Abstract:
In order to suppress fluctuations in specific components of posture angle in a target coordinate system while maintaining the position of the leading edge of the wrist, the velocity of movement of the leading edge of the wrist, and the permissible velocity of the shaft during velocity suppression, an articulated robot which moves while calculating the position in interpolated points on a teaching path, the posture and the angles in each axis is provided, wherein a judgment is made as to whether the velocity of the wrist shaft exceeds a permissible limit, and if the permissible limit is exceeded, a plurality of candidates for angle of the wrist shaft that maintain the velocity within permissible limits are calculated, and the candidate with the minimum fluctuation in the specific component of the posture angle of the weld line coordinate system is selected.

Description:
TECHNICAL FIELD 
     The present invention relates to a control unit, a control method, and a control program of an articulated robot and, in particular, to a technology for maintaining the speeds of drive shafts of wrist axes within an allowable range while maintaining the attitude of the wrist if the speeds of the drive shafts exceed the allowable range. 
     BACKGROUND ART 
     As illustrated in  FIG. 23 , a six-axis manipulator, which is a sort of an articulated robot, has a J1 axis, a J2 axis, and a J3 axis, which are joint axes that control an arm shaft mounted on a base. The J1 axis, the J2 axis, and the J3 axis are sequentially arranged from the base. In addition, the six-axis manipulator has a J4 axis, a J5 axis, and a J6 axis, which control wrist axes and are sequentially arranged from an arm portion to the top end of the wrist. In such a case, if joints angles θ 1  to θ 6  are given to the J1 axis to J6 axis, respectively, the XYZ coordinates of the position of an end effector (an effector; such as a welding device, attached to the top end of a robot arm) and the attitude angles of the end effector α, β, and γ (note that attitude angles α, β, and γ are in the form of Euler angles or the roll/pitch/yaw angles) can be obtained by calculating a solution to a forward kinematics problem. Conversely, if the XYZ coordinates of the position and the attitude angles α, β, and γ of the end effector are given, the joint angles θ 1  to θ 6  of the J1 axis to the J6 axis can be obtained by calculating a solution to an inverse kinematics problem. 
     As illustrated in  FIG. 24 , when the joint angle θ 5  of the J5 axis is substantially 0 degree and if the end effector is attempted to move at a constant speed, the joint angle θ 4  of the J4 axis and the joint angle θ 6  of the J6 axis rapidly change. Accordingly, the J4 axis and the J6 axis need to rotate at high speed. However, the speed of each of the joint shafts of the manipulator cannot exceed the upper limit. If the manipulator is forced to operate so that the speed exceeds its upper limit, the end effector may step off a predetermined path or the end effector may vibrate. As described above, even if the position and the attitude angle of the end effector of the articulated manipulator is slightly varied, a joint shaft that is required to rotate at a significantly high rotational speed may appear and, therefore, the articulated manipulator may stop. If such stoppage of the articulated manipulator occurs, it is difficult to maintain the speeds of the joint shafts and the accuracy of the path along which the end effector should move at the same time. Thus, the speed of each of the joint shafts may be decreased to lower than the rotational speed required for the joint shaft to maintain the accuracy of the path. Alternatively, a safety mechanism may be activated, stopping the operation of the manipulator. 
     Accordingly, PTLs 1 to 3 describe a method for operating an end effector while preventing abrupt change in the operations of the wrist shafts and maintaining the speed of each of the wrist shafts within a limited speed when the speed of one of the wrist shafts exceeds the limited speed. 
     CITATION LIST 
     Patent Literature 
     
         
         PTL 1: Japanese Unexamined Patent Application Publication No. 62-162109 
         PTL 2: Japanese Unexamined Patent Application Publication No. 6-324730 
         PTL 3: Japanese Unexamined Patent Application Publication No. 2003-300183 
       
    
     SUMMARY OF INVENTION 
     Technical Problem 
     However, it is widely known that when the speed of one of the joint shafts exceeds the allowable range and if the end effector is attempted to travel along a predetermined path while maintaining the speeds of the wrist shafts and operating the wrist shafts without abrupt change in the operation of each of the wrist shaft, the following three factors cannot be simultaneously satisfied: (1) the position, (2) the moving speed, and (3) the attitude angles. Accordingly, in widely used manipulators, the operation of the manipulator is controlled so that only one or two of the factors (1) to (3) are satisfied. 
     For example, PTLs 1 and 2 describe a method for maintaining (1) the position and (3) the attitude angles of an end effector. However, (2) the moving speed cannot be maintained and, thus, the moving speed is slowed down. Accordingly, if the end effector includes a welding device, the end effector moves along the working line for a period of time that is longer than the originally required period of time. Thus, the welding time is longer than that for another portion, and the strength of the weld portion may be decreased. In addition, since the moving speed is slowed down, a portion for which the welding time is increased may excessively bulge. Thus, the next manufacturing step (e.g., a step of welding a second layer) may be interfered by the excessive bulge. 
     In addition, PTL 3 describes a method for maintaining one of the moving speed and the position of an end effector. If the moving speed is maintained, the position cannot be maintained. Thus, if the end effector includes a welding device or a painting device, the end effector may step off a predetermined working line. As a result, welding or painting may not produce quality weld or quality paint. 
     Accordingly, it is an object of the present invention to provide a control unit, a control method, and a control program of an articulated robot capable of, when a wrist shaft needs to abruptly move so as to exceed a predetermined allowable range, maintaining the position of the top end of a wrist and the moving speed of the top end of the wrist, which are particularly required for a welding or painting operation, within the allowable range and reducing a variation in at least one particular component of attitude angles in a work coordinate system for the intended purpose. 
     Solution to Problem 
     To achieve the above-described object, the present invention is applied to a control unit of an articulated robot for controlling the articulated robot including a first articulated drive system having a working part that moves along a working line of a workpiece on a top end thereof and three drive shafts that are connected to the working part and that change the attitude of the working part and a second articulated drive system having at least three drive shafts that are connected to the first articulated drive system and that change the position of the first articulated drive system. The control unit includes the following means (11) to (16): 
     (11) interpolation data calculating means for calculating data describing the position and attitude of the working part at each of a plurality of interpolated points that lie on a previous teaching path connecting the work start point and attitude to the work end point and attitude of the working part in a base coordinate system of the articulated robot, 
     (12) angle calculating means for calculating the angles of all of the drive shafts in the first articulated drive system and the second articulated drive system, the angles representing the position and the attitude of the working part at each of the interpolated points by finding a solution to an inverse kinematics problem from the data calculated by the interpolation data calculating means, 
     (13) speed calculating means for calculating the speeds of two drive shafts located at both ends of the first articulated drive system when the attitude of the working part is moved to the next interpolated point on the basis of a difference between the angle of each of the drive shafts of the first articulated drive system at a current interpolated point and the angle at the next interpolated point calculated by the angle calculating means, 
     (14) attitude data converting means for converting the data calculated by the interpolation data calculating means into attitude data describing the attitude of the working part in a work coordinate system having an axis extending in a moving direction of the working part, an axis extending in a direction that is perpendicular to the axis in the moving direction, and an axis perpendicular to each of the two axes, 
     (15) recalculating means for, if the speed of at least one of the two drive shafts located at both the ends of the first articulated drive system and calculated by the speed calculating means is outside a predetermined allowable range, recalculating the angles of the drive shafts of the first articulated drive system so that the speeds of the two drive shafts located at both the ends of the first articulated drive system are within the allowable range without changing the moving speed of the working part and with reducing variation of one or two of particular components of the attitude data of the working part at the next interpolated point converted by the attitude data converting means and recalculating the angles of the drive shafts of the second articulated drive system on the basis of the calculated angles of the drive shafts of the first articulated drive system and the position of the working part calculated by the interpolation data calculating means, and 
     (16) drive instructing means for, if the speeds of the two drive shafts located at both ends of the first articulated drive system calculated by the speed calculating means are within the allowable range, driving the articulated robot on the basis of the angles of the drive shafts calculated by the angle calculating means and, if the speed of at least one of the two drive shafts located at both ends of the first articulated drive system calculated by the speed calculating means is outside the allowable range, driving the articulated robot on the basis of the angles of the drive shafts calculated by the recalculating means. 
     According to the present invention, even when the drive shaft of the first articulated drive system needs to abruptly change so as to exceed the allowable range, the position of the top end of the working part, the moving speed of the top end of the wrist, which are particularly required for a welding or painting operation, and the allowable range of the drive shafts of the first articulated drive system can be maintained. In addition, variation in at least one particular component of attitude angles in a work coordinate system corresponding to an intended purpose can be reduced. Furthermore, when a singularity region and a singularity avoidance path appearing in a path from the work start point to the work end point are calculated, an arithmetic unit (a CPU) that can handle significant load imposed in a pre-computation phase need to be provided and, thus, the cost increases. However, according to the present invention, drive can be controlled on the fly in accordance with a current state and the next state. Therefore, the peak processing load imposed on the arithmetic unit can be reduced and, thus, the cost can be reduced. 
