjected to the second-order integration in the period from the beginning to the end of the normal gait thereby to determine the overall center-of-gravity movement amount (the second term of the right side of expression 13) based on the gravitational force. Then, the sign of the sum of the overall center-of-gravity movement amount based on the floor reaction force vertical component and the overall center-of-gravity movement amount based on the gravitational force, which have been determined as described above, is reversed, and the sum with the reversed sign is divided by the time of one cycle Tcyc of the normal gait to determine the initial overall center-of-gravity vertical velocity.
Further, according to the present embodiment, a multi-mass-point model (geometric model) having mass points in, for example, the body 24 and other portions (legs 2, 2 and arms) is used to determine the vertical velocity of the body 24 which causes the vertical velocity of the center-of-gravity point of the multi-mass-point model to coincide with the initial overall center-of-gravity vertical velocity on the basis of the initial state, including the foot position/posture and the arm postures, determined in S200 and the initial body horizontal position/velocity (Xs, Vxs) determined in S202 (or S218 to be discussed later). The vertical velocity thus obtained is determined as the initial body vertical velocity Vzs.
As the multi-mass-point model, there is, for example, a 3-mass-point model which includes one body mass point having a mass of the body 24 (or the mass combining the body 24 and the arms) and two leg mass points having the masses of the two respective legs 2, 2. In this case, for example, the position of the body mass point is to be defined on the basis of the position/posture of the body 24, and the position of each leg mass point is to be defined on the basis of the foot position/posture of each leg 2. In the case where the 3-mass-point model is used, the vertical velocity of the body mass point can be calculated on the basis of the initial overall center-of-gravity vertical velocity and the initial state of the foot position/posture determined as described above. Then, based on the vertical velocity of the body mass point and the initial state of the body posture angle determined in S200, the initial body vertical velocity Vzs can be determined.
A multi-mass-point model having more mass points (e.g., a geometric model having a mass point in each link of the robot 1) may be used to determine the initial body vertical velocity Vzs more accurately. If the mass of a portion excluding the body 24 of the robot 1 is sufficiently smaller than the body 24, then the aforesaid initial overall center-of-gravity vertical velocity may be determined directly as the initial body vertical velocity Vzs, regarding that, for example, the vertical velocity of the overall center of gravity of the robot 1 substantially agrees with the vertical velocity of the body 24.
Meanwhile, the initial body vertical position Zs of the normal gait is determined by, for example, the body height determining technique previously proposed in Japanese Patent Application Laid-Open No. 10-86080 by the present applicant. At this time, the initial body vertical position Zs that prevents the knees of the legs 2, 2 from being fully stretched at the starting time is determined on the basis of the foot position/posture at the starting time (the supporting leg foot position/posture at the beginning) of the first turning gait and the free leg foot position/posture at the beginning of the first turning gait determined in S100 of FIG. 12 described above) and a predetermined geometric condition regarding the bending angle of the knee of each leg 2.
For example, if the knee bending angle of the leg 2 on the supporting leg side is denoted by θsup and the knee bending angle of the leg 2 on the free leg side is denoted by θswg, then the initial body vertical position is determined such that the sum of the reciprocals of the sine function values of the knee bending angles θsup and θswg is a predetermined value (a finite value). Here, the knee bending angles θsup and θswg denote the angles of the axial centers of the cruses relative to the axial centers of the thighs of the legs 2, and increase from zero as the knees are bent from the state wherein the legs 2 are fully stretched. The technique for determining the vertical position of the body 24 is described in detail in the aforesaid Japanese Patent Application Laid-Open No. 10-86080, so that no further description will be given herein.
Supplementally, the robot 1 has 6 degrees of freedom per leg, so that once the initial states of the foot position/posture trajectory and the body position/posture trajectory (the positions/postures and the temporal change rates thereof) are given, the initial states of the motions of the body 24 and the legs 2, 2 of the robot 1 will be all uniquely determined. Accordingly, for example, if the overall mass of the body 24 and the legs 2, 2 substantially agrees with the overall mass of the robot 1, then once the initial states of the motions of the body 24 and the legs 2, 2 are given, the initial overall center-of-gravity vertical velocity will be uniquely determined.
Inversely, since each leg has 6 degrees of freedom, even if one state related to the velocity (e.g., the initial body vertical velocity) in the initial states of the foot position/posture trajectory and the body position/posture trajectory is unknown, the unknown initial state will be uniquely determined once the initial overall center-of-gravity vertical velocity is given.
After the processing in S206, the gait generator 100 proceeds to S208 to provisionally generate a gait as a candidate of a normal gait (a gait for one step (one cycle) of a normal gait). More specifically, based on the normal gait parameters determined in S022 of FIG. 10, the instantaneous values of the desired ZMP, the desired floor reaction force vertical component, the desired foot position/posture, the desired body posture and the desired arm posture at each instant from the starting time to the ending time are sequentially determined. Then, the body position is sequentially determined using the dynamic model (inverted pendulum model) illustrated in FIG. 9 such that the determined desired ZMP and the determined desired floor reaction force vertical component are satisfied, thus generating the gait from the starting time to the ending time of the normal gait. In this case, the aforesaid initial body horizontal position/velocity (Xs, Vxs) and the initial body vertical position/velocity (Zs, Vzs) are set as the initial states of the position and the velocity of the body 24.
The gait is generated only in the gait generator 100 and not output from the gait generator 100 as the desired value for driving the actual robot 1.
To be more specifically, the processing in S208 is executed as illustrated by the flowchart of FIG. 18.
The gait generator 100 first carries out various types of initialization in S300. To be more specific, time Tk for generating a gait is initialized to starting time Ts of a normal gait. Further, a latest candidate value (the latest candidate value determined in S202 of FIG. 17 or S216 or S218, which will be discussed later) of the initial body horizontal position/velocity (Xs, Vxs) is substituted into the body horizontal position/velocity, and a latest value the latest value determined in S206 of FIG. 17) of the initial body vertical position/velocity (Zs, Vzs) is substituted into the body vertical position/velocity. Further, the initial value of a reference body posture angle is substituted into the body posture angle and the initial value of a reference body posture angular velocity is substituted into the body posture angular velocity.
Subsequently, the gait generator 100 proceeds to S304 via S302 to determine whether the time Tk (the current value) for generating a gait is time before ending time Te (=Ts+Tcyc), i.e., whether Tk≦Te. If the determination result is affirmative, then the gait generator 100 carries out the processing of S306 to S316 (the details will be discussed later) so as to determine the instantaneous value of the gait at time Tk.
Subsequently, the gait generator 100 proceeds to S318 to increase the time Tk for generating a gait by a predetermined notch time ΔTk and then carries out the determination in S304 again. Here, the notch time ΔTk may be set to agree with, for example, the control cycle Δt. However, in order to reduce the calculation volume, ΔTk may be set to be longer than Δt.
If the determination result in S304 is affirmative, the processing from S306 to S318 is repeated. If the determination result in S304 is negative, then the processing in FIG. 18, that is, the processing in S208 of FIG. 17, is terminated. Thus, the generation of the normal gait (the provisional normal gait) for one cycle from the starting time to the ending time of the normal gait is completed.
The gait generator 100 carries out the processing for determining the instantaneous value of the provisional normal gait in the aforesaid S306 to S316 as described below. First, in S306, the gait generator 100 determines an instantaneous value of the desired floor reaction force vertical component trajectory shown in FIG. 15 at time Tk on the basis of the normal gait parameters (more specifically, the floor reaction force vertical component trajectory parameters).
Further, in S308, the gait generator 100 determines an instantaneous value of the desired ZMP trajectory shown in FIG. 16 at time Tk on the basis of the normal gait parameters (more specifically, the ZMP trajectory parameters).
Subsequently, the gait generator 100 proceeds to S308 no determine the instantaneous values of the desired foot position/posture (the desired foot positions/postures of both the supporting leg and the free leg), the desired body posture, and the desired arm posture, respectively, at time Tk on the basis of the normal gait parameters (more specifically, the foot trajectory parameter, the body posture trajectory parameter, and the arm posture trajectory parameter). Regarding the desired arm posture, however, more specifically, the overall center-of-gravity positions of both arms are determined, whereas the motions of the arms (arm swinging motions) attributable to changes in the amounts of angular motions about the vertical axis (or the body trunk axis of the body 24) are not yet determined.
Subsequently, the gait generator 100 proceeds to S310 to calculate the body vertical position at time Tk such that the desired floor reaction force vertical component determined in S306 is satisfied (the sum of the inertial force in the vertical direction of the overall center of gravity of the robot 1 and the gravitational force balances with the desired floor reaction force vertical component).
To be more specific, the kinetic relational expressions indicated by expression 15 and expression 16 given below (expressions obtained by discretizing Newton's dynamic equations in the vertical direction) are used to calculate the overall center-of-gravity vertical velocity and the overall center-of-gravity vertical position of the robot 1.

Overall center-of-gravity vertical velocity at time Tk=Overall center-of-gravity vertical velocity at time (Tk−ΔTk)+(Floor reaction force vertical component/Overall mass of the robot at time Tk)+Gravitational acceleration)*ΔTk (where the gravitational acceleration takes a negative value  Expression 15

Overall center-of-gravity vertical position at time Tk=Overall center-of-gravity vertical position at time (Tk−ΔTk)+Overall center-of-gravity vertical velocity at time Tk*ΔTk  Expression 16

Then, in the present embodiment, the gait generator 100 determines the body vertical position by using, for example, the aforesaid 3-mass-point model (the 3-mass-point model described in relation to the processing in S206) on the basis of the overall center-of-gravity vertical position, the desired foot position/posture, and the reference body posture (the desired body posture) at time Tk calculated as described above. In this case, the positions of two leg mass points in the 3-mass-point model are determined on the basis of the desired foot position/posture. Further, the vertical position of the body mass point at which the vertical position of the overall center of gravity in the 3-mass-point model agrees with the overall center-of-gravity vertical position at time Tk obtained as described above is determined. Then, the body vertical position is determined on the basis of the vertical position of the body mass point and the desired body posture (the reference body posture).
A multi-mass-point model having more mass points (e.g., a model having a mass point in each link of the robot 1) may be used to determine the body vertical position more accurately. If the mass of a portion excluding the body 24 is sufficiently smaller than the body 24, then the overall center-of-gravity vertical position may be considered, in a simplified manner, to agree with the vertical position of the center of gravity of the body 24, and the body vertical position may be determined from the overall center-of-gravity vertical position and the desired body posture (reference body posture).
Subsequently, the gait generator 100 proceeds to S314 to determine the body horizontal acceleration (the acceleration of the body 24 in the horizontal direction) at time Tk such that the desired ZMP is satisfied (such that the dynamic balance condition that the horizontal component of a moment generated about the desired ZMP by the resultant force of the inertial force of the robot 1 and the gravitational force is zero is satisfied).
At this point, the instantaneous values (the values at current time Tk) of the foot position/posture, the arm postures, the body posture, and the body vertical position of the normal gait (provisional normal gait) have been determined, so that determining the remaining body horizontal position will determine the desired motion of the entire robot 1, excluding the motional degrees of freedom of the arms that cause changes in the amount of the angular motions about the vertical axis. Hence, once the body horizontal position is determined, all floor reaction forces except for a moment of the floor reaction force about the vertical axis will be uniquely determined.
In the present embodiment, the desired floor reaction force vertical component and the desired ZMP of the normal gait (provisional normal gait) are defined by the floor reaction force vertical component trajectory parameters and the desired ZMP trajectory parameters, respectively, of the normal gait parameters determined in S022 of FIG. 10. Therefore, the floor reaction force dependently determined according to a determined body horizontal position is only the floor reaction force horizontal component.
Supplementally, in the robot 1 according to the present embodiment, the degree of freedom of each leg 2 is six, so that determining the desired foot position/posture and the desired body position/posture will uniquely determine the position/posture of each portion of each leg 2. The arm motional degree of freedom causing a change in the amount of the angular motion about the vertical axis is used to cancel a spinning force, which will be described hereinafter.
In S314, the body horizontal acceleration is determined by using, for example, the aforesaid expression 04 related to the dynamic model (the inverted pendulum model) in FIG. 9. To be more specific, the vertical position and the horizontal position of the body mass point 24b at current time Tk are determined from the body vertical position at current time Tk, the body horizontal position at time (Tk−ΔTk), and the desired body posture at current time Tk. Alternatively, the body horizontal position at the time Tk may be estimated in an interpolation manner on the basis of the time series of the body horizontal position up to the time (Tk−ΔTk) or the gait state at the time (Tk−ΔTk), and the estimated body horizontal position may be used in place of the body horizontal position at the time (Tk−ΔTk).
Further, the value obtained by subtracting the gravitational force (=mb*g) acting on the body mass point 24b from the floor reaction force vertical component at current time Tk is divided by a mass mb of the body mass point 24b to determine the vertical acceleration of the body mass point 24b at current time Tk.
Then, the vertical position, the horizontal position, and the vertical acceleration of the body mass point 24b, which have been determined as described above, are substituted into zb, Xb, and d2Zb/dt2, respectively, of the aforesaid expression 04, and the horizontal position and the vertical position of the desired ZMP at current time Tk are substituted into Xzmp and Zzmp, respectively, of expression 04. Further, an expression with Mzmp_y of the expression 04 set to zero is solved on d2Xb/dt2, thereby calculating the body mass point horizontal acceleration d2Xb/dt2 at current time Tk. Then, the body mass point horizontal acceleration d2Xb/dt2 is determined as the body horizontal acceleration at current time k.
Alternatively, a more precise dynamic model may be used to exploratorily determine the body horizontal acceleration that zeros the horizontal component of a floor reaction force moment about the desired ZMP.
Subsequently, the gait generator 100 proceeds to S316 to subject the body horizontal acceleration determined in S314 to the second-order integration so as to calculate the body horizontal position at current time Tk. To be more specific, a value obtained by multiplying the body horizontal acceleration by notch time ΔTk is added to the body horizontal velocity at time Tk−ΔTk so as to determine the body horizontal velocity at current time Tk. Further, a value obtained by multiplying the body horizontal velocity by the notch time ΔTk is added to the body horizontal position at the time Tk−ΔTk so as to determine the body horizontal position at current time Tk.
This completes the detailed description of the processing for generating gaits carried out in S306 to S316.
After completing the processing in S208 of FIG. 17, the gait generator 100 proceeds to S210 to convert the terminal body horizontal position/velocity of the generated gait (provisional normal gait) into values observed from the supporting leg coordinate system corresponding to the supporting leg at that instant (the supporting leg coordinate system having the X′′′ axis and the Y′′′ axis in FIG. 12 as the two axes in the horizontal direction) and defines the values as (Xe, Vxe) (Xe: Terminal body horizontal position; Vxe: Terminal body horizontal velocity).
Subsequently, the gait generator 100 proceeds to S212 to calculate the difference between the initial body horizontal position/velocity (Xs, Vxs) and the terminal body horizontal position/velocity (Xe, Vxe), as illustrated. The difference (Xs−Xe, Vxs−Vxe) is referred to as the body horizontal position/velocity boundary condition error (errx, errv). The normal gait is a gait that satisfies the boundary condition, so that (Xs, Vxs) and (Xe, Vxe) must agree with each other. Hence, the body horizontal position/velocity boundary condition error (errx, errv) has to be zero or substantially zero. In the present embodiment, (Xs, Vxs) at which the body horizontal position/velocity boundary condition error (errx, errv) becomes substantially zero is exploratorily determined, as described below.
Subsequently, the gait generator 100 proceeds to S214 no determine whether the body horizontal position/velocity boundary condition error (errx, errv) falls within a permissible range appropriately set beforehand (whether both errx and erry fall within the permissible range).
If the determination result in S214 is negative, then the gait generator 100 proceeds to S216. In this S216, a plurality of (two in the present embodiment) initial value candidates (Xs+ΔXs, Vxs), (Xs, Vxs+ΔVxs) is determined in the vicinity of (Xs, Vxs). Here, ΔXs and ΔVxs mean predetermined minute change amounts relative to Xs and Vxs, respectively. Then, taking these initial value candidates as the initial states of the body horizontal position/velocity, the same processing as that in S208 described above is carried out to generate a normal gait (provisional normal gait) by using gait parameters. Further, the terminal body position/velocity of the generated normal gait are converted into values (Xe+ΔXe1, Vxe+ΔVxe1), (Xe+ΔXe2, Vxe+ΔVxe2), which are observed from the supporting leg coordinate system corresponding to the supporting leg at that instant (the supporting leg coordinate system having the X′′′ axis and the Y′′′ axis in FIG. 13 as the two axes in the horizontal direction). Here, (Xe+ΔXe1, Vxe+ΔVxe1) means the terminal body position/velocity corresponding to (Xs+ΔXs, Vxs), and (Xe+ΔXe2, Vxe+ΔVxe2) means the terminal body position/velocity corresponding to (Xs, Vxs+ΔVxs). In the processing for generating the normal gait (provisional normal gait) in this case, the initial states of the state amounts except for the body horizontal position/velocity may be set to be the same as the case where, for example, the initial value candidates of the body horizontal position/velocity are (Xs, Vxs). Further in S216, the same processing as that in the aforesaid S210 is carried out to determine the difference between each initial value candidate and its corresponding terminal body position/velocity, that is, the body horizontal position/velocity boundary condition errors corresponding to the initial value candidates (Xs+ΔXs, Vxs) and (Xs, Vxs+ΔVxs), respectively.
Subsequently, the gait generator 100 proceeds to S218 to determine the next initial value candidates of (Xs, Vxs) are determined by an exploratory method on the basis of the body horizontal position/velocity boundary condition errors relative to (Xs, Vxs) and the initial value candidates (Xs+ΔXs, Vxs) and (Xs, Vxs+ΔVxs) in the vicinity thereof. As the exploratory technique, a method in which a pseudo Jacobian (sensitivity matrix) is determined and a next candidate is determined by a steepest descent method or the like, or a simplex method may be used. For example, a sensitivity matrix is determined. The sensitivity matrix indicates the degree of change in the body horizontal position/velocity boundary condition error observed when the body horizontal position and the body horizontal velocity are changed from their initial value candidates (Xs, Vxs) by minute amounts on the basis of the body horizontal position/velocity boundary condition errors relative to (Xs, Vxs) and the initial value candidates (Xs+ΔXs, Vxs) and (Xs, Vxs+ΔVxs) in the vicinity thereof. Then, based on the sensitivity matrix, initial value candidates (Xs, Vxs) that reduce the body horizontal position/velocity boundary condition errors are newly determined. After determining the new initial value candidates (Xs, Vxs) of the body horizontal position/velocity as described above, the gait generator 100 returns to S206.
As long as the determination result given in S214 is negative, the gait generator 100 repeats the processing of S206 through S218. If the determination result in S214 turns to be affirmative, then the gait generator 100 leaves the repetition loop (S204) and proceeds to S220. In this case, the provisional normal gait generated immediately before the gait generator 100 leaves the repetition loop of S204 will be obtained as the normal gait that satisfies the boundary condition.
In S220, the initial value candidates of the initial body horizontal position/velocity (Xs, Vxs) and the initial body vertical position/velocity (Zs, Vzs) in the provisional normal gait lastly generated in S208 of the repetition loop of S204 are determined as the initial body horizontal position/velocity (X0, Vx0) and the initial body vertical position/velocity (Z0, Vz0), respectively, of the normal gait to be determined.
Subsequently, the gait generator 100 proceeds to S222 to calculate the normal gait initial divergent component (the value of the divergent component at the starting time Ts of a normal gait) q0.
Here, in the present embodiment, the value of the divergent component of a gait is defined as described below. In S222, the normal gait initial divergent component q0 is calculated according to the definition.
First, when the aforesaid expression 03 indicating the relationship between the motion of the body mass point 24b in the inverted pendulum model in FIG. 9 and a floor reaction force moment (the floor reaction force moment about the origin of the supporting leg coordinate system) is represented by a state equation, the following expression 100 is derived. Here, it is assumed that the relative change amount (the divergence in height of the body 24) of the height (the vertical position) of the body 24 with respect to a mean height when the robot 1 travels is sufficiently small, so that Zb of the second term of the right side of expression 03 agrees with a fixed value h, which is set beforehand as the mean height of the body mass point 24b. Here, a floor reaction force moment Mb_y of the aforesaid expression 03 is denoted by Min as an input moment to the inverted pendulum.




  
    
      
        
          
            
              d
              
                d
                t
              
            
            ⁢
            XVb
          
          =
          
            
              
                [
                
                  
                    
                      0
                    
                    
                      1
                    
                  
                  
                    
                      
                        
                          (
                          
                            g
                            +
                            
                              
                                
                                  d
                                  2
                                
                                ⁢
                                
                                  
                                
                                ⁢
                                Zb
                              
                              
                                
                                  d
                                  t
                                
                                ⁢
                                
                                  
                                
                                ⁢
                                2
                              
                            
                          
                          )
                        
                        h
                      
                    
                    
                      0
                    
                  
                
                ]
              
              *
              XVb
            
            +
            
              
                [
                
                  
                    
                      0
                    
                  
                  
                    
                      
                        1
                        
                          h
                          *
                          mb
                        
                      
                    
                  
                
                ]
              
              *
              Min
            
          
        
        ⁢
        
          

        
        ⁢
        
          
        
        ⁢
        
          
            
              where
              ⁢
              
                
              
              ⁢
              XVb
            
            ≡
            
              [
              
                
                  
                    Xb
                  
                
                
                  
                    Vxb
                  
                
              
              ]
            
          
          ,
          
            Vxb
            ≡
            
              
                d
                Xb
              
              
                d
                t
              
            
          
        
      
    
    
      
        Expression
        ⁢
        
          
        
        ⁢
        100
      
    
  




Rewriting the expression 100 to an expression based on a discrete-time system provides the state equation of expression 102 given below.

XVb(k+1)=A(k)*XVb(k)+B(k)*Min(k)  Expression 102

The variables followed by suffixes (k) and (k+1) mean the value at the k-th time and the value at the k+1-th time, respectively, in the discrete-time system. In the following description, the k-th time and the k+1-th time may be denoted simply by time k and time k+1, respectively, in some cases.
As defined in the note related to expression 100, XVb in expression 102 denotes a state variable vector (longitudinal vector) taking the horizontal position Xb of the body mass point 24b and the horizontal velocity Vxb, which is the temporal change rate thereof, as the state variables.
Further, A(k) and B(k) in expression 102 denote a secondary square matrix (state transition matrix) and a secondary longitudinal vector, respectively, and the component values thereof are determined as indicated by the following expressions 104a to 104c and 106a to 106c. A symbol ΔT denotes a notch time of the discrete-time system, and ω0 denotes the angular frequency value defined by expression 108 of the following note. Further, exp( ) denotes an exponential function of the base of a natural logarithm.




  
    
      
        
          
        
        ⁢
        
          
            
              In
              ⁢
              
                
              
              ⁢
              the
              ⁢
              
                
              
              ⁢
              case
              ⁢
              
                
              
              ⁢
              where
              ⁢
              
                
              
              ⁢
              g
            
            +
            
              
                
                  d
                  2
                
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                  t
                
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                ⁢
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          >
          0
        
      
    
    
      
        
      
    
  
  
    
      
        
          A
          ⁡
          
            (
            k
            )
          
        
        =
        
          [
          
            
              
                
                  
                    
                      
                        
                          
                            exp
                            ⁡
                            
                              (
                              
                                ω
                                ⁢
                                
                                  
                                
                                ⁢
                                0
                                *
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                                ⁢
                                
                                  
                                
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                              )
                            
                          
                          +
                        
                      
                    
                    
                      
                        
                          exp
                          ⁡
                          
                            (
                            
                              
                                -
                                ω0
                              
                              *
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                              ⁢
                              
                                
                              
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                            )
                          
                        
                      
                    
                  
                  2
                
              
              
                
                  
                    
                      
                        
                          
                            exp
                            ⁡
                            
                              (
                              
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                                ⁢
                                
                                  
                                
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                                *
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                                ⁢
                                
                                  
                                
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                              )
                            
                          
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                          ⁡
                          
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                              ⁢
                              
                                
                              
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                              ⁡
                              
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                                  ⁢
                                  
                                    
                                  
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                                  *
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                                  ⁢
                                  
                                    
                                  
                                  ⁢
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                            ⁡
                            
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                              )
                            
                          
                        
                      
                    
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                  *
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                            exp
                            ⁡
                            
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                                ⁢
                                
                                  
                                
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                                *
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                              ⁢
                              
                                
                              
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                            )
                          
                        
                      
                    
                  
                  2
                
              
            
          
          ]
        
      
    
    
      
        Expression
        ⁢
        
          
        
        ⁢
        104
        ⁢
        a
      
    
  
  
    
      
        
          B
          ⁡
          
            (
            k
            )
          
        
        =
        
           
          
            
              [
              
                
                  
                    
                      
                        -
                        1
                      
                      +
                      
                        
                          
                            exp
                            ⁡
                            
                              (
                              
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                                *
                                Δ
                                ⁢
                                
                                  
                                
                                ⁢
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                              )
                            
                          
                          +
                          
                            exp
                            ⁡
                            
                              (
                              
                                
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                                  ω0
                                
                                *
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                                ⁢
                                
                                  
                                
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                              )
                            
                          
                        
                        2
                      
                    
                  
                
                
                  
                    
                      
                        
                          
                            exp
                            ⁡
                            
                              (
                              
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                                ⁢
                                
                                  
                                
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                                *
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                                ⁢
                                
                                  
                                
                                ⁢
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                              )
                            
                          
                          -
                          
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                            ⁡
                            
                              (
                              
                                
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                                ⁢
                                
                                  
                                
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                              )
                            
                          
                        
                        2
                      
                      *
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              ]
            
            *
            
              1
              
                ω0
                2
              
            
            *
            
              1
              
                h
                *
                mb
              
            
          
        
      
    
    
      
        Expression
        ⁢
        
          
        
        ⁢
        106
        ⁢
        a
      
    
  
  
    
      
        
          
        
        ⁢
        
          
            
              In
              ⁢
              
                
              
              ⁢
              the
              ⁢
              
                
              
              ⁢
              case
              ⁢
              
                
              
              ⁢
              where
              ⁢
              
                
              
              ⁢
              g
            
            +
            
              
                
                  d
                  2
                
                ⁢
                zb
              
              
                
                  d
                  t
                
                ⁢
                
                  
                
                ⁢
                2
              
            
          