     For example, the recalculating means can include angle candidate calculating means for calculating, on the basis of the angle of each of the drive shafts of the first articulated drive system at the current interpolated point, a plurality of candidates of the angle of each of the drive shafts so that the angle of the drive shaft references and follows the angle at the next interpolated point calculated by the angle calculating means and, in addition, the speeds of two drive shafts located at both ends of the first articulated drive system at the next interpolated point are within the allowable range, attitude data calculating means for calculating attitude data that defines the attitude of the working part at the next interpolated point in the work coordinate system when each of the candidates of the angle calculated by the angle candidate calculating means is employed, and angle selecting means for selecting, from among the plurality of attitude data calculated by the attitude data calculating means, attitude data having the smallest variation of the particular component for the attitude data of the working part at the next interpolated point converted by the attitude data converting means and selecting the angle corresponding to the attitude data as the angle of the drive shaft. 
     In this manner, when the position and attitude of the working part are moved, variation in the particular component appropriate for the intended work purpose of the working part can be reduced. 
     In addition, when the angle of the drive shaft of the first articulated drive system is defined as ±180°, the angle calculating means can calculate a solution to an inverse kinematics problem in which the sign of the angle of the drive shaft located in the middle of the first articulated drive system at the next interpolated point is the same as the sign of the angle of the drive shaft at the work start point. In this manner, control can be performed such that the angle of the drive shaft located in the middle of the first articulated drive system does not pass through 0°. Thus, a singularity can be avoided. 
     In addition, if the speeds of the two drive shafts located at both ends of the first articulated drive system calculated by the speed calculating means are within the allowable range, the angle calculating means can calculate a solution to an inverse kinematics problem in which the sign of the angle of the drive shaft located in the middle of the first articulated drive system at the next interpolated point is the same as the sign of the angle of the drive shaft at the work start point. However, if the speed of at least one of the two drive shafts located at both ends of the first articulated drive system calculated by the speed calculating means is outside the allowable range, the angle calculating means can calculate a solution to an inverse kinematics problem in which the sign of the angle of the drive shaft located in the middle of the first articulated drive system at the next interpolated point is opposite to the sign of the angle of the drive shaft at the work start point. 
     Furthermore, a configuration obtained by combining these configurations can be provided. That is, if the signs of the angles of the drive shaft located in the middle of the first articulated drive system at the work start point and at the work end point are the same, it is desirable that the angle calculating means calculate a solution to an inverse kinematics problem in which the sign of the angle of the drive shaft located in the middle of the first articulated drive system at the next interpolated point is the same as the sign of the angle of the drive shaft at the work start point. When the signs of the angles of the drive shaft located in the middle of the first articulated drive system at the work start point and the work end point are opposite to each other and if the speeds of the two drive shafts located at both ends of the first articulated drive system calculated by the speed calculating means are within the allowable range, it is desirable that the angle calculating means calculate a solution to an inverse kinematics problem in which the sign of the angle of the drive shaft located in the middle of the first articulated drive system at the next interpolated point is the same as the sign of the angle of the drive shaft at the work start point. If the speed of at least one of the two drive shafts located at both ends of the first articulated drive system calculated by the speed calculating means is outside the allowable range, it is desirable that the angle calculating means calculate a solution to an inverse kinematics problem in which the sign of the angle of the drive shaft located in the middle of the first articulated drive system at the next interpolated point is opposite to the sign of the angle of the drive shaft at the work start point. In this manner, the angle of the drive shaft located in the middle of the first articulated drive system at the work end point can be set as taught. 
     Still furthermore, the recalculating means can recalculate the angle of the drive shaft so that among the particular components of the attitude data of the working part converted by the attitude data converting means, as a particular component has a higher predetermined weight, an amount of reduction in variation of the particular component is higher. Accordingly, by appropriately assigning a weight, an amount of reduction in variation of the particular component can be controlled as needed. 
     In a particular configuration according to the present invention, the working part can be a torch. In addition, the attitude data can be expressed in the work coordinate system having an X-axis extending in a direction in which the working part moves, a Y-axis defined as a cross product of the X-axis and a direction of gravitational force, a Z-axis extending in a direction defined as a cross product of the X-axis and the Y-axis, a torch inclination angle defined as a rotation angle about the X-axis, a torch forward tilting angle defined as a rotation angle about the Y-axis, and a torch rotation angle defined as a rotation angle about the Z-axis, and the particular component can be one or two of the torch inclination angle, the torch forward tilting angle, and the torch rotation angle. As illustrated in  FIG. 25 , by expressing the attitude of the working part provided at the top end of the wrist in a weld line coordinate system Σline (the work coordinate system) having an X-axis extending in the direction in which the working part moves using the position of the top end of the wrist XYZ and the attitude of the top end of the wrist αβγ defined in an orthogonal coordinate system Σbase, the attitude of the working part can be expressed as inclination components about the axes, as illustrated in  FIGS. 26 to 28 . The converted rotation angles about the coordinate axes of the weld line coordinate system Σline are defined as the torch inclination angle Rx (the direction of the rotation angle about an Xline axis in a right screw direction is positive, as illustrated in  FIGS. 26 and 27 ), the torch forward tilting angle Ry (the direction of the rotation angle about a Yline axis in a right screw direction is positive, as illustrated in  FIGS. 26 and 28 ), and the torch rotation angle Rz (the direction of the rotation angle about a Zline axis in a right screw direction is positive). 
     At that time, if the working part is a single torch having, at the top end thereof one point of operation having an effect of work on the workpiece, the particular component can be each of the torch inclination angle and the torch forward tilting angle. In this manner, variation of each of the torch inclination angle and the torch forward tilting angle that are important for the operation of a single torch having one point of operation can be reduced. 
     In contrast, if the working part is a tandem torch having, at the top end thereof, two points of operation each having an effect of work on the workpiece, the particular component can be each of the torch inclination angle and the torch rotation angle. In this manner, variation of each of the torch inclination angle and the torch rotation angle that are important for the operation of a tandem torch having two points of operation can be reduced. 
     Furthermore, after the speed allowance determining means determines that a drive shaft outside the allowable range is present, the drive instructing means can instruct drive of the articulated robot on the basis of the angles of the drive shafts calculated by the recalculating means. Subsequently, if a difference between the angle of the first articulated drive system calculated by the angle calculating means and the angle of the first articulated drive system calculated by the recalculating means is less than or equal to a predetermined value, the drive instructing means can instruct drive of the articulated robot on the basis of the angles of the drive shafts calculated by the angle calculating means instead of the angles of the drive shafts calculated by the recalculating means. 
     At that time, upon switching from drive control of the articulated robot based on the angles of the drive shafts calculated by the recalculating means to drive control of the articulated robot based on the angles of the drive shafts calculated by the angle calculating means, the drive instructing means can gradually vary each of the angles of the drive shafts within a predetermined fluctuation range. In this manner, vibration of the working line along which a workpiece moves can be prevented and, therefore, movement that does not track the working line can be prevented. For example, the angle may be an intermediate angle between the angle calculated by the recalculating means and the angle calculated by the angle calculating means through drive control of the articulated robot. 
     Furthermore, the speed calculating means can calculate acceleration instead of speed, and the recalculating means and the drive instructing means can make determination on the basis of the acceleration instead of the speed. 
     It should be noted that the present invention can be considered as an invention of a method for controlling an articulated robot that executes the steps performed in the control unit of the articulated robot or an invention of a control program that causes a computer to execute the steps. 
     Advantageous Effects of Invention 
     According to the present invention, even when a slight motion of the top end of the wrist causes abrupt change in the axis of the wrist to a value outside a predetermined allowable amount, the position of the top end of the wrist that is particularly important for a welding or painting operation, the moving speed of the top end of the wrist, and the allowable speed of the axis of the wrist can be maintained. In addition, a variation of at least one of particular components of the attitude angle of the work coordinate system for an intended purpose can be reduced. In addition, when a singularity region and a singularity avoidance path appearing in a path from the work start point to the work end point are calculated, an arithmetic unit (a CPU) that can handle significant load imposed in a pre-computation phase need to be provided and, thus, the cost increases. However, according to the present invention, drive can be controlled on the fly in accordance with the current state and the next state. Therefore, the peak processing load imposed on the arithmetic unit can be reduced and, thus, the cost can be reduced. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a block diagram of a schematic configuration of an articulated robot X controlled using an example of an articulated robot control method according to an embodiment of the present invention. 