          =
          0
        
      
    
    
      
        
      
    
  
  
    
      
        
          
        
        ⁢
        
          
            A
            ⁡
            
              (
              k
              )
            
          
          =
          
            [
            
              
                
                  1
                
                
                  
                    Δ
                    ⁢
                    
                      
                    
                    ⁢
                    T
                  
                
              
              
                
                  0
                
                
                  1
                
              
            
            ]
          
        
      
    
    
      
        Expression
        ⁢
        
          
        
        ⁢
        104
        ⁢
        b
      
    
  
  
    
      
        
          
        
        ⁢
        
          
            B
            ⁡
            
              (
              k
              )
            
          
          =
          
            
              [
              
                
                  
                    
                      
                        
                          (
                          
                            Δ
                            ⁢
                            
                              
                            
                            ⁢
                            T
                          
                          )
                        
                        2
                      
                      2
                    
                  
                
                
                  
                    
                      Δ
                      ⁢
                      
                        
                      
                      ⁢
                      T
                    
                  
                
              
              ]
            
            *
            
              1
              
                h
                *
                mb
              
            
          
        
      
    
    
      
        Expression
        ⁢
        
          
        
        ⁢
        106
        ⁢
        b
      
    
  
  
    
      
        
          
        
        ⁢
        
          
            
              In
              ⁢
              
                
              
              ⁢
              the
              ⁢
              
                
              
              ⁢
              case
              ⁢
              
                
              
              ⁢
              where
              ⁢
              
                
              
              ⁢
              g
            
            +
            
              
                
                  d
                  2
                
                ⁢
                Zb
              
              
                
                  d
                  t
                
                ⁢
                
                  
                
                ⁢
                2
              
            
          
          <
          0
        
      
    
    
      
        
      
    
  
  
    
      
        
          
        
        ⁢
        
          
            A
            ⁡
            
              (
              k
              )
            
          
          =
          
            [
            
              
                
                  
                    cos
                    ⁡
                    
                      (
                      
                        ω0
                        *
                        Δ
                        ⁢
                        
                          
                        
                        ⁢
                        T
                      
                      )
                    
                  
                
                
                  
                    
                      sin
                      ⁡
                      
                        (
                        
                          ω0
                          *
                          Δ
                          ⁢
                          
                            
                          
                          ⁢
                          T
                        
                        )
                      
                    
                    ω0
                  
                
              
              
                
                  
                    
                      -
                      ω0
                    
                    *
                    
                      sin
                      ⁡
                      
                        (
                        
                          ω0
                          *
                          Δ
                          ⁢
                          
                            
                          
                          ⁢
                          T
                        
                        )
                      
                    
                  
                
                
                  
                    cos
                    ⁡
                    
                      (
                      
                        ω0
                        *
                        Δ
                        ⁢
                        
                          
                        
                        ⁢
                        T
                      
                      )
                    
                  
                
              
            
            ]
          
        
      
    
    
      
        Expression
        ⁢
        
          
        
        ⁢
        104
        ⁢
        c
      
    
  
  
    
      
        
          
        
        ⁢
        
          
            B
            ⁡
            
              (
              k
              )
            
          
          =
          
            
              [
              
                
                  
                    
                      
                        -
                        1
                      
                      +
                      
                        cos
                        ⁡
                        
                          (
                          
                            ω0
                            *
                            Δ
                            ⁢
                            
                              
                            
                            ⁢
                            T
                          
                          )
                        
                      
                    
                  
                
                
                  
                    
                      
                        -
                        ω0
                      
                      *
                      
                        sin
                        ⁡
                        
                          (
                          
                            ω0
                            *
                            Δ
                            ⁢
                            
                              
                            
                            ⁢
                            T
                          
                          )
                        
                      
                    
                  
                
              
              ]
            
            *
            
              1
              
                ω0
                2
              
            
            *
            
              1
              
                h
                *
                mb
              
            
          
        
      
    
    
      
        Expression
        ⁢
        
          
        
        ⁢
        106
        ⁢
        c
      
    
  
  
    
      
        
          
        
        ⁢
        
          
            where
            ⁢
            
              
            
            ⁢
            ω0
          
          ≡
          
            
              
              
                
                  g
                  +
                  
                    
                      
                        d
                        2
                      
                      ⁢
                      Zb
                    
                    
                      
                        d
                        t
                      
                      ⁢
                      
                        
                      
                      ⁢
                      2
                    
                  
                
                h
              
              
            
          
        
      
    
    
      
        Expression
        ⁢
        
          
        
        ⁢
        108
      
    
  




In this case, as is obvious from expressions 104a to 104c, 106a to 106c and expression 108, the component values of A(k) and B(k) are dependent upon the value of the vertical acceleration d2Zb/dt2 (the motional acceleration in the vertical direction d2Zb/dt2) of the body mass point 24b. Hence, the component values of A(k) and B(k) will be the values dependent upon the inertial force in the vertical direction of the body mass point 24b (=−mb*d2Zb/dt2), i.e., the function value of the inertial force. The gravitational force acting on the body mass point 24a has a fixed value. In other words, therefore, the component values of A(k) and B(k) are the function values of the resultant force of the inertial force of the body mass point 24b in the vertical direction and the gravitational force acting on the body mass point 24b or a floor reaction force vertical component balancing the resultant force.
Supplementally, if the mass mb of the body mass point 24b of the inverted pendulum agrees with the overall mass of the robot 1 as in the present embodiment, then the floor reaction force vertical component that balances the resultant force of the inertial force in the vertical direction of the body mass point 24b and the gravitational force acting on the body mass point 24b agrees with the floor reaction force vertical component (the translational floor reaction force vertical component of a total floor reaction force) acting on the robot 1.
Further, in the running gait illustrated in FIG. 6, g+d2Zo/dt2>0 holds in a one-leg supporting period, whereas g+d2Zo/dt2=0 holds in a floating period.
In a system represented by the state equation of expression 102 described above, if an initial value XVb(0) of the state variable vector XVb (the value of XVb at time at which k=0 (time 0)) and the time series of the input moment Min (the horizontal component Mb_y of the floor reaction force moment) from time 0 to time k-1 are given, then the value XVb(k) of the state variable vector XVb at arbitrary time k (>0) will be given by the following expression 110.




  
    
      
        
          
            XVb
            ⁡
            
              (
              k
              )
            
          
          =
          
            
              
                φ
                ⁡
                
                  (
                  
                    k
                    ,
                    0
                  
                  )
                
              
              *
              
                XVb
                ⁡
                
                  (
                  0
                  )
                
              
            
            +
            
              
                ∑
                
                  i
                  =
                  0
                
                
                  k
                  -
                  1
                
              
              ⁢
              
                
                  φ
                  ⁡
                  
                    (
                    
                      k
                      ,
                      
                        i
                        +
                        1
                      
                    
                    )
                  
                
                *
                
                  B
                  ⁡
                  
                    (
                    i
                    )
                  
                
                *
                
                  Min
                  ⁡
                  
                    (
                    i
                    )
                  
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          
        
        ⁢
        
          
            where
            ⁢
            
              
            
            ⁢
            
              φ
              ⁡
              
                (
                
                  k
                  ,
                  j
                
                )
              
            
          
          ≡
          
            
              A
              ⁡
              
                (
                
                  k
                  -
                  1
                
                )
              
            
            *
            
              A
              ⁡
              
                (
                
                  k
                  -
                  2
                
                )
              
            
            *
            ...
            *
            
              A
              ⁡
              
                (
                j
                )
              
            
          
        
        ⁢
        
          
        
        ⁢
        
          

        
        ⁢
        
          
        
        ⁢
        
          (
          
            
              j
              =
              0
            
            ,
            1
            ,
            ...
            ⁢
            
              
            
            ,
            k
          
          )
        
      
    
    
      
        Expression
        ⁢
        
          
        
        ⁢
        110
      
    
  




Regarding φ(k,j) defined by the note in expression 110, if j=k, then φ(k,j)≡Identity matrix.
Attention will now be paid to the behavior of the inverted pendulum model in the normal gait described above. It is assumed that the initial time Ts of the normal gait is time k=0, the ending time Te of the normal gait (=Ts+Tcyc) is time k=kcyc (provided kcyc≡Tcyc/ΔT), and the state variable vector XVb defined by the motion of the normal gait at the starting time Ts is XVb(0). Further, in the state variable vector XVb at the ending time Te of the normal gait (time k=kcyc), the component dependent on the state variable vector value XVb(0) at the starting time Ts of the normal gait is denoted by XVb(kcyc). At this time, the relationship between XVb(kcyc) and XVb(0) will be represented by the following expression 112 on the basis of the above expression 110.

XVb(kcyc)=φ(kcyc,0)*XVb(0)  Expression 112

    
    
        where φ(kcyc,0)=A(kcyc-1)* . . . *A(1)*A(0)
    
    


Further, the two characteristic values of a matrix φ(kcyc,0) of the right side of expression 112 are denoted by λ1 and λ2, characteristic vectors (longitudinal vectors) corresponding to the respective characteristic values are denoted by (a11, a21)T and (a12, a22)T, and a second-order square matrix having these characteristic vectors as a first row and a second row is denoted by Γcyc. A matrix obtained by diagonalizing φ(kcyc,0) by using the matrix Γcyc is denoted by Λ. In other words, Λ is defined by expression 114 given below. Hereinafter, the matrix Γcyc will be referred to as the diagonalizing matrix.




  
    
      
        
          Λ
          ≡
          
            
              Γ
              cyc
              
                -
                1
              
            
            *
            
              φ
              ⁡
              
                (
                
                  
                    k
                    cyc
                  
                  ,
                  0
                
                )
              
            
            *
            
              Γ
              cyc
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            where
            ⁢
            
              
            
            ⁢
            Λ
          
          ≡
          
            [
            
              
                
                  
                    λ
                    ⁢
                    
                      
                    
                    ⁢
                    1
                  
                
                
                  0
                
              
              
                
                  0
                
                
                  
                    λ
                    ⁢
                    
                      
                    
                    ⁢
                    2
                  
                
              
            
            ]
          
        
        ⁢
        
          

        
        ⁢
        
          
            Γ
            cyc
          
          ≡
          
            [
            
              
                
                  
                    a
                    ⁢
                    
                      
                    
                    ⁢
                    11
                  
                
                
                  
                    a
                    ⁢
                    
                      
                    
                    ⁢
                    12
                  
                
              
              
                
                  
                    a
                    ⁢
                    
                      
                    
                    ⁢
                    21
                  
                
                
                  
                    a
                    ⁢
                    
                      
                    
                    ⁢
                    22
                  
                
              
            
            ]
          
        
        ⁢
        
          

        
        ⁢
        
          
            
              φ
              ⁡
              
                (
                
                  
                    k
                    cyc
                  
                  ,
                  0
                
                )
              
            
            *
            
              [
              
                
                  
                    
                      a
                      ⁢
                      
                        
                      
                      ⁢
                      11
                    
                  
                
                
                  
                    
                      a
                      ⁢
                      
                        
                      
                      ⁢
                      21
                    
                  
                
              
              ]
            
          
          =
          
            λ
            ⁢
            
              
            
            ⁢
            1
            *
            
              [
              
                
                  
                    
                      a
                      ⁢
                      
                        
                      
                      ⁢
                      11
                    
                  
                
                
                  
                    
                      a
                      ⁢
                      
                        
                      
                      ⁢
                      21
                    
                  
                
              
              ]
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            
              φ
              ⁡
              
                (
                
                  
                    k
                    cyc
                  
                  ,
                  0
                
                )
              
            
            *
            
              [
              
                
                  
                    
                      a
                      ⁢
                      
                        
                      
                      ⁢
                      12
                    
                  
                
                
                  
                    
                      a
                      ⁢
                      
                        
                      
                      ⁢
                      22
                    
                  
                
              
              ]
            
          
          =
          
            λ
            ⁢
            
              
            
            ⁢
            2
            *
            
              [
              
                
                  
                    
                      a
                      ⁢
                      
                        
                      
                      ⁢
                      12
                    
                  
                
                
                  
                    
                      a
                      ⁢
                      
                        
                      
                      ⁢
                      22
                    
                  
                
              
              ]
            
          
        
      
    
    
      
        Expression
        ⁢
        
          
        
        ⁢
        114
      
    
  




The following expression 116 is derived from the expression 114 and the above expression 112.

Γcyc−1*XVb(kcyc)=Λ*Fcyc−1*XVb(0)  Expression 116

The matrix φ(kcyc,0) to be diagonalized by the diagonalizing matrix Γcyc denotes the product of the state transition matrixes A(0), A(1), . . . , A(kcyc-1) at each time (more specifically, at each time of notch time ΔT from time 0 to time kcyc-1) in a period from the starting time (time 0) to the ending time (time kcyc) of one cycle of a normal gait, as indicated by the note to the above expression 112. Hence, the matrix φ(kcyc,0) depends on the time series of the inertial force of the body mass point 24b in the period of one cycle of the normal gait. Hence, each component value of the diagonalizing matrix Γcyc accordingly also depends on the time series of the inertial force of the body mass point 24b in the period of one cycle of the normal gait.
Here, a vector obtained by linearly converting a state variable vector XVb(k) at arbitrary time k by an inverse matrix Γcyc−1 of the diagonalizing matrix Γcyc (hereinafter referred to as the converted state variable vector) is denoted by (p(k), q(k))T. The converted state variable vector (p(k), q(k))T is defined by expression 118 given below.