         FIG. 2  is a flowchart illustrating an example of an overall control process of the articulated robot control method. 
         FIG. 3  is a flowchart of a speed/angle calculating process for each of rotation shafts at an interpolated point. 
         FIG. 4  is a flowchart illustrating an example of a speed reduction necessity determination process. 
         FIG. 5  is a flowchart of an example of a speed reduction process. 
         FIG. 6  is a flowchart of an example of a return process from the speed reduction process. 
         FIG. 7  illustrates an example of a path of interpolated points. 
         FIG. 8(A)  illustrates an example of variations of the angle of a J6 axis in an original path and in an exception path; and  FIG. 8(B)  illustrates an example of an interpolated point in the original path and an interpolated point in the exception path. 
         FIG. 9  is a diagram illustrating an example of a variation of the angle of a first joint drive shaft in a path that avoids a singularity. 
         FIG. 10  illustrates an example of a variation of the speed of a J4 axis. 
         FIG. 11  illustrates an example of a variation of each of the attitude angles in a welding line coordinate system during the same-speed operation. 
         FIG. 12  illustrates an example of a variation of each of the attitude angles in a welding line coordinate system according to the control method of the present invention. 
         FIG. 13  illustrates another example of the second joint drive shaft. 
         FIG. 14  is a flowchart of another example of the overall control process of the articulated robot control method. 
         FIG. 15  is a diagram illustrating an example of a variation of the angle of the first joint drive shaft in a path that passes through a singularity. 
         FIG. 16  is a diagram illustrating an example of a variation of the angle of the first joint drive shaft when the control method according to a first embodiment is employed. 
         FIG. 17  illustrates an example of a variation of each of attitude angles in the welding line coordinate system during the same-speed operation. 
         FIG. 18  illustrates an example of a variation of each of attitude angles in the welding line coordinate system when the control method according to a first embodiment is employed. 
         FIG. 19  is a flowchart illustrating another example of the overall control process of the articulated robot control method. 
         FIG. 20  illustrates an example of an end effector having two points of operation according to a third embodiment. 
         FIG. 21  illustrates an example of a variation of each of the attitude angles of two points of operation of the end effector of the articulated robot in the welding line coordinate system in a path that avoids the singularity. 
         FIG. 22  is a block diagram of the schematic configuration of an articulated robot X 2  controlled using an example of an articulated robot control method according to a fourth embodiment. 
         FIG. 23  illustrates a schematic configuration of a widely used 6-axis manipulator. 
         FIG. 24  is a diagram illustrating an example of a variation of the angle of a first joint drive shaft in a path that passes through a singularity in a widely used 6-axis manipulator. 
         FIG. 25  illustrates an example of conversion from a coordinate system defining the position and attitude of an end effector of a widely used 6-axis manipulator into a welding line coordinate system. 
         FIG. 26  illustrates an example of an inclination component of each of the axes in the welding line coordinate system. 
         FIG. 27  illustrates an example of a torch inclination angle in the welding line coordinate system. 
         FIG. 28  illustrates an example of a torch forward tilting angle and a torch rotation angle in the welding line coordinate system. 
         FIG. 29  is a block diagram of a schematic configuration of a computer system Y according to a fifth embodiment. 
         FIG. 30  is a diagram illustrating an apparatus for announcing that a singularity is being avoided. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     For ease of understanding of the present invention, embodiments of the present invention are described below with reference to the accompanying drawings. It should be appreciated that the following embodiments are only specific examples of the present invention, and are not intended to limit the technical scope of the invention in any way. 
     The configuration of an articulated robot X according to an embodiment of the present invention is described first with reference to a block diagram illustrated in  FIG. 1 . 
     The articulated robot X includes a control unit  10 , an operation unit  21 , and a manipulator body  30 . Note that although, in addition to the components illustrated in  FIG. 1 , the articulated robot X includes other components that a widely used articulated robot includes, these components are not illustrated in  FIG. 1 . The control unit  10  includes a main controller  11 , a storage unit  12 , and a drive instructing unit  13 . The control unit  10  is an example of a control unit of the articulated robot according to the present invention. 
     The manipulator body  30  includes a second articulated drive system having a J1 axis  31 , a J2 axis  32 , and a J3 axis  33 , a first articulated drive system having a J4 axis  34 , a J5 axis  35 , and a J6 axis  36 , and an end effector  39 . The second articulated drive system corresponds to a human arm, and the first articulated drive system corresponds to a human wrist. The end effector  39  has an effect on a workpiece. The manipulator body  30  is a robot that is driven in accordance with operation information and that works in the same manner as the upper arm of a human does. Note that the manipulator body  30  is an example of an articulated robot. 
     The J1 axis  31  to the J6 axis  36  are formed from, for example, electric motors. The J1 axis  31  to the J6 axis  36  are rotatingly driven in positive and negative direction in accordance with an instruction received from the drive instructing unit  13 . By rotatingly driving the plurality of shafts in a cooperative manner, the motion of the human wrist and arm can be carried out. In particular, the second articulated drive system can freely produce the position (X, Y, Z) of the end effector  39  in a base coordinate system Σbase of the articulated robot regardless of the operations of the drive shafts of the first articulated drive system. 
     The end effector  39  is an effector attached to the top end of the manipulator body  30  (the top end of the J6 axis  36 ). Examples of the end effector  39  include a welding device (a torch), a painting device, a tool, a grabber, and a sensor that operate using a single point of operation. Note that the end effector  39  is an example of a working part. 
     In addition, a torch having a single point of operation is referred to as a “single torch”. 
     The operation unit  21  includes, for example, a sheet key and an operation button, and an operation lever operated by a user. The operation unit  21  serves as an input interface that receives an operational input from the user. For example, the operation unit  21  receives the position and attitude of the end effector  39  when the operation starts, the position and attitude of the end effector  39  when the operation ends, an operation path from the work start point and the work end point, an operation time, weight information used for reducing a variation in each of the components of the attitude angle of the end effector  39  in a desired weld line coordinate system Σline (an operation coordinate system), and a program including such information. Thereafter, the operation unit  21  outputs such received information to the control unit  10 . That is, the operation unit  21  is means for teaching the work start point and attitude and the work end point and attitude of the end effector  39 . In addition, the operation unit  21  is means for setting the weight information. 
     The storage unit  12  is formed from, for example, a hard disk or a volatile memory, such as a DRAM. The storage unit  12  stores, for example, the work start point and attitude and the work end point and attitude of the end effector  39 , an operation path from the work start point and attitude of the end effector  39  and the work end point and attitude, an operation time, the weight information used for reducing a variation in each of the components of the attitude angle of the end effector  39 , and the angles and speeds (and the accelerations in some cases) of the J1 axis  31  to the J6 axis  36  at interpolated points calculated by the main controller  11  (for a path that passes through a singularity and a path that avoids a singularity) (note that the main controller  11  is described in more detail below). 
     In response to a control instruction received from the main controller  11 , the drive instructing unit  13  reads the angle information or the speed information on the J1 axis  31  to the J6 axis  36  at every sampling period so as to move the end effector  39  to the next interpolated point stored in the storage unit  12  (one of the path that passes through a singularity and the path that avoids a singularity) and outputs the angle information or the speed information to the manipulator body  30 . Note that the main controller  11  and the drive instructing unit  13  are an example of drive instructing means for performing a drive instruction step. 
     The main controller  11  includes a CPU and a ROM. The CPU is calculating means for performing various control of the articulated robot X and arithmetic calculation. The ROM is a memory for storing, for example, a control program and a computing program executed by the CPU and data that are to be referenced by the CPU when the CPU executes the programs. 
     An example of a procedure for operating the manipulator body  30  using mainly the main controller  11  of the articulated robot X is described next with reference to flowcharts illustrated in  FIGS. 2 to 6 . Note that “S 11 ”, “S 12 ”, . . . are reference symbols indicating the procedure (steps). 
     A difference between widely used control of the manipulator body  30  and the control of the articulated robot X according to an embodiment of the present invention is described first with reference to  FIG. 2 . 
     In widely used control of the manipulator body  30 , as described below, a teaching step (step S 11 ) is performed in order to teach an operation trajectory to the main controller  11 . In addition, a step of calculating and storing the angle of each of the drive shafts in order to operate the manipulator body  30  so that the manipulator body  30  has the position and attitude at an interpolated point in the taught operation trajectory (step S 12 ) is performed. Thereafter, a step of reading the calculated angles and instructing the performance of an operation (step S 14 ) and a step of determining whether the manipulator body  30  has reached the work end point and attitude (step S 15 ) are performed in order to operate the manipulator body  30  from the position and attitude at the current interpolated point to the position and attitude at the next interpolated point. Thereafter, by repeating steps S 12 , S 14 , and S 15  at predetermined sampling periods, the manipulator body  30  is operated from the work start point and attitude to the work end point and attitude along the operation trajectory. Furthermore, by moving the end effector  39  of the manipulator body  30  at a predetermined constant speed, the main controller  11  performs the operation of the end effector  39 . Note that when the end effector  39  is moved at a constant speed and if the J5 axis  35  of the first articulated drive system passes through the vicinity of 0° (a singularity), the speed of the J4 axis  34  or the J6 axis  36  may exceed a predetermined allowable range. 
     Thus, in addition to the above-described steps required for widely used control of a manipulator body  30 , the control of the articulated robot X according to the present embodiment includes a step of determining whether the speed of at least one of the J4 axis  34  and the J6 axis  36  of the first articulated drive system exceeds the allowable range and, thus, a speed reduction process is required (step S 13 ) and a speed reduction step of if the speed reduction process is required (YES in step S 13 ), recalculating and restoring the angle of each of the drive shafts in order to operate the manipulator body  30  at an interpolated point in an operation trajectory that avoids a singularity (step S 20 ). In this manner, the manipulator body  30  can be operated from the position and attitude at the current interpolated point to the recalculated position and attitude at the next interpolated point while avoiding a singularity. 
     The overall control process of the articulated robot X performed by the main controller  11  is described next with reference to  FIG. 2 . Detailed description of each of the processes is subsequently made. 
     First, a user teaches the operation trajectory of the robot to the articulated robot X through the operation unit  21  in a point-to-point manner. That is, the user moves the end effector  39  to each of the teaching points using the operation unit  21  and causes the articulated robot X to store the operation positions and attitudes of the end effector  39  in the storage unit  12  of the control unit  10  (step S 11 ). Note that step S 11  is an example of the teaching step. 
     The main controller  11  divides a section between any adjacent two of the above-described teaching points by a predetermined sampling period (e.g., 1/16 second or 1/32 second) to obtain interpolated points by interpolation. Thereafter, the main controller  11  calculates the angles of the J1 axis  31  to the J6 axis  36  and the speeds (and the acceleration in some cases) of the J4 axis  34  to the J6 axis  36  of the first articulated drive system for moving the end effector  39  to the next interpolated point. Thereafter, the main controller  11  stores the calculated angles and speeds in the storage unit  12  (step S 12 ). At that time, each of the angles of the J1 axis  31  to the J6 axis  36  is expressed as ±180°. However, the expression of the angle is not limited to ±180°. For example, the angle may be in the range from 0° to 360°. Note that step S 12  is described in more detail below. 
     Subsequently, the main controller  11  determines whether the speed or the acceleration of one of or both of the J4 axis  34  and the J6 axis  36  of the first articulated drive system calculated in step S 12  for moving the end effector  39  to the next interpolated point is within or outside the allowable range (hereinafter referred to as “necessity/unnecessity of the speed reduction process”) or whether one or both of the J4 axis  34  and the J6 axis  36  are being subjected to an avoidance process (hereinafter referred to as a “speed reduction process”) after it is determined that one of the drive shafts has already been outside the allowable range (step S 13 ). Note that step S 13  is described in more detail below. 
     If it is determined that the speed reduction process is necessary or the speed reduction process is currently being performed (YES in step S 13 ), the main controller  11  recalculates the angle of one or both of the J4 axis  34  and the J6 axis  36  so that the speed or the acceleration is within the allowable range by reducing an amount of reduction in one or two of the components of the attitude data of the end effector  39  at the next interpolated point calculated in step S 12  without changing the moving speed of the end effector  39 . Thereafter, the main controller  11  recalculates the angles of the other shafts corresponding to the above-described recalculated angle and stores the recalculated angles in the storage unit  12 . In this manner, the main controller  11  performs the speed reduction process (step S 20 ). Note that in the above description of step S 20 , the speed or acceleration of each of the shafts is used for determining whether the speed reduction process is necessary or not. In the following specific description of step S 20 , only the speed is used for the determination as an example. 
     However, if it is determined that the speed reduction process is unnecessary and the speed reduction process is not currently being performed (No in step S 13 ) or if the speed reduction process is performed (step S 20 ), the drive instructing unit  13  reads, from the storage unit  12 , the angles of the J1 axis  31  to the J6 axis  36  for moving the end effector  39  to the next interpolated point in response to an instruction from the main controller  11  and outputs the angles to actuators of the drive shafts in the manipulator body  30  (step S 14 ). At that time, if it is determined that the speed reduction process is unnecessary and the speed reduction process is not currently being performed, the manipulator body  30  is controlled on the basis of the angles of the J1 axis  31  to the J6 axis  36  calculated in step S 12  for moving the end effector  39  to the next interpolated point. However, if the speeds of the J4 axis  34  and the J6 axis  36  are outside the allowable range and, thus, the speed reduction process is performed, the manipulator body  30  is controlled on the basis of the angles of the J1 axis  31  to the J6 axis  36  calculated in step S 20  for moving the end effector  39  to the next interpolated point. Note that step S 14  is an example of the drive instruction step, and the main controller  11  and the drive instructing unit  13  that perform the process in step S 14  correspond to the drive instructing means. 
     Subsequently, the main controller  11  determines whether the position and attitude of the end effector  39  after movement reach the work end point and attitude (step S 15 ). If the work end point and attitude have not been reached (NO in step S 15 ), step S 12  and the subsequent steps are performed again at predetermined sampling periods. However, if the work end point and attitude have been reached (YES in step S 15 ), the processing is completed. 
     As described above, the main controller  11  computes the angles of the J1 axis  31  to the J6 axis  36  for moving the end effector  39  from the current position and attitude to the next interpolated point at predetermined sampling periods and operates the articulated robot X. 
     An example of the procedure (corresponding to step S 12  illustrated in  FIG. 2 ) for calculating the angles of the J1 axis  31  to the J6 axis  36  and the speeds of the J4 axis  34  to the J6 axis  36  of the first articulated drive system for moving the articulated robot X from the current interpolated point to the next interpolated point is described next with reference to  FIG. 3 . 
     First, the main controller  11  calculates, using interpolation, the position and attitude of the end effector  39  at each of n points (n is any number based on the sampling periods) set between the work start point and attitude P 0  and the work end point and attitude P n  previously taught in step S 11 . In this case, the moving amount for one sampling period can be written in the form: ΔP=(P n −P 0 )/n={ΔX=(X n −X 0 )n, ΔY=(Y n −Y 0 )/n, ΔZ=(Z n −Z 0 )/n, Δα=(α n −α 0 )/n, Δβ=(β n −β 0 )/n, Δγ=(γ n −γ 0 )/n}. Note that the above-described interpolated points are expressed using the base coordinate system Σbase of the articulated robot X. 
     As illustrated in  FIG. 7 , if the interpolated point at the current position is P i , the main controller  11  calculates the position and attitude of the next interpolated point P i+1  using the equation: P i+1 =P 0 +ΔP×(i+1) or P i+1 =P i +ΔP (step S 121 ). Note that step S 121  is an example of an interpolation data calculation step, and the main controller  11  that performs the process in the interpolation data calculation step corresponds to interpolation data calculating means. 
     Subsequently, the main controller  11  calculates the angles (θ 1 , θ 2 , θ 3 , θ 4 , θ 5 , θ 6 ) of the J1 axis  31  to the J6 axis  36  by solving the inverse kinematics problem from the position and attitude (X i+1 , Y i+1 , Z i+1 , α i+1 , β i+1 , γ i+1 ) of the next interpolated point P i+1  and stores the calculated angles in the storage unit  12  (step S 122 ). At that time, two solutions of the inverse kinematics problem can be obtained for the J4 axis  34  to the J6 axis  36 . In this case, from the two solutions of the inverse kinematics problem, the main controller  11  selects the solution in which the sign of the angle of the J5 axis  35  of the first articulated drive system is the same as the sign of the J5 axis  35  at the taught work start point of the end effector  39 . In this manner, the angle of the J5 axis  35  does not pass through an angle of 0° and, thus, passage through a singularity can be avoided. 
     Note that if the main controller  11  performs the speed reduction process (described below), the main controller  11  calculates, in addition to the angles of the J1 axis  31  to the J6 axis  36  at the interpolated point in the path that passes through the singularity, the angles of the J1 axis  31  to the J6 axis  36  at an interpolated point in the path that does not pass through the singularity and stores the angles in the storage unit  12 . Thus, the stored angles are used for comparison performed in a return process described below (step S 310  in  FIG. 5  and a flowchart in  FIG. 6 ). 
     Note that step S 122  is an example of an angle calculation step, and the main controller  11  that performs the angle calculation step corresponds to angle calculating means. 