(p(k), q(k))T≡Γcyc−1*XVb(k)  Expression 118

The following expression 120 is derived from the expression 118 and the above expression 116.

(p(kcyc), q(kcyc))T=Λ*(p(0), q(0))T  Expression 120

In this expression 120, if λ1>1, then the absolute value of p(kcyc)>the absolute value of the initial value p(0), and if λ1≦1, then the absolute value of p(kcyc)≦the absolute value of the initial value p(0). Similarly, if λ2>1, then the absolute value of q(kcyc)>the absolute value of the initial value q(0), and if λ2≦1, then the absolute value of q(kcyc)≦the absolute value of the initial value q(0).
Meanwhile, the normal gait in the present embodiment is a gait repeating the one-leg supporting period and the floating period alternately (the running gait in FIG. 6), so that it may be considered that a state in which g+d2Zb/dt2≦0 and a state in which g+d2Zb/dt2>0 are alternately set rather than the state in which g+d2Zb/dt2≦0 being always maintained. In such a normal gait, generally, one of the two characteristic values λ1 and λ2 of φ(kcyc,0) takes a value that is larger than 1, while the other takes a value that is smaller than 1.
Therefore, hereinafter, λ1<1 and λ2>1 applies. More specifically, the first component p(k) of the converted state variable vector (p(k), q(k))T denotes the component corresponding to the characteristic value λ1, which is smaller than 1, and the second component q(k) thereof denotes the component corresponding to the characteristic value λ2, which is larger than 1. At this time, p(k) has a meaning as the state amount of a motional component having convergent property in a normal gait infinitely repeated, while q(k) has a meaning as the state amount of a motional component having divergent property in the normal gait infinitely repeated.
Hence, in the present embodiment, the second component q(k) of the converted state variable vector (p(k), q(k))T defined by expression 118 is defined as the aforesaid divergent component. The divergent component q(k) thus defined takes a linearly coupled value of the state variables Xb(k) and Vxb(k). In this case, in the linear coupling, the weighting coefficients by which Xb(k) and Vxb(k) are multiplied are dependent on the time series of the inertial force of the body mass point 24b in the period of one cycle of the normal gait. The first component p(k) of the converted state variable vector (p(k), q(k))T defined by expression 118 is referred to as the convergent component.
The convergent component p(k) and the divergent component q(k) defined by the above expression 118 are the convergent component p(k) and the divergent component q(k), respectively, on a sagittal plane (the convergent component and the divergent component corresponding to the state variable vector XVb having, as its components, the horizontal position Xb and the horizontal velocity Vxb of the body mass point 24b in the X-axis direction). In the same manner, the convergent component and the divergent component on a lateral plane are defined.
To be more specific, the convergent component and the divergent component on the lateral plane are defined by an expression in which the components Xb and Vxb of the state variable vector XVb(k) of the right side of expression 118 have been replaced by the horizontal position and the horizontal velocity, respectively, of the body mass point 24b in the Y-axis direction. In this case, the matrix Γcyc−1 of expression 118 remains the same in both axial directions, namely, the X-axis direction and the Y-axis direction.
According to the definition of the divergent component q described above, the normal gait initial divergent component q0 is calculated in S222 as described below.
The gait generator 100 calculates the instantaneous value of the inertial force of the body mass point 24b at each time Tk for every notch time ΔT in the period of one cycle from the starting time Ts to the ending time Ts (each time k from time k=0 to time k=kcyc-1 in terms of the discrete-time system) of the normal gait on the basis of normal gait parameters. In this case, if the mass mb of the body mass point 24b of the inverted pendulum agrees with the overall mass of the robot 1, then the resultant force of the inertial force in the vertical direction of the body mass point 24b and the gravitational force acting on the body mass point 24b in the normal gait balances with a floor reaction force vertical component in the normal gait.
In the present embodiment, therefore, the gait generator 100 calculates the instantaneous value of the floor reaction force vertical component at each time in the period of one cycle of the normal gait on the basis of the aforesaid floor reaction force vertical component trajectory parameter of the normal gait parameters. The instantaneous value is the same as the value calculated in S306 of FIG. 18. Then, the gait generator 100 uses the value obtained by dividing each instantaneous value of the calculated floor reaction force vertical component by the mass mb of the body mass point 24b (=the overall mass of the robot 1) as the value of (g+d2Zb/dt2) of the above expression 100 to calculate the state transition matrix A(k)(k=0, 1, . . . , kcyc-1) according the above expressions 104a to 104c.
In the running gait illustrated in FIG. 6, the floor reaction force vertical component will not take any negative value. In actuality, therefore, A(k) will be calculated according to either expression 104a or 104b.
Supplementally, as an alternative, a multi-mass-point model (geometric model), such as the aforesaid 3-mass-point model, may be used to calculate the inertial force in the vertical direction (or the vertical acceleration) of the body 24 of the robot 1 in the normal gait, then the calculated inertial force (or the vertical acceleration) may be used as the inertial force (or the vertical acceleration) of the body mass point 24b to calculate the state transition matrix A(k) at each time (k=0, 1, . . . , kcyc-1). For example, the instantaneous value of the inertial force of the body mass point 24b in the normal gait may be calculated as described below by using the aforesaid 3-mass-point model.
The instantaneous value of the inertial force in the vertical direction of two leg mass points in the aforesaid 3-mass-point model is calculated on the basis of a foot trajectory parameter of a normal gait, and the instantaneous value of the inertial force in the vertical direction of the overall center of gravity of the robot 1 is calculated on the basis of a floor reaction force vertical component trajectory. Further, the value obtained by subtracting the instantaneous value of the inertial force in the vertical direction of the two leg mass points from the instantaneous value of the inertial force in the vertical direction of the overall center of gravity is calculated as the instantaneous value of the inertial force in the vertical direction of the body mass point 24b. In this case, the resultant force of the inertial force in the vertical direction of the body mass point 24b and the gravitational force acting on the body mass point 24b (or g+d2Zb/dt2) may take a negative value.
After calculating kcyc pieces of A(k)(k=0, 1, . . . , kcyc-1) in the period of one cycle from the starting time Ts to the ending time Ts of the normal gait as described above, the gait generator 100 multiplies the values of A(k) to calculate the matrix φ(kcyc,0)(=A(kcyc-1)* . . . *A(1)*A(0)) of the right side of expression 112.
Further, the gait generator 100 calculates the characteristic values λ1 and λ2 of the matrix φ(kcyc,0) and the characteristic vectors (a11, a21)T and (a12, a22)T corresponding thereto, and determines, from the characteristic vectors, the aforesaid diagonalizing matrix Γcyc according to the note to the above expression 114. Then, the gait generator 100 calculates the inverse matrix Γcyc of the diagonalizing matrix Γcyc.
Further, the gait generator 100 determines the initial body mass point position/velocity, which is the pair of the horizontal position and horizontal velocity of the body mass point 24b of the inverted pendulum at the starting time Ts of the normal gait, from the initial body horizontal position/velocity (X0, Vx0) of the normal gait determined in S220 and the initial state of the body posture angle of the normal gait.
Then, the gait generator 100 calculates the normal gait initial divergent component q0 according to the above expression 118 from the inverse matrix Γcyc−1 determined as described above and the initial body mass point horizontal position/velocity. To be more specific, a component in the X-axis direction (a state amount vector in the X-axis direction) and a component in the Y-axis direction (a state amount vector in the Y-axis direction) of the initial body mass point horizontal position/velocity are respectively multiplied by Γ−1 to calculate the initial divergent component q0 in each of the X-axis direction and the Y-axis direction.
After calculating the initial divergent component q0 of the normal gait as described above, the gait generator 100 proceeds to S224 to convert the initial divergent component q0 of the normal gait into a value observed from a current time's gait supporting leg coordinate system, determining the converted value as q0′′. Further, the gait generator 100 converts the initial body vertical position/velocity (Z0, Vz0) into values observed from the current time's gait supporting leg coordinate system, determining the converted values as (Z0′′, Vz0′′).
Supplementally, the (Z0′′, Vz0′′) agree with the body vertical position/velocity at the end of a second turning gait observed from the supporting leg coordinate system (the supporting leg coordinate system having the X′′-axis and the Y′′-axis as two axes on the horizontal plane in FIG. 13) of the second turning gait. Further, q0′′ also agrees with the divergent component at the end of the second turning gait observed from the supporting leg coordinate system of the second turning gait. Hence, these properties may be used to calculate (Z0′′, Vz0′′) and q0′′.
This completes the processing in S024 of FIG. 10, namely, the subroutine processing for determining the initial state of the normal gait.
Subsequently, the gait generator 100 proceeds to S026 of FIG. 10 to determine the gait parameters (some being provisionally determined) of the current time gait. More specifically, in S026, the processing illustrated by the flowchart of FIG. 19 is carried out.
First, in S600, the gait generator 100 determines the foot trajectory parameter of the current time gait such that the foot position/posture trajectory of a current time gait connects to the foot position/posture trajectory of a normal gait.
To be more specific, the initial free leg foot position/posture of the current time gait (the free leg foot position/posture at the start of the current time gait) is set to the supporting leg foot position/posture at the end of the last time gait observed from the current time's gait supporting leg coordinate system (the present free leg foot position/posture).
The initial supporting leg foot position/posture of the current time gait (the supporting leg foot position/posture at the start of the current time gait) is set to the free leg foot position/posture at the end of the last time gait observed from the current time's gait supporting leg coordinate system (the present supporting leg foot position/posture).
Further, the free leg foot position/posture at the end of the current time gait are determined according to a next time gait's supporting leg coordinate system observed from the current time's gait supporting leg coordinate system (the required values of the expected landing position/posture of the free leg foot 22 of a first step related to the current time gait). More specifically, the free leg foot position/posture at the end of the current time gait are determined such that the representative point of the free leg foot 22 agrees with the origin of the next time gait's supporting leg coordinate system observed from the current time's gait supporting leg coordinate system when the foot 22 has been rotated from the free leg foot position/posture at the end of the current time gait by a predetermined angle in the pitch direction without a slippage until substantially the entire bottom surface of the foot 22 comes in contact with the ground while holding the foot 22 in contact with a floor.
At the end of the current time gait, the supporting leg foot 22 is off the floor and in the air. To determine the trajectory after the supporting leg foot 22 leaves the floor, first, the position/posture of the supporting leg foot 22 of the current time gait at the end of the next time gait, that is, the free leg foot position/posture at the end of the next time gait are determined. The free leg foot position/posture at the end of the next time gait are determined according to the next but one time's gait supporting leg coordinate system observed from the current time's gait supporting leg coordinate system (the required values of the expected landing position/posture of the free leg foot 22 of the second step related to the current time gait).
To be more specific, the free leg foot position/posture at the end of the next time gait are determined such that the representative point of the foot 22 agrees with the origin of the next but one time's gait supporting leg coordinate system observed from the current time's gait supporting leg coordinate system when the foot 22 has been rotated from the foot position/posture by a predetermined angle in the pitch direction without a slippage until substantially the entire bottom surface of the foot 22 comes in contact with the ground while holding the foot 22 in contact with a floor.
Then, the supporting leg foot position/posture at the end of the current time gait are determined by generating the foot position/posture trajectory from the supporting leg foot position/posture at the start of the current time gait determined as described above to the free leg foot position/posture at the end of the next time gait by the aforesaid finite-duration setting filter up to the end of the current time gait.
Subsequently, the gait generator 100 proceeds to S602 to determine the body posture trajectory parameters of the current time gait. The body posture trajectory parameters are determined such that the body posture trajectory defined thereby continuously connects to the body posture trajectory of a normal gait (such that the body posture angle and the angular velocity at the end of the current time gait agree with the body posture angle and the angular velocity, respectively, at the start of the normal gait). In this case, according to the present embodiment, the body posture defined by the body posture trajectory parameters of the current time gait is set to the aforesaid reference body posture, which is steadily a fixed posture (the posture in which the body trunk axis of the body 24 is oriented in the vertical direction), as with the body posture of the normal gait.
If the body posture trajectory of the current time gait is set to continuously connect to the body posture trajectory of the normal gait, then the body posture trajectory may be set to temporally change from the start to the end of the current time gait.
Subsequently, the gait generator 100 proceeds to S604 to determine the arm posture trajectory parameters of the current time gait. The arm posture trajectory parameters are determined in the same manner as that for the arm posture trajectory parameters of a normal gait such that the arm posture trajectory of the current time gait uninterruptedly continues to the arm posture trajectory of the normal gait.
As with the arm posture trajectory parameters of the normal gait, the arm posture trajectory parameters of the current time gait determined here are parameters (e.g., the parameters defining the relative height of the hand distal end of an arm in relation to the body 24 and the relative center-of-gravity position of the entire arm) other than those related to the angular momentum changes of both arms about the vertical axis (or the body trunk axis of the body 24).
Subsequently, the gait generator 100 proceeds to S606 to determine the floor reaction force vertical component trajectory parameters of the current time gait such that the floor reaction force vertical component trajectory defined thereby becomes a virtually continuous trajectory, as illustrated in FIG. 7. However, the floor reaction force vertical component trajectory parameters of the current time gait are determined such that both the overall center-of-gravity vertical position/velocity of the robot 1 and the floor reaction force vertical component trajectory of the current time gait continuously connect to the aforesaid normal gait.
To be more specific, first, the initial overall center-of-gravity vertical position/velocity of the normal gait observed from the current time's gait supporting leg coordinate system are determined mainly on the basis of the values (Z0′′, Vz0′′) obtained by converting the initial body vertical position/velocity of the normal gait lastly determined by the processing in S024 of FIG. 10 (the processing for determining the initial state of the normal gait) into the values observed from the current time's gait supporting leg coordinate system, i.e., (Z0′′, Vz0′′) determined in S224 of FIG. 17.
For example, the initial overall center-of-gravity vertical position/velocity of the normal gait are determined using the aforesaid 3-mass-point model (the 3-mass-point model described in relation to the processing in S206). In this case, the positions and velocities of two leg mass points in the 3-mass-point model are determined on the basis of the desired foot position/posture and the temporal change rate (changing velocity) thereof at the start of the normal gait observed from the current time's gait supporting leg coordinate system. Further, the position/velocity of the body mass point in the 3-mass-point model are determined from the aforesaid (Z0′′, Vz0′′) and the body posture angle (=reference body posture angle) at the start of the normal gait and the temporal change rate thereof. Then, based on the positions and the velocities of these three mass points, the center-of-gravity positions and velocities of the three mass points) are calculated as the initial overall center-of-gravity vertical position/velocity of the normal gait.
A multi-mass-point model having more mass points (e.g., a geometric model having a mass point in each link of the robot 1) may be used to determine the initial overall center-of-gravity vertical position/velocity of the normal gait more accurately. If the mass of a portion excluding the body 24 is sufficiently smaller than the body 24, then the initial overall center-of-gravity vertical position/velocity of the normal gait may be determined from the aforesaid (Z0′′, Vz0′′) and the body posture angle at the start of the normal gait (=reference body posture angle) and the temporal change rate thereof.
The initial overall center-of-gravity vertical position/velocity of the normal gait determined as described above are substituted into the terminal overall center-of-gravity vertical position/velocity of the above expression 13 and the following expression 41, and the overall center-of-gravity vertical position and velocity of the instantaneous values of the last time gait (more specifically, the values indicating the terminal state of the last time gait observed from the current time's gait supporting leg coordinate system) are substituted into the initial overall center-of-gravity vertical position and velocity of the above expression 13 and the following expression 41, thereby determining the floor reaction force vertical component trajectory parameters of the current time gait such that the relationship between expression 13 and expression 41 is satisfied. The integral values in expression 13 and expression 41 are to be the integral values obtained during the period from the start to the end of the current time gait.