     Subsequently, the main controller  11  subtracts the angles of the J4 axis  34  to the J6 axis  36  at the current interpolated point P i  stored in the storage unit  12  from the angles of the J4 axis  34  to the J6 axis  36  at the calculated next interpolated point P i+1 , respectively, and calculates the speeds of the J4 axis  34  to the J6 axis  36  of the first articulated drive system. Thereafter, the main controller  11  stores the calculated speeds in the storage unit  12  (step S 123 ). Note that as described below, when the speed reduction process (step S 20 ) is performed, the main controller  11  calculates the speeds of the J4 axis  34  to the J6 axis  36  of the first articulated drive system at the interpolated point in a system that passes through a singularity and stores the calculated speeds in the storage unit  12 . Thereafter the speeds are used to calculate the allowable range of the speeds in step S 131  described below and to calculate the candidates of the speeds (the acceleration as needed) at the next interpolated point in, for example, step S 211 . 
     Herein, step S 123  is an example of a speed calculation step, and the main controller  11  that performs the speed calculation step corresponds to speed calculating means. 
     An example of the speed reduction necessity determination procedure corresponding to step S 13  illustrated in  FIG. 2  is described next with reference to  FIG. 4 . 
     First, the main controller  11  calculates an allowable range of the speeds of the J4 axis  34  and the J6 axis  36  of the first articulated drive system when the position and attitude of the end effector  39  is moved from the current interpolated point P i  to the next interpolated point P i+1  (step S 131 ). For example, an upper limit and a lower limit are determined by adding and subtracting a predetermined value or a predetermined ratio to and from the value of the speed at the current interpolated point P i . In this manner, the allowable range of the speed can be calculated. Alternatively, the allowable range of the speed of each of the axes may be determined in advance so as to be within a range that does not have an impact on the quality of the workpiece (e.g., the operating condition of the end effector  39 , such as a temperature in the case of welding or a thickness of a coating film in the case of coating, or a condition that avoids an abnormal operation of the articulated robot, such as vibration). Still alternatively, different allowable ranges may be set for the J4 axis  34  and the J6 axis  36 . 
     Subsequently, the main controller  11  determines whether the speed of at least one of the J4 axis  34  and the J6 axis  36  of the first articulated drive system at the next interpolated point exceeds the allowable range or a flag indicating that the speed reduction process is currently being performed is set (step S 132 ). 
     If the speeds of both of the J4 axis  34  and the J6 axis  36  of the first articulated drive system at the next interpolated point are within the allowable range and the speed reduction process is not currently being performed (NO in step S 132 ), the drive instructing unit  13  reads, from the storage unit  12 , the angles of the J1 axis  31  to the J6 axis  36  calculated in step S 12  in response to an instruction received from the main controller  11  and outputs the angles to the manipulator body  30  (step S 14 ). However, if an axis having a speed outside the allowable range is present or the speed reduction process is currently being performed (YES in step S 132 ), the main controller  11  performs the speed reduction process (step S 20 ) described below. 
     A specific example of the speed reduction process of the articulated robot X corresponding to step S 20  illustrated in  FIG. 2  is described below with reference to  FIG. 5 . 
     Note that while the following example is described with reference to a speed reduction process performed when the J5 axis  35  illustrated in  FIG. 24  is at an angle of about 0 degree and, thus, the speed of the J4 axis  34  or the J6 axis  36  exceeds the allowable range, the same can apply to the case in which the speed of the J4 axis  34  or the J6 axis  36  exceeds the allowable range for another reason. Accordingly, the speed reduction process is performed if the speed of one of the J4 axis  34  and the J6 axis  36  exceeds the allowable range or if the speeds of two of the drive shafts exceed the allowable range. Note that when an axis that is outside the allowable range at the next interpolated point is found for the first time, the speed at the current interpolated point is within the allowable range. 
     First, if a drive shaft having a speed that is outside the allowable range at the next interpolated point is one of the J4 axis  34  and the J6 axis  36  or each of the J4 axis  34  and the J6 axis  36  or if the flag indicating that the speed reduction process is being performed has already been set, the main controller  11  determines whether the speed reduction process is performed for one of the J4 axis  34  and the J6 axis  36  or both of the J4 axis  34  and the J6 axis  36  so as to branch the processing (step S 201 ). As described above, the determination as to whether the speed is within the allowable range is made by determining whether the speed is between the upper limit and the lower limit. At that time, if the speeds of the J4 axis  34  and the J6 axis  36  are not outside the allowable range and the flag indicating the speed reduction process is currently being performed is not set (“Others” in step S 201 ), the main controller  11  completes the speed reduction process. 
     However, if the speed of the J6 axis  36  is outside the allowable range, the processing proceeds to step S 211 . If the speed of the J4 axis  34  is outside the allowable range, the processing proceeds to step S 221 . If the speeds of the J4 axis  34  and the J6 axis  36  are outside the allowable range, the processing proceeds to step S 231 . 
     (Speed Reduction Process Steps S 211  to S 217  for J6 Axis  36 ) 
     If the speed of the J6 axis  36  is outside the allowable range or the flag indicating the speed reduction process for the J6 axis  36  is currently being performed is set (“J6 axis outside range” in step S 201 ), the main controller  11  calculates, on the basis of the angle of the J6 axis  36  at the current interpolated point, a plurality of candidates of the angle of the J6 axis  36  that follow the angle at the next interpolated point calculated in step S 12  and that allow the speed of the J6 axis  36  at the next interpolated point to be within the allowable range (step S 211 ). 
     For example, the main controller  11  calculates candidates of the speed of the J6 axis  36  through the following procedures (21) to (23). 
     (21) First, the main controller  11  calculates a reduction reference speed V6b using the following equation (21a):
 
 V 6 b=E (θ now −θ old )  (21a)
 
where θ now  denotes the angle of the J6 axis  36  at the next interpolated point, θ old  denotes the angle of the J6 axis  36  at the current interpolated point, and E denotes a predetermined coefficient (e.g., 0.1).
 
(22) Subsequently, the main controller  11  determines whether the reduction reference speed V6b is higher than or equal to a speed limiter V max . If the reduction reference speed V6b is higher than or equal to the speed limiter V max , the reduction reference speed V6b is set to the previous speed Vθ old . The speed limiter V max  is defined as, for example, the maximum value of a speed within the allowable range.
 
(23) Subsequently, on the basis of the reduction reference speed V6b and a predetermined value D (e.g., the absolute value of an amount of variation in speed that is known to have acceleration in a predetermined allowable range), the main controller  11  calculates three candidates of the speed (Vθ 6a =V 6b −D, Vθ 6b =V 6b , and Vθ 6c =V 6b +D). For example, the predetermined value D is a value that is about 10% of the speed limiter V max . In addition, if Vθ 6a  is higher than the speed limiter V max , Vθ 6a  is set to V max .
 
     Thereafter, the main controller  11  calculates, from the angle θ6 of the J6 axis  36  at the current interpolated point, three candidates of the angle of the J6 axis  36  (θ 6a , θ 6b , θ 6c ) at the next interpolated point corresponding to the above-described candidates of the speed (Vθ 6a , Vθ 6b , Vθ 6c ). That is, as the next interpolated point, the following angles are calculated: the angle that maintains the reduction reference speed V6b that does not exceed at least the allowable range or the speed at the current interpolated point (it is obvious that the speed is within the allowable range), and the angles that are deviated from the angle by a slight amount (±D (corresponding to the absolute value of an amount of variation of the speed)). Note that the process performed in step S 211  is an example of an angle candidate calculation step, and the main controller  11  that performs the process corresponds to angle candidate calculating means. 
     Subsequently, the main controller  11  calculates the angles of the other J1 axis  31  to J5 axis  35  at the next interpolated point, corresponding to each of the calculated candidates of the angle of the J6 axis  36  (step S 212 ). For example, as indicated by the following operations (1) to (3), by using the position (X i+1 , Y i+1 , Z i+1 ) of the end effector  39  at the next interpolated point P i+1  calculated in step S 122  and the angles (θ 4 , θ 5 ) of the J4 axis  34  and the J5 axis  35  of the first articulated drive system, the main controller  11  recalculates the angles (θ 1 , θ 2 , θ 3 , θ 4 , θ 5 , θ 6 ) of the J1 axis  31  to the J6 axis  36  of the first articulated drive system and the second articulated drive system for each of the candidates of the angle (θ 6a , θ 6b , θ 6c ) of the J6 axis  36 . 
     (1) Calculating [θ 1a , θ 2a , θ 3a , θ 4 , θ 5 , θ 6a ] from [X i+1 , Y i+1 , Z i+1 , θ 4 , θ 5 , θ 6a ] for the candidate θ 6a . 