Terminal overall center-of-gravity vertical velocity−Initial overall center-of-gravity vertical velocity=First-order integration of (Floor reaction force vertical component/Mass of the robot)+First-order integration of gravitational acceleration  Expression 41

(where the gravitational acceleration takes a negative value)

More specifically, first, at least two parameters of the floor reaction force vertical component trajectory parameters (e.g., the time of breakpoints) defining the floor reaction force vertical component trajectory illustrated in FIG. 7 are defined as independent unknown variables, and the values of the unknown variables are determined by solving the simultaneous equation formed of expression 13 and expression 41.
As the floor reaction force vertical component trajectory parameters defined as the unknown variables, for example, the height of the trapezoid (the peak value of the floor reaction force vertical component) and the width (the duration of the one-leg supporting period) in the floor reaction force vertical component trajectory illustrated in FIG. 7 may be selected. In this case, the slopes on both sides of the trapezoid in FIG. 7 will take values determined on the basis of a current time gait cycle or the like, or values of time of breakpoints of the floor reaction force vertical component trajectory except for the time at which a one-leg supporting period is switched to a floating period, the values being determined on the basis of a current time gait cycle and the like. Supplementally, if only one unknown variable is selected, then there will be generally no solution that satisfies the simultaneous equation of expression 13 and expression 41.
Supplementally, in the present embodiment, the floor reaction force vertical component trajectory parameters of the current time gait determined as described above correspond to the up-and-down-direction inertial force parameters in the present invention. Hence, the processing in S606 implements the means for determining the up-and-down-direction inertial force parameters in the present invention.
Subsequently, the gait generator 100 proceeds to S608 to determine the ZMP trajectory parameters (e.g., the time and positions of breakpoints of a ZMP trajectory) defining the ZMP trajectory such that the ZMP trajectory of the current time gait will have a high stability allowance and develop no sudden change. For example, the ZMP trajectory parameters are provisionally determined such that the ZMP trajectory has the pattern as illustrated in FIG. 3. The ZMP trajectory parameters of the current time gait are provisionally determined such that the ZMP trajectory of the current time gait will uniterruptedly connect to the ZMP trajectory of the aforesaid normal gait (such that the position of the ZMP at the end of the current time gait agrees with the position of the ZMP at the start of the normal gait).
In this case, in a running gait, the time and positions of breakpoints of the ZMP trajectory in a one-leg supporting period may be set in the same manner as that for setting the ZMP trajectory parameters of the normal gait described above. Further, the ZMP trajectory parameters may be set such that the desired ZMP trajectory in the floating period linearly and continuously changes from the start of a floating period to the position of the ZMP at the start of the normal gait.
The ZMP trajectory parameters of the current time gait determined in S608 are provisionally determined parameters and are to be therefore corrected as will be described later. Thereafter, the desired ZMP of the current time gait defined by the provisionally determined ZMP trajectory parameters until the correction is completed will be hereinafter referred to as the provisional desired ZMP. The gait parameters of the current time gait that include the provisionally determined ZMP trajectory parameters are referred to as the provisional current time gait parameters.
Referring back to the description with reference to FIG. 10, after carrying out the processing in S026 as described above, the gait generator 100 carries out the processing for correcting the gait parameters (specifically, the ZMP trajectory parameters) of the current time gait in S028. In this processing, the ZMP trajectory parameters of the gait parameters for causing the body position/posture trajectory of the current time gait to continue or approach to the normal gait are corrected.
This processing is carried out as illustrated by the flowchart of FIG. 20.
First, the gait generator 100 proceeds to S702 via S700 and generates a provisional current time gait until the ending time of the current time gait on the basis of the provisional current time gait parameters including the provisionally determined ZMP trajectory parameters.
In S702, the processing illustrated by the flowchart of FIG. 21 is carried out.
First, in S800, the gait generator 100 initializes, for example, the time Tk for generating a provisional current time gait. To be more specific, the time Tk for generating a provisional current time gait is initialized to current time t. Further, the motional state (the motional state observed in a current time's gait supporting leg coordinate system) of a desired gait at time t-Δt, such as the desired body position and desired body velocity, the desired body posture angle and the angular velocity thereof, the desired foot position/posture, the desired arm posture and the like already determined by the gait generator 100 at time t-Δt is set as the initial motional state immediately before the current time t of the provisional current time gait
Subsequently, the gait generator 100 proceeds to S804 via S802 to determine whether time Tk (current value) for generating the provisional current time gait is time before ending time of a current time gait Tcurr (whether Tk≦Tcurr applies). If the determination result is affirmative, then the gait generator 100 carries out the processing of S806 to S816 (the details thereof will be discussed later) thereby to determine the instantaneous value of the gait at time Tk.
Subsequently, the gait generator 100 proceeds to S818 wherein the gait generator 100 increments the time Tk for generating the provisional current time gait by predetermined notch time ΔTk, and then repeats the determination in S804. Here, the notch time ΔTk may be set to coincide with, for example, a control cycle Δt. However, the ΔTk may be set to be longer than Δt so as to reduce the calculation volume.
If the determination result in S804 is affirmative, then the processing from S806 to S818 is repeated. If the determination result in S804 turns to negative, then the processing illustrated in FIG. 21, that is, the processing in S702 of FIG. 20, is terminated. Thus, the generation of the provisional current time gait from the starting time to the ending time of the current time gait is completed.
The gait generator 100 carries out the processing for determining the instantaneous values of the provisional current time gait in the aforesaid S806 to S816 as follows. The instantaneous values of the provisional current time gait are determined in the same manner as that for determining the instantaneous values of the normal gait (provisional normal gait) in S306 to S316 of FIG. 18.
First, in S806, the gait generator 100 determines the instantaneous value at time Tk of the desired floor reaction force vertical component trajectory illustrated in FIG. 7 on the basis of the provisional current time gait parameters (more specifically, the floor reaction force vertical component trajectory parameters).
Subsequently, in S808, the gait generator 100 determines the instantaneous value of the desired ZMP trajectory (the provisional desired ZMP trajectory) illustrated in FIG. 8 at time Tk on the basis of the provisional current time gait parameters (more specifically, the provisionally determined ZMP trajectory parameters).
Subsequently, the gait generator 100 proceeds to S810 to determine the instantaneous values of the desired foot position/posture, the desired body posture, and the desired arm posture at time Tk on the basis of the provisional current time gait parameters (more specifically, the foot trajectory parameters, the body posture trajectory parameters, and the arm posture trajectory parameters). Regarding the desired arm postures, more specifically, the overall center-of-gravity positions of both arms are determined, whereas the motions of the arms (arm swinging motions) that change the amounts of angular motions about the vertical axis (or the body trunk axis of the body 24) are not yet determined.
Subsequently, the gait generator 100 proceeds to S812 to calculate the body vertical position at time Tk such that the desired floor reaction force vertical component determined in S806 is satisfied (such that the sum of the inertial force of the overall center of gravity of the robot 1 in the vertical direction and the gravitational force is balanced with the desired floor reaction force vertical component). The same calculation method as that used in S312 of FIG. 18 (the processing for calculating the instantaneous value of the body vertical position of the normal gait) may be applied. However, the multi-mass-point model used in S812 may be different from the model used in S312.
Subsequently, the gait generator 100 proceeds to S814 to carry out the processing for determining the body horizontal acceleration of the provisional current time gait at time Tk.
To be more specific, if time Tk for generating the provisional current time gait agrees with current time t (the time of the current control cycle of the gait generator 100), then the gait generator 100 determines the body horizontal acceleration of the provisional current time gait at time Tk such that a model manipulation floor reaction force moment (the value at the current control cycle) supplied from the compensating total floor reaction force moment distributor 110 is generated about the desired ZMP (such that the horizontal component of a moment generated about the desired ZMP by the resultant force of the inertial force of the robot 1 and the gravitational force balances out the model manipulation floor reaction force moment).
In other words, the body horizontal acceleration at time Tk is determined such that the moment generated about the desired ZMP by the resultant force of the inertial force of the robot 1 and the gravitational force agrees with a moment with a sign reversed from the sign of the model manipulation floor reaction force moment.
If time Tk for generating the provisional current time gait is further in the future than current time t (if Tk>current time t), then the gait generator 100 determines the body horizontal acceleration at time Tk such that the desired ZMP is satisfied (such that the dynamic balance condition that the horizontal component of a moment generated about the desired ZMP due to the resultant force of the inertial force of the robot 1 and the gravitational force is zero is satisfied).
In these cases, the processing for calculating the body horizontal acceleration of the provisional current time gait at time Tk is carried out using, for example, the dynamic model (the inverted pendulum model) in FIG. 9.
To be more specific, the vertical position and the horizontal position of the body mass point 24b at time Tk are determined from the body vertical position of the provisional current time gait at time Tk, the body horizontal position at time (Tk−ΔTk), and the desired body posture at time Tk. If time Tk is current time t, then the body horizontal position in the initial motional state set in S800 is used as the body horizontal position at time (Tk−ΔTk).
Supplementally, the body horizontal position at time Tk may be estimated by interpolation on the basis of the time series of the body horizontal position up to time (Tk−ΔTk) or the gait state at time (Tk−ΔTk), and the estimated body horizontal position may be used in place of the body horizontal position at time (Tk−ΔTk).
Further, the value obtained by subtracting the gravitational force acting on the body mass point 24b (=mb*g) from the floor reaction force vertical component of the provisional current time gait at time Tk is divided by the mass mb of the body mass point 24b, thereby determining the vertical acceleration of the body mass point 24b at time Tk.
Further, if Tk is equal to current time t, then the body mass point horizontal acceleration d2Xb/dt2 at time Tk is calculated by solving, on d2Xb/dt2, an expression obtained by substituting Zb, Xb and d2Zb/dt2 of the aforesaid expression 04 by the vertical position, the horizontal position, and the vertical acceleration, respectively, of the body mass point 24b determined as described above, substituting Xzmp and Zzmp of the expression 04 by the horizontal position and the vertical position of the desired ZMP at time Tk, and by causing Mzmp_y of the expression 04 to coincide with the model manipulation floor reaction force moment (current value). Then, the body mass point horizontal acceleration d2Xb/dt2 is determined as the body horizontal acceleration at time Tk.
If Tk>current time t, then the body horizontal acceleration at time Tk is calculated by solving an expression, which is obtained by setting Mzmp_y of the expression 04 to zero, on d2Xb/dt2. The processing in this case is the same as that applied to the case where Tk is equal to current time t, except for setting Mzmp_y of the expression 04 to zero.
Alternatively, a more precise dynamic model may be used to exploratorily determine the body horizontal acceleration that causes the horizontal component of a floor reaction force moment about the desired ZMP to coincide with the model manipulation floor reaction force moment or to become zero.
Subsequently, the gait generator 100 proceeds to S816 to subject the body horizontal acceleration determined in S814 to the second-order integration so as to calculate the body horizontal position at current time Tk. The calculation method is the same as that used in S314 of FIG. 18.
This completes the detailed description of the processing (the processing for generating provisional current time gaits) carried out by the gait generator 100 in S702 of FIG. 20.
After executing the processing in S702 as described above, the gait generator 100 carries out the processing in S704.
In S704, the gait generator 100 calculates a terminal divergent component qe1 (a divergent component qe1 at the end of a provisional current time gait) on the basis of body horizontal position/velocity (Xe, Vxe) at the end of the provisional current time gait generated in S702.
To be more specific, the gait generator 100 first determines the horizontal position/velocity (the horizontal position and the horizontal velocity) of the body mass point 24b of the inverted pendulum model in FIG. 9 on the basis of (Xe, Vxe) and the body posture (the reference body posture in the present embodiment) at the end of the provisional current time gait. Then, from the body mass point horizontal position/velocity, the terminal divergent component qe1 of the provisional current time gait is calculated according to the above expression 118, as with S222 of FIG. 17 described above. In this case, Γ−1 used to calculate qe1 is the same as that calculated by the processing in S222.
Subsequently, the gait generator 100 proceeds to S706 to calculate a terminal divergent component error errq (=qe1-q0′′), which is the difference between the terminal divergent component qe1 of the provisional current time gait determined as described above and the initial divergent component q0′′ determined in S224 of FIG. 17.
Further, the gait generator 100 proceeds to S708 to determine whether the terminal divergent component error errq determined as described above falls within a permissible range (a range in the vicinity of 0), that is, whether errq is zero or almost zero. More specifically, the determination in S708 is carried out on the terminal divergent component error errq in each axial direction of the X-axis direction and the Y-axis direction. If the terminal divergent component errors errq in both the X-axis direction and the Y-axis direction fall within the permissible range, then the determination result in S708 turns to be affirmative. If the terminal divergent component error errq in one of the axial directions does not fall within the permissible range, then the determination result in S708 turns to be negative.
If the determination result in S708 is negative, the gait generator 100 proceeds to S710 to generate a provisional current time gait up to ending time, as with the aforesaid S702, by using a desired ZMP trajectory obtained by correcting a present provisional desired ZMP trajectory by a correction amount of a trapezoidal pattern, applying a=Δa (Δa: a predetermined minute amount), as illustrated in FIG. 22. In other words, the gait generator 100 generates a provisional current time gait anew by using a desired ZMP trajectory obtained by correcting the provisional desired ZMP trajectory used for generating the provisional current time gait in S702. In this case, the current time gait parameters other than the desired ZMP are the same as those used in S702.
Here, referring to FIG. 22, the “a” mentioned above denotes the height of the correction amount of the trapezoidal pattern (hereinafter referred to as the ZMP correction amount in some cases) for correcting the provisional desired ZMP trajectory (to be added to the provisional desired ZMP trajectory) in order to cause the terminal divergent component of the provisional current time gait to coincide with the initial divergent component of the normal gait as much as possible (to consequently converge the body horizontal position/posture trajectory of the current time gait to the body horizontal position/posture trajectory of the normal gait).
In this case, according to the present embodiment, the provisional desired ZMP trajectory is corrected during the period in which substantially entire bottom surface of the supporting leg foot 22 is in contact with the ground (entire sole surface in contact with the ground period). Hence, the ZMP correction amount is set such that the ZMP correction amount is not zero (≠0) during the entire sole surface in contact with the ground period, while the ZMP correction amount is zero (=0) during a period other than the entire sole surface in contact with the ground period. Further, the time of breakpoints of the ZMP correction amounts of the aforesaid trapezoidal pattern is set according to the time of breakpoints of the provisional desired ZMP trajectory in the entire sole surface in contact with the ground period. In S710, a=Δa (Δa: a predetermined minute amount) applies in order to observe a change in the aforesaid terminal divergent component error errq when a present provisional desired ZMP trajectory has been corrected by a minute amount by the ZMP correction amount of the aforesaid trapezoidal pattern.
Supplementally, the aforesaid processing in S710 has been described, taking, as an example, the case where the position of the desired ZMP in the X-axis direction is corrected. In actuality, however, the position of the desired ZMP in the Y-axis direction is also corrected. As with the correction of the position in the X-axis direction, the correction of the position in the Y-axis direction is made such that the desired ZMP trajectory during the entire sole surface is in contact with the ground period is changed from the provisional desired ZMP trajectory according to the trapezoidal pattern. In this case, the aforesaid Δa may be set to the same value in each axial direction or may be set to values that are different from each other.
If correcting the desired ZMP trajectory in one of the axial directions of the X-axis direction and the Y-axis direction exerts no influences or sufficiently small influences on the terminal divergent component in the other axial direction, then the processing from S710 to S716, which will be discussed later, may be carried out in the X-axis direction and the Y-axis direction separately.
After generating the provisional current time gait in S710 as described above, the gait generator 100 proceeds to S712 to calculate a terminal divergent component qe2 in the provisional current time gait in the same manner as that in S704 on the basis of the body horizontal position/velocity (Xe2, Vxe2) at the end of the provisional current time gait determined in S710.
In the present embodiment, Δa has been set to a minute amount of a predetermined value in S710. Alternatively, however, Δa may be variably set such that Δa approaches zero as the terminal divergent component error errq is reduced by repetitive operation described below. In general, however, even when Δa is set to a constant, the terminal divergent component error errq can be set to fall within a permissible range by performing the repetitive calculation a few time.
Subsequently, the gait generator 100 proceeds to S714 and calculates a parameter sensitivity r (the ratio of a change in the terminal divergent component error relative to Δa) according to the expression in the flowchart. More specifically, the gait generator 100 calculates the parameter sensitivity r by dividing the difference between the terminal divergent component qe2 calculated in S712 and the terminal divergent component qe1 calculated in S704 (=qe2−qe1) by Δa. In this case, to be more specific, for example, the component of (qe2−qe1) in the X-axis direction is divided by Δa related to the ZMP correction amount in the X-axis direction thereby to calculate the parameter sensitivity r in the X-axis direction. Further, the component of (qe2−qe1) in the Y-axis direction is divided by Δa related to the ZMP correction amount in the Y-axis direction thereby to calculate the parameter sensitivity r in the Y-axis direction.
Subsequently, the gait generator 100 proceeds to S716 and sets, as the height “a” of the ZMP correction amount of the trapezoidal pattern, the value obtained by reversing the sign of the value determined by dividing the terminal divergent component error errq determined in S706 by the parameter sensitivity r determined in S714, i.e., a=−errq/r, and then determines anew, as the provisional desired ZMP, the desired ZMP obtained by correcting the provisional desired ZMP pattern on the basis of the ZMP correction amount, as illustrated in FIG. 22. In this case, the ZMP correction amount height “a” is calculated separately for the X-axis direction and the Y-axis direction, respectively.
If correcting the desired ZMP trajectory in one of the axial directions, namely, the X-axis direction and the Y-axis direction, exerts influences on the terminal divergent component in the other axial direction, then the influences are preferably taken into account in determining the height “a” of the ZMP correction amount in each axial direction.
Subsequently, the gait generator 100 carries out the processing from S702 again. At this time, as long as the determination result given in S708 is negative, the processing of S702 through S716 described above is repeated. If the determination result in S708 turns to be affirmative, then the gait generator 100 leaves the repetition loop (S700) and proceeds to S718.
By carrying out the loop processing of S702 through S716 described above, the ZMP correction amount (consequently the desired ZMP trajectory of the current time gait) which allows the terminal divergent component qe1 to agree or almost agree with the initial divergent component q0′′ of the normal gait is exploratorily determined.
In S718 following the loop processing, the gait generator 100 determines the present provisional desired ZMP trajectory (the provisional desired ZMP trajectory set immediately before leaving the repetition loop in S700) as the final desired ZMP trajectory of the current time gait, and determines the ZMP trajectory parameters based thereon. This terminates the processing in S028 of FIG. 10 (the processing for correcting the current time gait parameters).
In the present embodiment, the ZMP correction amount has been set to be the trapezoidal pattern. Alternatively, however, other patterns, such as a triangular pattern or a pattern having a continuously changing curvature, may be used.
Referring back to FIG. 10, after correcting the current time gait parameters in S028 as described above, the gait generator 100 proceeds to S030 to determine floor reaction force moment permissible range parameters that define the permissible range of a floor reaction force moment (more specifically, the horizontal component of a floor reaction force moment) about the desired ZMP at each time from the start to the end of the current time gait. The permissible range of the floor reaction force moment defined by the floor reaction force moment permissible range parameters is used as previously described in the compensating total floor reaction force moment distributor 110 and also used in the determination processing in S030, which will be discussed later.
The result obtained by dividing the floor reaction force moment by a floor reaction force vertical component corresponds to the amount of deviation of the ZMP (the central point of a floor reaction force) from a desired ZMP. Hence, the floor reaction force moment permissible range may be converted into a ZMP permissible range (floor reaction force central point permissible range) as the permissible range of the position of a ZMP (the floor reaction force central point), and the parameters defining the ZMP permissible range may be determined.
The floor reaction force moment permissible range determined in S030 means the permissible range of an actual floor reaction force moment about the desired ZMP controlled by the control processing (compliance control) by the aforesaid composite-compliance operation determiner 104 when used in the compensating total floor reaction force moment distributor 110. The floor reaction force moment permissible range will be described below.
The compliance control implemented by the processing carried out by the composite-compliance operation determiner 104 controls the position/posture of the foot 22 such that the floor reaction force moment generated about the desired ZMP will be the desired floor reaction force moment for compliance control. When the compliance control faithfully is implemented as desired, the actual floor reaction force central point will be a point, the position of which is deviated in the horizontal direction from the desired ZMP by a value obtained by dividing the desired floor reaction force moment by a floor reaction force vertical component. The actual floor reaction force central point cannot deviate from a ZMP-existable range indicated by a so-called supporting polygon (in a strict expression, the range in which the actual floor reaction force central point can exist). If the actual floor reaction force central point excessively approaches the boundary of the ZMP-existable range, then problems will be posed. For example, the proper ground contact feeling of the foot 22 deteriorates or the bottom surface of the foot 2 floats.
The floor reaction force moment permissible range is to impart restrictions to the floor reaction force moment for compliance control in order to prevent the aforesaid problems. For this reason, the floor reaction force moment permissible range is preferably determined such that the floor reaction force central point permissible range obtained by dividing the floor reaction force moment permissible range by a floor reaction force vertical component is included in the ZMP-existable range.
More specifically, the floor reaction force central point permissible range (ZMP permissible range) should be determined on the basis of the supporting polygon. In this case, the floor reaction force central point permissible range can be generally set to have a complicated shape. In the present embodiment, however, the floor reaction force central point permissible range is set to, for example, a region of a rectangular shape (a rectangular shape having sides parallel to the X-axis direction and the Y-axis direction) on a floor surface in order to simplify the calculation. In this case, the floor reaction force moment permissible range obtained by converting the floor reaction force central point permissible range into a floor reaction force moment is set independently for a component in the X-axis direction and a component in the Y-axis direction, respectively.
For example, if the supporting polygon and the desired ZMP are in the situation illustrated in FIG. 23, then the floor reaction force central point permissible range (ZMP permissible range) is set to be included in the supporting polygon, as illustrated. At the same time, the floor reaction force central point permissible range (ZMP permissible range) is set to include the desired ZMP.
The supporting polygon indicated in the form of a stippled region in FIG. 23 illustrates a supporting polygon of a walking gait (a supplemental description will be given later of the gait generation related to a walking gait) in a two-leg supporting period. This example schematically illustrates a state wherein the tiptoe of the right foot 22R is in contact with the ground, while the heel of the left foot 22L is in contact with the ground.
In the one-leg supporting period of a walking gait or the running gait in FIG. 6, the supporting polygon provides the ground contact surface (the surface of contact with a floor surface) of the supporting leg foot 22. In this case, a floor reaction force central point permissible range is set to include a desired ZMP and also to be included in the supporting polygon or to substantially match the supporting polygon. If the desired ZMP deviates from the supporting polygon or is excessively close to the boundary of the supporting polygon, then, temporarily, for example, an arbitrary region in the supporting polygon that does not include the desired ZMP or a point in the supporting polygon that is different from the desired ZMP (a region having a zero area) is set as the floor reaction force central point permissible range.
Further, in the floating period of the running gait in FIG. 6, the floor reaction force central point permissible range is set to be, for example, the region having zero width in both X-axis direction and the Y-axis direction, the center thereof being the desired ZMP. This means that the floor reaction force central point permissible range is set to the point of the desired ZMP itself, meaning that the region has a zero area.
When setting the floor reaction force central point permissible range as described above, the supporting polygon in the current time gait is calculated on the basis of the foot position/posture trajectory parameters of the current time gait parameters determined in S028 (or S026).
In the present embodiment, the range obtained by converting the floor reaction force central point permissible range set as described above to a floor reaction force moment is determined as the standard permissible range of floor reaction force moments. The standard permissible range is a permissible range based on an assumption that the floor in an environment in which the robot 1 travels is a standard floor (e.g., a floor having a flat surface with its frictional coefficient and hardness meeting predetermined requirements).
Further, according to the present embodiment, the gait generator 100 determines floor reaction force moment permissible range parameters by correcting, as necessary, the standard permissible range of floor reaction force moments according to the floor geometry information for generating gaits input from the floor geometry shaper 114.
To be more specific, in the case where the floor recognized from the input floor geometry information for generating gaits is not a floor with a flat surface, and the floor makes it difficult to change the expected landing position/posture of the free leg foot 22 in a current time gait or a next time gait from the position/posture specified by required parameters (e.g., a floor formed of scattered paving stones or the like), and if the actual posture of the robot 1 deviates from a desired posture, then the deviation of the posture of the actual robot 1 is preferably restrained by the desired floor reaction force moment for the compliance control, i.e., by holding the foot 22 of the actual robot 1, as much as possible. In this case, therefore, the gait generator 100 determines the floor reaction force moment permissible range parameters such that the floor reaction force moment permissible range is expanded further than the standard permissible range within an extent that the floor reaction force central point permissible range corresponding to the floor reaction force moment permissible range does not deviate from the aforesaid supporting polygon.
Further, in the case where, for example, the robot 1 is to go up or down a staircase, the free leg foot 22 is usually landed such that a portion near the heel or a portion near a tiptoe of the free leg foot 22 of the robot 1 extends beyond a step surface of the staircase. In this case, the area of the supporting polygon is smaller than that when the robot 1 travels on a standard floor. Hence, if the floor recognized on the basis of received floor geometry information for generating gaits (the floor on which the robot 1 is about to travel) is a staircase, then the gait generator 100 determines the floor reaction force moment permissible range parameters such that the floor reaction force moment permissible range is narrower than the standard permissible range.
Further, if, for the example, the hardness of the floor recognized on the basis of received floor geometry information for generating gaits is less than that of a standard floor, then it is difficult in the actual robot 1 to set a large desired floor reaction force moment for compliance control to be generated about a desired ZMP. In this case, therefore, the gait generator 100 determines the floor reaction force moment permissible range parameters such that the floor reaction force moment permissible range is narrower than the standard permissible range.
Thus, in S030, the floor reaction force moment permissible range or a floor reaction force central point permissible range corresponding thereto is determined such that it depends not only on a desired ZMP trajectory and a supporting polygon specified by foot position/posture trajectory parameters but also on a floor geometry, including the properties of a floor.
In the present embodiment, the standard permissible range of a floor reaction force moment has been corrected, as appropriate, according to a floor geometry. Alternatively, however, the floor reaction force central point permissible range set on the basis of a desired ZMP trajectory and a supporting polygon may be corrected according to a floor geometry, and the corrected floor reaction force central point permissible range may be converted to a floor reaction force moment permissible range.
After determining the floor reaction force central point permissible range in S030 as described above, the gait generator 100 proceeds to S031 to determine whether the desired ZMP trajectory specified by the ZMP trajectory parameters determined in S028 is a proper trajectory. In this case, according to the present embodiment, the gait generator 100 determines whether the desired ZMP trajectory is a proper trajectory by determining whether each instantaneous value (the instantaneous value at each predetermined notch time) of the desired ZMP trajectory specified by the ZMP trajectory parameters of a current time gait exists in the floor reaction force central point permissible range corresponding to the floor reaction force moment permissible range determined in the aforesaid S030.
More specifically, the gait generator 100 determines the floor reaction force central point permissible range corresponding to each instantaneous value of the desired ZMP on the basis of the floor reaction force moment permissible range.
The gait generator 100 then determines that the desired ZMP trajectory specified by the ZMP trajectory parameters of the current time gait is a proper trajectory if the desired ZMP at each time of the current time gait exists in the floor reaction force central point permissible range at that time.
If the desired ZMP at any time of the current time gait deviates from the floor reaction force central point permissible range at that time, then the gait generator 100 determines that the desired ZMP trajectory specified by the ZMP trajectory parameters of the current time gait is not a proper trajectory. The gait generator 100 assumes that each instantaneous value of the desired ZMP in a floating period in which both legs 2 and 2 of the robot 1 are not in contact with the ground always falls in the floor reaction force central point permissible range.
If the determination result in S031 is negative (if the desired ZMP trajectory is not a proper trajectory), then the gait generator 100 carries out the processing from S020 again. In this case, in S020, the gait generator 100, for example, changes the expected landing position/posture of the free leg foot 22 of the current time gait (consequently, the position/posture in the next time gait's supporting leg coordinate system) to position/posture shifted from current values (i.e., the expected landing position/posture determined by the processing in S020 at a control cycle immediately preceding the current control cycle). To be more accurate, the aforesaid expected landing position/posture to be changed means at least one of the expected landing position and the expected landing posture.
In this case, the change amount or amounts of the expected landing position/posture are determined by the aforesaid determination processing in S031 on the basis of the direction of deviation or the deviation amount of the desired ZMP deviating from the floor reaction force central point permissible range. The change amount or amounts are basically determined such that the desired ZMP will be included or will be easily included in a supporting polygon defined by the updated expected landing position/posture. In addition, the change amount or amounts are determined such that the free leg foot 22 will not come in contact with a stepped portion indicated by the floor geometry information for generating gaits (a stepped portion that has been shaped) in the foot position/posture trajectory of the free leg foot 22 of the current time gait defined on the basis of the updated expected landing position/posture.
Alternatively, the expected landing position/posture of the free leg foot 22 of the next time gait (consequently, the position/posture in the next but one time's gait supporting leg coordinate system) may be changed in addition to the expected landing position/posture of the free leg foot 22 of the current time gait. Furthermore, the expected landing time of the free leg foot 22 may be changed whenever the expected landing position/posture of the free leg foot 22 of the current time gait or the next time gait are changed.
Thus, after carrying out the processing in S020 again, the gait generator 100 carries out again the processing from S022 and after in the manner described above. In other words, the processing from S020 to S028 is repeated until the determination result in S030 changes to be affirmative.
Supplementally, the floor reaction force central point permissible range used in the determination processing in S031 does not have to be the same as the floor reaction force central point permissible range corresponding to the floor reaction force moment permissible range determined in S030 (specifically, the permissible range used in the processing by the compensating total floor reaction force moment distributor 110, which will be discussed later). For example, the floor reaction force central point permissible range used in the determination processing in S031 may be a range having a different area or boundary configuration from the area or boundary configuration of the floor reaction force central point permissible range corresponding to the floor reaction force moment permissible range determined in S030 (specifically, the permissible range used in the processing by the compensating total floor reaction force moment distributor 110, which will be discussed later).