     (2) Calculating [θ 1b , θ 2b , θ 3b , θ 4 , θ 5 , θ 6b ] from [X i+1 , Y i+1 , Z i+1 , θ 4 , θ 6 , θ 6b ] for the candidate θ 6b . 
     (3) Calculating [θ 1c , θ 2c , θ 3c , θ 4 , θ 6 , θ 6c ] from [X i+1 , Y i+1 , Z i+1 , θ 4 , θ 5 , θ 6c ] for the candidate θ 6c . 
     In this manner, as illustrated in  FIG. 8  described below, a candidate P′ i+1  of the next interpolated point at which the speed does not exceed the allowable range is calculated. By regarding the candidate P′ i+1  of the next interpolated point as the next interpolated point, an exception path (refer to  FIG. 8(B) ) in which the speed of the J6 axis  36  does not exceed the allowable range and which avoids the original interpolated point P i+1  (the singularity) can be obtained. 
     After the three candidates of the angle (θ 6a , θ 6b , θ 6c ) at the next interpolated point at which the speed of the J6 axis  36  is maintained within the allowable range are obtained in this manner, determination as to which one of the candidates is selected for the next interpolated point is made. Although the angles (θ 4 , θ 5 , θ 6 ) of the J4 axis  34  to the J6 axis  36  of the first articulated drive system are of interest in the above-described calculation, one of the candidates needs to be finally selected with a focus on the attitude of the end effector  39  that is important for a desired task. Accordingly, the angles of the J1 axis  31  to the J6 axis  36  need to be converted into data defining the attitude of the end effector  39 . 
     Thereafter, in order to determine which one of the candidates is selected as the next interpolated point, the main controller  11  calculates the components of data (torch inclination angle Rx, torch forward tilting angle Ry, torch rotation angle Rz) defining the attitude of the end effector  39  in the weld line coordinate system Σline at the next interpolated point for each of the calculated candidates (step S 213 ). Note that the process performed in step S 213  is an example of an attitude data calculation step, and the main controller  11  that performs the process in the attitude data calculation step corresponds to attitude data calculating means. Also note that as illustrated in  FIG. 25 , the weld line coordinate system Σline is a work coordinate system having an X-axis extending in the direction in which the end effector  39  moves (a direction of movement), a Y-axis defined as a cross product of the X-axis and the direction of gravitational force (X-axis×direction of gravitational force), and a Z-axis defined as a cross product of the X-axis and the Y-axis (X-axis and ×Y-axis). As illustrated in  FIGS. 26 to 28 , the rotation angle about the X-axis is expressed by the torch inclination angle Rx, the rotation angle about the Y-axis is expressed by the torch forward tilting angle Ry, the rotation angle about the Z-axis is expressed by the torch rotation angle Rz. For example, the main controller  11  calculates the components of the data representing the attitude of the end effector  39  for the candidates θ 6a  to θ 6c  in the above-described operations (1) to (3) through the following operations (1′) to (3′), respectively: 
     (1′) Calculating [R xa , R ya , R za ] from [θ 1a , θ 2a , θ 3a , θ 4 , θ 5 , θ 6a ], 
     (2′) Calculating [R xb , R yb , R zb ] from [θ 1b , θ 2b , θ 3b , θ 4 , θ 5 , θ 6b ], and 
     (3′) Calculating [R xc , R yc , R zc ] from [θ 1c , θ 2c , θ 3c , θ 4 , θ 5 , θ 6c ]. 
     Subsequently, the main controller  11  converts data in order to convert the position and attitude (X i+1 , Y i+1 , Z i+1 , α i+1 , β i+1 , γ i+1 ) of the end effector  39  at the interpolated point P i+1  in the original path calculated in step S 121  in an orthogonal coordinate system Σbase into data in the weld line coordinate system Σline (the torch inclination angle Rx, the torch forward tilting angle Ry, the torch rotation angle Rz) in which the X-axis represents a direction in which the end effector  39  moves (step S 214 ). Note that the process performed in step S 214  is an example of an attitude data conversion step, and the main controller  11  that performs the process in the attitude data conversion step corresponds to attitude data converting means. 
     Also note that the equation for converting the orthogonal coordinate system Σbase into the weld line coordinate system Σline is given as the following equation (Math 1). 
                             R   total               line     =         [         1       0       0           0         cos   ⁢           ⁢   Rx             -   sin     ⁢           ⁢   Rx             0         sin   ⁢           ⁢   Rx           cos   ⁢           ⁢   Rx           ]     ⁡     [           cos   ⁢           ⁢   Ry         0         sin   ⁢           ⁢   Ry             0       1       0               -   sin     ⁢           ⁢   Ry         0         cos   ⁢           ⁢   Ry           ]       ⁡     [           cos   ⁢           ⁢   Rz             -   sin     ⁢           ⁢   Rz         0             sin   ⁢           ⁢   Rz           cos   ⁢           ⁢   Rz         0           0       0       1         ]                   =     [           cos   ⁢           ⁢   Ry   ⁢           ⁢   cos   ⁢           ⁢   Rz             -   cos     ⁢           ⁢   Ry   ⁢           ⁢   sin   ⁢           ⁢   Rz           sin   ⁢           ⁢   Ry                 sin   ⁢           ⁢   Rx   ⁢           ⁢   sin   ⁢           ⁢   Ry   ⁢           ⁢   cos   ⁢           ⁢   Rz     +     cos   ⁢           ⁢   Rx   ⁢           ⁢   sin   ⁢           ⁢   Rz                 -   sin     ⁢           ⁢   Rx   ⁢           ⁢   sin   ⁢           ⁢   Ry   ⁢           ⁢   sin   ⁢           ⁢   Rz     +     cos   ⁢           ⁢   Rx   ⁢           ⁢   cos   ⁢           ⁢   Rz               -   sin     ⁢           ⁢   Rx   ⁢           ⁢   cos   ⁢           ⁢   Ry                   -   cos     ⁢           ⁢   Rx   ⁢           ⁢   sin   ⁢           ⁢   Ry   ⁢           ⁢   cos   ⁢           ⁢   Rz     +     sin   ⁢           ⁢   Rx   ⁢           ⁢   sin   ⁢           ⁢   Rz               cos   ⁢           ⁢   Rx   ⁢           ⁢   sin   ⁢           ⁢   Ry   ⁢           ⁢   sin   ⁢           ⁢   Rz     +     sin   ⁢           ⁢   Rx   ⁢           ⁢   cos   ⁢           ⁢   Rz             cos   ⁢           ⁢   Rx   ⁢           ⁢   cos   ⁢           ⁢   Ry           ]             ⁢     
     ⁢       By   ⁢           ⁢   using   ⁢           ⁢   α     ,   β   ,     and   ⁢           ⁢   γ     ,     the   ⁢           ⁢   following   ⁢           ⁢   equations   ⁢           ⁢   can   ⁢           ⁢   be   ⁢           ⁢   obtained   ⁢     :         ⁢     
     ⁢         R   tool           base         =         [           cos   ⁢           ⁢   α             -   sin     ⁢           ⁢   α         0             sin   ⁢           ⁢   α           cos   ⁢           ⁢   α         0           0       0       1         ]     ⁡     [           cos   ⁢           ⁢   β         0         sin   ⁢           ⁢   β             0       1       0               -   sin     ⁢           ⁢   β         0         cos   ⁢           ⁢   β           ]       ⁡     [         1       0       0           0         cos   ⁢           ⁢   γ             -   sin     ⁢           ⁢   γ             0         sin   ⁢           ⁢   γ           cos   ⁢           ⁢   γ           ]         ,     
     ⁢       R   line           base         =     [           Xm   ⁡     [   x   ]             Ym   ⁡     [   x   ]             Zm   ⁡     [   x   ]                 Xm   ⁡     [   y   ]             Ym   ⁡     [   y   ]             Zm   ⁡     [   y   ]                 Xm   ⁡     [   z   ]             Ym   ⁡     [   z   ]             Zm   ⁡     [   z   ]             ]                 [     Math   .           ⁢   1     ]               
By computing the following equation:
 
                       R   tool           line         =       R   base           line         ·     R   tool           base                       =       R   line   T       base         ·     R   tool           base                         =     [           Rm   ⁢           ⁢   11           Rm   ⁢           ⁢   12           Rm   ⁢           ⁢   13               Rm   ⁢           ⁢   21           Rm   ⁢           ⁢   22           Rm   ⁢           ⁢   23               Rm   ⁢           ⁢   31           Rm   ⁢           ⁢   32           Rm   ⁢           ⁢   33           ]       ,                     
Rx, Ry, and Rz can be obtained as follows:
 
 Rx=a  tan( Rm 23/ Rm 33),  Ry=a  sin( Rm 13),  Rz=a  tan( Rm 12 /Rm 11)
 
     The speed of the J6 axis  36  is originally outside the allowable range. Accordingly, in order to maintain the trajectory and reduce the speed of the J6 axis  36 , the amount of variation corresponding to the excess speed of the J6 axis  36  needs to be reduced by selecting at least one of the J1 axis  31  to the J5 axis  35  (other than the J6 axis  36 ) which is further rotatable and rotating the selected axis more. Unfortunately, determination as to which one of the J1 axis  31  to the J5 axis  35  is further rotatable with the trajectory unchanged cannot be made from a region defined by the angles θ1 to θ6. In contrast, in a region defined by the components (Rx, Ry, Rz) of the weld line coordinate system θline that is closely related to the type of task of the end effector  39 , which one of the J1 axis  31  to the J5 axis  35  is further rotatable with the trajectory unchanged can be determined. 
     Accordingly, as illustrated in  FIG. 5 , the main controller  11  acquires information (weight information) indicating a component having variation to be reduced from among the components (torch inclination angle Rx, torch forward tilting angle Ry, torch rotation angle Rz) of data indicating the attitude of the end effector  39  in the weld line coordinate system Σline converted in step S 213  (step S 215 ). Note that the main controller  11  may freely determine which one of the components has an increased weight using an input through the operation unit  21 . For example, according to the present embodiment, the end effector  39  is a welding torch having a single work point. Because of the nature of a welding task using a welding torch, the angle of the torch with respect to the workpiece (the material) and the moving speed of the torch are important. In contrast, rotation about the axis of the torch is not important. Thus, according to the present embodiment, it is assumed that the weight information is predetermined so that the torch inclination angle Rx and the torch forward tilting angle Ry are components having a large weight (i.e., components to be reduced), and the torch forward tilting angle Ry is a component having a small weight (i.e., a component that is not to be reduced). The weight information is used in the form of coefficients for the components of the evaluation equation used to select a candidate having a reduced variation in step S 216  described below. 
     Subsequently, from among the plurality of calculated candidates at the next interpolated point, the main controller  11  selects a candidate having the smallest variation of a particular component (one or two of the torch inclination angle Rx, the torch forward tilting angle Ry, and the torch rotation angle Rz) having a large weight for reduction obtained in step S 215  (step S 216 ). For example, when variations of the torch inclination angle and the torch forward tilting angle are reduced and a variation of the torch rotation angle is allowed, weighting coefficients A, B, and C are set so that A=1, B=1, and C=0 (i.e., the particular components are the torch inclination angle and the torch forward tilting angle). Thereafter, the following calculations (1″) to (3″) are performed for the candidates in the above-described operations (1′) to (3′), respectively: 
     (1″) [Fa=A(Rx−R xa ) 2 +B(Ry−R ya ) 2 +C(Rz−R za ) 2 ], 
     (2″) [Fb=A(Rx−R xb ) 2 +B(Ry−R yb ) 2 +C(Rz−R zb ) 2 ], and 
     (3″) [Fc=A(Rx−R xc ) 2 +B(Ry−R yc ) 2 +C(Rz−R zc ) 2 ], 
     where Rx, Ry, and Rz denote the torch inclination angle, the torch forward tilting angle, and the torch rotation angle at the next interpolated point in the original path. 
     By weighting the components whose variations are to be reduced in the above-described steps (1″) to (3″), differences Fa to Fc between the attitude angles of the end effector  39  at the next interpolated point in the original path calculated in step S 214  and the attitude angles of the end effector  39  of the candidates at the next interpolated point in the exception path calculated in step S 213  can be obtained. Thereafter, among Fa to Fc, the smallest value (the smallest variation) is selected, and the angles of the J1 axis  31  to the J6 axis  36  for the selected candidate are employed as the angles of the axes in the operation for avoiding a singularity. Note that the process performed in step S 216  is an example of an angle selection step, and the main controller  11  that performs the process in the angle selection step corresponds to angle selecting means. In addition, the main controller  11  stores the angles of the J1 axis  31  to the J6 axis  36  of the selected candidate and the speed of the J6 axis  36  in the storage unit  12 . In this manner, the angles of the J1 axis  31  to the J6 axis  36  are recalculated so that among the components of the attitude data of the end effector  39 , as a component has a higher predetermined weight, an amount of reduction in variation of the component is higher. For example, if the weighting coefficient A=0.2, the weighting coefficient B=0, and the weighting coefficient C=1, then the variation of the torch rotation angle Rz is reduced the most, and the variation of the torch forward tilting angle Ry is the largest. 
     Subsequently, if the flag indicating that the speed reduction process is currently being performed for the J6 axis  36  is not set, the main controller  11  sets the flag so as to indicate that the speed reduction process is currently being performed for the J6 axis  36  (step S 217 ). 
     Note that steps S 211  to S 213  and steps S 216  and S 217  are an example of a recalculation step, and the main controller  11  that performs the process in the steps corresponds to recalculating means. 
     As illustrated in  FIGS. 8(A) and 8(B) , by performing the above-described process (steps S 211  to S 217 ), the next interpolated point P′ i+1  in the exception path that avoids a singularity can be found from the position P i  of the current interpolated point, instead of the next interpolated point P i+1  in the original path that passes through the singularity. 
     Such calculation (step S 201  and steps S 211  to S 217 ) is repeated until the next interpolated point becomes an interpolated point of the original path (“Others” in step S 201 ). Thus, an exception path that avoids a singularity is calculated. Note that the control unit  10  does not perform such calculation processes in one go in advance. The processes are performed by the main controller  11  as needed in accordance with the current state and the next state. Accordingly, the processing load instantaneously imposed on the main controller  11  is reduced and, therefore, the cost can be reduced. 
     Note that among the candidates of angles (θ 6a , θ 6b , θ 6c ) at the next interpolated point, the angle of the J6 axis  86  at the reduction reference speed V6b that is originally within the allowable range or at the current interpolated point is included. Accordingly, the speed of the J6 axis  36  at the next interpolated point can be maintained within the allowable range using any one of the candidates employed. 
     A return process (step S 310 ) of the J6 axis  36  from the speed reduction process subsequently performed by the main controller  11  is described in detail below. 
     (J4-Axis- 34  Speed Reduction Process Steps S 221  to S 227 ) 
     If the speed of the J4 axis  34  is outside the allowable range or the flag indicating that the speed reduction process for the J4 axis  34  is currently being performed is set (“J4 Axis outside range” in step S 201 ), the main controller  11  calculates a plurality of candidates of the angle of the J4 axis  34  that are within the allowable range in the same manner as in the above-described calculation of the candidates of the speed and angle of the J6 axis  86  (step S 221 ). That is, a reduction reference speed V 4b  of the J4 axis  34  is calculated. Thereafter, three candidates of the speed (Vθ 4a =V 4b −G, Vθ 4b =V 4b , Vθ 4c =V 4b +G) are calculated, and three candidates of the angle (θ 4a , θ 4b , θ 4c ) are calculated. Note that the predetermined value G is, for example, the absolute value of an amount of variation of speed that is known to maintain acceleration within a predetermined allowable range. Also note that the process performed in step S 221  is an example of the angle candidate calculation step. 
     The processes in steps S 222  to S 227  and step S 320  below are the same as those in steps S 212  to S 217  and step S 310  described above for the J6 axis  36 , respectively. Accordingly, descriptions of the processes in steps S 222  to S 227  and step S 320  are not repeated. 
     (J4-Axis  34  and J6-Axis  36  Speed Reduction Process Step S 231  to S 237 ) 
     If the speeds of the J4 axis  34  and the J6 axis  36  are within the allowable range or if the flag indicating that the speed reduction process is currently being performed for the J4 axis  34  is set and the flag indicating that the speed reduction process is currently being performed is set for the J6 axis  36  (“J4 axis/J6 axis outside range” in step S 201 ), the main controller  11  calculates one or a plurality of candidates of the speed and angle of each of the J4 axis  34  and the J6 axis  36  (step S 231 ). 