Referring back to FIG. 10, if the determination result in S031 is affirmative or if the determination result in S016 is negative, the gait generator 100 proceeds to S032 to determine current time gait instantaneous values (the instantaneous values of the desired foot position/posture or the like of the current time gait at a present control cycle). In this S032, the current time gait instantaneous values are determined such that the model manipulation floor reaction force moment determined as previously described by the posture stabilization control calculator 112 is generated about a desired ZMP.
To be specific, gait instantaneous values are determined as illustrated by the flowchart of FIG. 24. The gait generator 100 first carries out the processing from S1000 to S1006 in the same manner as that for the processing from S806 to S812 of FIG. 21 (or from S306 to S312 of FIG. 18) thereby to calculate the instantaneous values of the desired floor reaction force vertical component, the desired ZMP, the desired foot position/posture, the desired body posture, the desired arm posture, and the desired body vertical position at current rime t (the present control cycle) of a current time gait.
These instantaneous values are calculated in the same manner as that of the processing from S806 to S812 of FIG. 21 (or from S306 to S312 of FIG. 18) except that the current time gait parameters that have been lastly corrected in S028 of FIG. 10 are used as the gait parameters.
Subsequently, the gait generator 100 proceeds to S1008 to determine the instantaneous values of the floor reaction force moment permissible range at the current time t of the current time gait on the basis of the floor reaction force moment permissible range parameters determined in S030 of FIG. 10. The instantaneous values of the floor reaction force moment permissible range are output from the gait generator 100 to the compensating total floor reaction force moment distributor 110 (refer to FIG. 3). Further, the model manipulation floor reaction force moment calculated according to the above expression 52 (the value at the current time t) in the distributor 110 is supplied to the gait generator 100.
Subsequently, the gait generator 100 proceeds to S1010 to determine the body horizontal acceleration at the current time t of the current time gait such that the model manipulation floor reaction force moment imparted from the compensating total floor reaction force moment distributor 110 is generated about the desired ZMP (such that the horizontal component of the moment generated about the desired ZMP by the resultant force of the inertial force of the robot 1 and the gravitational force is balanced with the model manipulation floor reaction force moment).
In other words, the body horizontal acceleration at the current time t of the current time gait is determined such that the moment generated about the desired ZMP by the resultant force of the inertial force of the robot 1 and the gravitational force agrees with the model manipulation floor reaction force moment with its sign reversed.
In this case, the body horizontal acceleration of the current time gait is calculated in the same manner as that of the processing in S814 of FIG. 21 by using, for example, the dynamic model (the inverted pendulum model) in FIG. 9.
To be more specific, at the current time t of the current time gait, the vertical position and the horizontal position of the body mass point 24b at the current time t are determined on the basis of the body vertical position, the body horizontal position at time (t-Δt), and the desired body posture at the current time t. Alternatively, the body horizontal position at the time t may be estimated in an interpolation manner on the basis of the time series of the body horizontal position up to the time (t-Δt) or the gait state at the time (t-Δt), and the estimated body horizontal position may be used in place of the body horizontal position at the time (t-Δt).
Further, the value obtained by subtracting the gravitational force (=mb*g) acting on the body mass point 24b from the floor reaction force vertical component at the current time t of the current time gait is divided by the mass mb of the body mass point 24b to determine the vertical acceleration of the body mass point 24b at the current time t.
Then, the vertical position, the horizontal position, and the vertical acceleration of the body mass point 24b, which have been determined as described above, are substituted into Zb, Xb, and d2Zb/dt2, respectively, of the above expression 04, and the horizontal position and the vertical position of the desired ZMP at the current time t are substituted into Xzmp and Zzmp, respectively, of expression 04. Further, an expression with Mzmp_y of the expression 04 coinciding with the model manipulation floor reaction force moment is solved on d2Xb/dt2, thereby calculating the body mass point horizontal acceleration d2Xb/dt2 at the current time t. Then, the body mass point horizontal acceleration d2Xb/dt2 is determined as the body horizontal acceleration at the current time t.
Alternatively, a more precise dynamic model may be used no exploratorily determine the body horizontal acceleration that causes the horizontal component of a floor reaction force moment about the desired ZMP to coincide with the model manipulation floor reaction force moment.
Subsequently, the gait generator 100 proceeds to S1012 to subject the body horizontal acceleration determined in S1010 as described above to the second-order integration so as to calculate the body horizontal position at the current time t. The calculating method is the same as that used in S314 of FIG. 18 (or S816 of FIG. 21). This completes the processing in S032 of FIG. 10.
Subsequently, the gait generator 100 proceeds to S034 to determine arm motions for cancelling a spin force (to zero or substantially zero the vertical component of the floor reaction force moment generated about the desired ZMP due to the motions of portions except for arms of the robot 1). To be more specific, the floor reaction force moment vertical component trajectory at the desired ZMP in the case where the arms are not swung (strictly speaking, each instantaneous value with a reversed sign of the vertical component trajectory of the moment acting on the desired ZMP due to the resultant force of the gravitational force and the inertial force of the robot when a gait is generated without arm swings) is determined.
In other words, the instantaneous value of the vertical component of the floor reaction force moment about the desired ZMP that balances with the instantaneous value of the motion (not including arm swinging motion) of the current time gait generated by the processing in S032 is determined. Then, the instantaneous value of the floor reaction force moment vertical component is divided by an equivalent inertial moment of an arm swinging motion so as to determine an angular acceleration of an arm swinging motion necessary to cancel the spin force. If an arm swing is excessively large, then the instantaneous value of the floor reaction force moment vertical component may be divided by a value that is larger than the equivalent inertial moment.
Subsequently, the gait generator 100 subjects the angular acceleration to the second-order integration, then sets the angle obtained by passing the integration result through a low-cut filter for preventing the integration value from becoming excessive as the arm swing motion angle. However, in the arm swing motion, the right and left arms are longitudinally swung in opposite directions to avoid causing changes in the positions of the centers of gravity of both arms. Alternatively, an arm swing motion for cancelling the spin force may be generated also in the normal gait and the arm swing motion in the current time gait may be determined such that the connection thereof to the one in the normal gait is ensured.
Subsequently, the gait generator 100 proceeds to S036 to add the control cycle Δt to the time t and carries out the processing from S014 again.
Thus, the instantaneous values of the current time gait are generated in a time series manner.
In this case, the trajectory (time series) of the desired motion of the current time gait of the robot 1 (the desired foot positions/postures, the desired body position/posture, and the desired arm postures) is determined such that the desired floor reaction force vertical component trajectory defined by the desired floor reaction force vertical component parameters (the parameters determined in S606 of FIG. 19) is satisfied (such that the total sum of the vertical inertial force of the overall center of gravity of the robot 1 and the gravitational force acting on the overall center of gravity balances out a desired floor reaction force vertical component).
Further, the trajectory of the desired motion of the current time gait is determined with another requirement that the trajectory is converged (gradually approximated) to the motion trajectory of a normal gait as a virtual normative motion in the future. More specifically, the trajectory of motion of the current time gait is determined such that the divergent component at the end of the current time gait agrees with the divergent component at the beginning of the normal gait.
Further, using the current time gait parameters determined as described above, the desired motion of the current time gait is determined such that the model manipulation floor reaction force moment will be additionally generated about the desired ZMP in the dynamic model (the inverted pendulum model in the present embodiment) indicating the relationship between a motion of the robot 1 and a floor reaction force.
In the present embodiment, when determining the foot trajectory parameter among the current time gait parameters, the gait generator 100 determines the foot trajectory parameter by reflecting the floor geometry information for generating gaits output from the floor geometry shaper 114 rather than actual floor geometry information. More specifically, the foot trajectory parameter is determined such that the free leg foot 22 will not come in contact with the stepped portion DF, which is an object to be processed and which is formed by shaping a rising surface in the position/posture trajectory of the free leg foot 22 specified by the foot trajectory parameter. Thus, the expected landing position/posture of the free leg foot 22 are set such that the foot 22 will not approach too close to a stepped portion (the stepped portion with which the free leg foot 22 should not come in contact) of an actual floor surface.
Then, the gait generator 100 determines whether the foot trajectory parameter is proper for each control cycle, and corrects the foot trajectory parameter accordingly, as necessary. To be more specific, the gait generator 100 carries out the determination processing in S101 of FIG. 12 at each control cycle. At this time, if it is determined that the free leg foot 22 will come in contact in the future with the stepped portion DF (the stepped portion DF formed by shaping the rising surface) in the floor geometry information for generating the current time gait (at the current control cycle) input from the floor geometry shaper 114 in the position/posture trajectory of the free leg foot 22 specified by the foot trajectory parameter, then the gait generator 100 corrects the foot trajectory parameter to avoid the contact.
For example, if the actual motion trajectory of the free leg foot 22 (a relative motion trajectory with respect to an actual floor surface) deviates from an original motion trajectory, i.e., a motion trajectory expected at a previous control cycle, due to a slippage or the like of the supporting leg foot 22 while the free leg foot 22 is moving, and this is expected to cause the free leg foot 22 to come in contact with the stepped portion DF in the floor geometry information for generating gaits by the time the free leg foot 22 lands, then the foot trajectory parameter will be corrected to avoid the contact.
Here, the deviation of the actual motion trajectory (the relative motion trajectory with respect to an actual floor surface) of the free leg foot 22 does not usually develop into a significant deviation in a short time, such as in one control cycle. In addition, the rising surface of the stepped portion DF in the floor geometry information for generating gaits is shaped into a gentle slope surface. Therefore, even if the actual motion trajectory of the free leg foot 22 deviates due to a slippage or the like of the supporting leg foot 22, this will usually cause only a very small change in the geometry of the stepped portion DF, which is indicated by the floor geometry information for generating gaits, on the longitudinal plane which includes the motion trajectory.
Therefore, when a foot trajectory parameter is to be corrected, the correction will be relatively small. This means that the foot trajectory parameter can be updated to avoid the contact between the free leg foot 22 and the stepped portion DF without causing a sudden change in the motion of the robot 1.
As a result, according to the present embodiment, a desired motion of a gait that allows the continued motion of the robot 1 to be secured can be generated with high reliability without causing the free leg foot 22 of the robot 1 to come in contact with a stepped portion on a floor.
Here, a supplemental description will be given of the correspondence relationship between the present embodiment described above and the present invention.
In the present embodiment, the processing by the gait generator 100 (the processing illustrated by the flowchart of FIG. 10) implements the desired motion determining unit in the present invention. In this case, the motion of a desired gait (the desired foot position/posture, the desired body position/posture, and the desired arm posture) sequentially output from the gait generator 100, i.e., the motion of the desired gait determined in S032 of FIG. 10 corresponds to the desired motion in the present invention.
Further, the processing from S020 to S026 of FIG. 10 carried out at each control cycle by the gait generator 100 implements the leg motion parameter updating unit in the present invention. In this case, the next time's gait supporting leg coordinate system (or the expected landing position/posture of the free leg foot 22 of the current time gait) and the next but one time's gait supporting leg coordinate system (or the expected landing position/posture of the free leg foot 22 of the next time gait) determined first in S020 at each control cycle correspond to the requirements related to a travel route of the robot in the present invention. The foot trajectory parameter determined lastly in S026 (S600 in FIG. 19) corresponds to the leg motion parameter in the present invention. The determination processing in S101 of FIG. 12 carried out in S022 implements the unit which determines whether a leg motion is appropriate in the present invention.
Further, the processing carried out by the composite-compliance operation determiner 104, the robot geometric model 102, and the joint displacement controller 108 implements the operation control unit in the present invention. The processing carried out by the composite-compliance operation determiner 104 imparts the compliance function to the operation control unit.
Further, the processing carried out by the floor geometry shaper 114 implements the floor geometry information output unit in the present invention. In this case, the floor geometry information for generating gaits output by the floor geometry shaper 114 corresponds to the floor geometry information in the present invention. The stepped portion DF (the stepped portion which is an object to be processed) included in the floor geometry information for generating gaits corresponds to the stepped portion in the present invention.
[Modifications]
The following will describe some modifications of the embodiments described above.
In the aforesaid embodiments, the floor geometry shaper 114 has generated the floor geometry information for generating gaits in real time concurrently with the operation control over the robot 1. However, as an alternative, for example, the floor geometry information for generating gaits may be prepared and stored beforehand in a memory of the robot 1 or a floor geometry information output unit composed of an external server before the robot 1 starts to travel. Then, the stored floor geometry information for generating gaits may be output from the floor geometry information output unit to the gait generator 100 while the robot 1 is in motion.
Further, the aforesaid embodiments have given descriptions, taking the desired gait for the robot 1 to run as an example. Alternatively, however, a desired gait for the robot 1 to walk may be generated. In this case, for example, a trajectory set according to the line graph pattern as illustrated in FIG. 25 may be used as a floor reaction force vertical component trajectory (a trajectory for one step) to generate the desired gait by the same technique as that in the aforesaid embodiments. In the example of FIG. 25, the floor reaction force vertical component trajectory is set to have a trapezoidal shape bulging in the direction in which the floor reaction force vertical component increases (bulging upward) in a two-leg supporting period, while it is set to have a trapezoidal shape bulging in the direction in which the floor reaction force vertical component decreases (bulging downward) in a one-leg supporting period.
However, the floor reaction force vertical component trajectory in a desired gait for the robot 1 to walk may be a trajectory in which the value of the floor reaction force vertical component is maintained substantially at a constant value.
In the aforesaid embodiments, in order to make the descriptions easy to understand, the gait generator 100 has generated desired gaits by using the relatively simple dynamic model illustrated in FIG. 9. Alternatively, however, the desired gaits may be generated by using a complicated dynamic model with a higher dynamic accuracy. For example, the dynamic model (the dynamic model provided with a flywheel and a plurality of mass points) presented in an embodiment of Japanese Patent No. 4246638 by the applicant of the present application may be used to generate the desired gaits. Further alternatively, a multi-mass-point model provided with a mass point in each link of the robot 1 may be used to generate the desired gaits.
When generating the desired gaits by using these dynamic models, the permissible range limiting the frictional force between the feet 22 of the robot 1 and a floor surface may be variably set according to the timing of a gait or a floor condition, and a desired gait may be generated with a requirement that the frictional force generated according to the inertial force of the robot 1 falls within the permissible range. The technique for generating such a desired gait may be, for example, the technique proposed by the applicant of the present application in an embodiment of the aforesaid Japanese Patent No. 4246638.
In the aforesaid embodiments, the manipulated variable of the dimension of the floor reaction force moment about a desired ZMP (a model manipulation floor reaction force moment and a desired floor reaction force moment for compliance control) has been used as the feedback manipulated variable (additional external force) for converging the body posture angle error Δ0 to zero. Alternatively, however, another type of manipulated variable may be used, e.g., the correction amount of a desired ZMP, which allows the body posture angle error Δ0 to be manipulated.
In the aforesaid embodiments, the divergent component q(k) has been defined according to the aforesaid expression 118. Alternatively, however, the divergent component may be defined in a simplified manner as with the one in Japanese Patent No. 3726081. More specifically, the divergent component q(k) may be defined as follows.

q(k)=Horizontal position of body mass point+Horizontal velocity of body mass point/ωa 

where ωa: specified value set beforehand
Then, the initial divergent component of a normal gait and the terminal divergent component of a current time gait may be calculated according to the above definition.

## Claims

1. A control device for a legged mobile robot that determines a desired motion of the legged mobile robot, which travels by moving a plurality of legs extended from a base body, thereby controlling motion of the robot so as to cause an actual motion of the robot to follow the determined desired motion, the control device comprising:
a desired motion determining unit which determines a leg motion parameter specifying a motion trajectory of a distal end of a leg of the robot on the basis of at least information on a floor geometry of an environment in which the robot travels and a requirement related to a travel route of the robot, thereby sequentially determining the desired motion having the motion trajectory of the distal end of the leg specified by the leg motion parameter;
a motion control unit which controls the motion of the robot so as to cause the actual motion of the robot to follow the determined desired motion; and
a floor geometry information output unit which outputs the floor geometry information to the desired motion determining unit,
wherein, among the floor geometry information output by the floor geometry information output unit to the desired motion determining unit, at least the floor geometry information on a stepped portion, the contact with which a leg of the robot should avoid and which is a predetermined type of stepped portion existing around the travel route of the robot and having an actual rising surface between a lower step surface and an upper step surface, is floor geometry information in which a rising surface indicated by the floor geometry information between the lower step surface and the upper step surface is shaped to have a gentler slope surface than the actual rising surface.

2. A control device for a legged mobile robot according to claim 1,
wherein the stepped portion of the predetermined type is a stepped portion in which a tilt angle of at least the actual rising surface thereof on an acute angle side relative to a horizontal surface is an angle closer to 90° than a predetermined angle.

3. The control device for a legged mobile robot according to claim 1,
wherein the desired motion determining unit comprises:
a proper leg motion determining unit which sequentially determines whether there will be contact between the distal end of a free leg and a stepped portion of the predetermined type by the time the free leg lands on the basis of the floor geometry information output from the floor geometry information output unit and a latest leg motion parameter that has been determined in a case where it is assumed that an actual motion of the distal end of the free leg of the robot were continued after a current time according to at least the motion trajectory specified by the determined latest leg motion parameter; and
a leg motion parameter updating unit which updates the leg motion parameter such that the contact will be avoided in the case where the determination result is affirmative.

4. A control device for a legged mobile robot that determines a desired motion of a legged mobile robot, which travels by moving a plurality of legs extended from a base body, thereby controlling the motion of the robot so as to cause an actual motion of the robot to follow the determined desired motion, the control device comprising:
a desired motion determining unit which determines a leg motion parameter specifying a motion trajectory of a distal end of a leg of the robot on the basis of at least information on a floor geometry of an environment in which the robot travels and a requirement related to a travel route of the robot, thereby sequentially determining the desired motion having the motion of the distal end of the leg specified by the leg motion parameter;
a motion control unit which controls the motion of the robot so as to cause the actual motion of the robot to follow the determined desired motion; and
a floor geometry information output unit which outputs the floor geometry information to the desired motion determining unit,
wherein, among the floor geometry information output by the floor geometry information output unit to the desired motion determining unit, at least the floor geometry information on a stepped portion, the contact with which a leg of the robot should avoid and which is a predetermined type of stepped portion existing around the travel route of the robot is the information on a floor geometry in which the rising surface between a lower step surface and an upper step surface of the stepped portion indicated by the floor geometry information has been shaped to have a gentler slope surface than an actual rising surface,
wherein the desired motion determining unit comprises:
a proper leg motion determining unit which sequentially determines whether there will be contact between the distal end of a free leg and a stepped portion of the predetermined type by the time the free leg lands on the basis of the floor geometry information output from the floor geometry information output unit and a latest leg motion parameter that has been determined in a case where it is assumed that an actual motion of the distal end of the free leg of the robot were continued after a current time according to at least the motion trajectory specified by the determined latest leg motion parameter; and
a leg motion parameter updating unit which updates the leg motion parameter such that the contact will be avoided in the case where the determination result is affirmative, and
wherein the leg motion parameter updating unit updates the leg motion parameter such that the landing position of the distal end of the free leg in the future is closer to the landing position immediately before the distal end of the free leg leaves a floor than the landing position of the distal end of the free leg in the future specified by the leg motion parameter before updating in the case where the height of the distal end of the free leg in the motion trajectory is set to be greater than the height specified by the leg motion parameter before updating in order to avoid the contact.

5. The control device for a legged mobile robot according to claim 1, wherein the rising surface shaped to have a gentler slope surface than the actual rising surface of the stepped portion, has a greater length than the actual rising surface when measured between the lower step surface and the upper step surface.

6. The control device for a legged mobile robot according to claim 1, wherein the rising surface indicated by the floor geometry information is shaped to have the gentler slope surface than the actual rising surface by changing actual floor geometry information on the stepped portion, including actual floor geometry information on the actual rising surface, the lower step surface, and the upper step surface of the stepped portion.

7. The control device for a legged mobile robot according to claim 2, wherein a tilt angle of the rising surface indicated by the floor geometry information on the acute angle side is less than the tilt angle of the actual rising surface on the acute angle.