     For example, in step S 231 , three candidates of the speed of the J6 axis  36  can be calculated as in step S 211 , and three candidates of the speed of the J4 axis  34  can be calculated as in step S 221 . Thereafter, the three candidates for the J4 axis  34  and the three candidates for the J6 axis  36  can be combined into nine candidates. That is, the main controller  11  generates three speed candidates (Vθ 6a =V 6b −D, Vθ 6b =V 6b , Vθ 6c =V 6b +D) from the reduction reference speed V6b of the J6 axis  36  and the predetermined value D and generates three speed candidates (Vθ 4a =V 4b −G, Vθ 4b =V 4b , Vθ 4c =V 4b +G) from the reduction reference speed V 4b  of the J4 axis  34  and the predetermined value G. Furthermore, the main controller  11  calculates three candidates of the angle of the J6 axis  36  (θ 6a , θ 6b , θ 6c ) at the next interpolated point corresponding to the above-described speed candidates from the angle θ 6  of the J6 axis  36  at the current interpolated point and calculates three candidates of the angle of the J4 axis  34  (θ 4a , θ 4b , θ 4c ) at the next interpolated point corresponding to the above-described speed candidates from the angle θ 4  of the J4 axis  34  at the current interpolated point. Thereafter, the main controller  11  combines the candidates for the J4 axis  34  and the candidates for the J6 axis  36  so as to calculate nine candidates (θ 4a , θ 6a ), (θ 4a , θ 6b ), (θ 4a , θ 6c ), (θ 4b , θ 6a ), (θ 4b , θ 6b ), (θ 4b , θ 6c ), (θ 4c , θ 6a ), (θ 4c , θ 6b ), and (θ 4c , θ 6c ). That is, for each of the J4 axis  34  and the J6 axis  36  at the next interpolated point, the angle that maintains the speed that does not exceed the allowable range at the current interpolated point and the angle that is slightly deviated from the angle due to the angle are calculated. Note that the process performed in step S 231  is an example of the angle candidate calculation step. 
     Subsequently, the main controller  11  calculates the angles of the other axes (the J1 axis  31  to the J3 axis  83  and the J5 axis  35 ) corresponding to each of the calculated candidates of the angles of the J4 axis  34  and the J6 axis  36  at the next interpolated point (step S 232 ). For example, for each of the pairs of candidates (θ 4a , θ 6a ) to (θ 4c , θ 6c ) for the J4 axis  34  and the J6 axis  36 , the main controller  11  recalculates the angles (θ 1 , θ 2 , θ 3 ) of the J1 axis  81  to the J3 axis  33  of the second articulated drive system using the position (X i+1 , Y i+1 , Z i+1 ) of the end effector  39  at the next interpolated point P i+1  calculated in step S 122  and the angle (θ 5 ) of the J5 axis  35  of the first articulated drive system. 
     (1) For the candidate (θ 4a , θ 6a ), calculating [θ 1aa , θ 2aa , θ 3aa , θ 4a , θ 5 , θ 6a ] from [X i+1 , Y i+1 , Z i+1 , θ 4a , θ 5 , θ 6a ] 
     (2) For the candidate (θ 4a , θ 6b ), calculating [θ 1ab , θ 2ab , θ 3ab , θ 4a , θ 5 , θ 6b ] from [X i+1 , Y i+1 , Z i+1 , θ 4a , θ 5 , θ 6b ] 
     (3) For the candidate (θ 4a , θ 6c ), calculating [θ 1ac , θ 2ac , θ 3ac , θ 4a , θ 5 , θ 6c ] from [X i+1 , Y i+1 , Z i+1 , θ 4a , θ 5 , θ 6c ] 
     (4) For the candidate (θ 4a , θ 6a ), calculating [θ 1ba , θ 2ba , θ 3ba , θ 4b , θ 5 , θ 6a ] from [X i+1 , Y i+1 , Z i+1 , θ 4b , θ 5 , θ 6a ] 
     (5) For the candidate (θ 4b , θ 6b ), calculating [θ 1bb , θ 2bb , θ 3bb , θ 4b , θ 5 , θ 6a ] from [X i+1 , Y i+1 , Z i+1 , θ 4b , θ 5 , θ 6b ] 
     (6) For the candidate (θ 4b , θ 6c ), calculating [θ 1bc , θ 2bc , θ 3bc , θ 4b , θ 5 , θ 6c ] from [X i+1 , Y i+1 , Z i+1 , θ 4b , θ 5 , θ 6c ] 
     (7) For the candidate (θ 4c , θ 6a ), calculating [θ 1ca , θ 2ca , θ 3ca , θ 4c , θ 5 , θ 6a ] from [X i+1 , Y i+1 , Z i+1 , θ 4c , θ 5 , θ 6a ] 
     (8) For the candidate (θ 4c , θ 6b ), calculating [θ 1cb , θ 2cb , θ 3cb , θ 4b , θ 5 , θ 6b ] from [X i+1 , Y i+1 , Z i+1 , θ 4c , θ 5 , θ 6b ] 
     (9) For the candidate (θ 4c , θ 6c ), calculating [θ 1cc , θ 2cc , θ 3cc , θ 4c , θ 5 , θ 6c ] from [X i+1 , Y i+1 , Z i+1 , θ 4c , θ 5 , θ 6c ] 
     In this manner, the candidate P′ i+1  having a speed that does not exceed the allowable range for the next interpolated point can be calculated. By regarding the candidate P′ i+1  of the next interpolated point as the next interpolated point, an exception path that does not exceed the allowable range and that avoids the next interpolated point P i+1  (a singularity) can be obtained. 
     Subsequently, in order to select a candidate with a focus on the attitude of the end effector  39 , the candidates of the angles of the J1 axis  31  to the J6 axis  36  are converted into data defining the attitude of the end effector  39 . 
     More specifically, the main controller  11  calculates the components of data (torch inclination angle Rx, torch forward tilting angle Ry, torch rotation angle Rz) defining the attitude of the end effector  39  in the weld line coordinate system at the calculated next interpolated point (step S 233 ). 
     For example, the main controller  11  calculates the components of the data representing the attitude of the end effector  39  for the candidates of the angles in the above-described operations (1) to (9) through the following operations (1′) to (9′): 
     (1′) Calculating [(R xaa , R yaa , R zaa ] from [θ 1aa , θ 2aa , θ 3aa , θ 4a , θ 5 , θ 6a ], 
     (2′) Calculating [(R xab , R yab , R zab ] from [θ 1ab , θ 2ab , θ 3ab , θ 4a , θ 5 , θ 6b ], 
     (3′) Calculating [(R xac , R yac , R zac ] from [θ 1ac , θ 2ac , θ 3ac , θ 4a , θ 5 , θ 6c ], 
     (4′) Calculating [(R xba , R yba , R zba ] from [θ 1ba , θ 2ba , θ 3ba , θ 4b , θ 5 , θ 6a ], 
     (5′) Calculating [(R xbb , R ybb , R zbb ] from [θ 1bb , θ 2bb , θ 3bb , θ 4b , θ 5 , θ 6b ], 
     (6′) Calculating [(R xbc , R ybc , R zbc ] from [θ 1bc , θ 2bc , θ 3bc , θ 4b , θ 5 , θ 6c ], 
     (7′) Calculating [(R xca , R yca , R zca ] from [θ 1ca , θ 2ca , θ 3ca , θ 4c , θ 5 , θ 6a ], 
     (8′) Calculating [(R xcb , R ycb , R zcb ] from [θ 1cb , θ 2cb , θ 3cb , θ 4c , θ 5 , θ 6b ], and 
     (9′) Calculating [(R xcc , R ycc , R zcc ] from [θ 1cc , θ 2cc , θ 3cc , θ 4c , θ 5 , θ 6c ]. 
     Thereafter, the main controller  11  calculates the components of data (torch inclination angle Rx, torch forward tilting angle Ry, torch rotation angle Rz) defining the attitude of the end effector  39  in the weld line coordinate system at the next interpolated point P i+1  calculated in step S 234  (step S 234 ). Note that step S 234  is an example of the attitude data conversion step, and the main controller  11  that performs the process in the attitude data conversion step corresponds to the attitude data converting means. 
     Subsequently, from among the plurality of components (torch inclination angle Rx, torch forward tilting angle Ry, torch rotation angle Rz) of the data defining the attitude of the end effector  39  in the weld line coordinate system Σline converted in step S 233 , the main controller  11  acquires information (weight information) indicating a component having a variation that is to be reduced (step S 235 ). 
     Furthermore, from among the plurality of calculated candidates at the next interpolated point, the main controller  11  selects a candidate having the smallest variation of a particular component (one of the torch inclination angle Rx, the torch forward tilting angle Ry, and the torch rotation angle Rz) having a large weight for reduction obtained in step S 235  (step S 236 ). For example, when variation of the torch inclination angle and variation of the torch forward tilting angle are reduced but a variation of the torch rotation angle is allowed, then the weighting coefficients are set so that A=1, B=1, and C=0. Thereafter, the following operations (1″) to (9″) are performed for the candidates in the above-described operations (1′) to (9′), respectively: 
     (1″) [F aa =A(Rx−R xaa ) 2 +B(Ry−R yaa ) 2 +C(Rz−R zaa ) 2 ], 
     (2″) [F ab =A(Rx−R xab ) 2 +B(Ry−R yab ) 2 +C(Rz−R zab ) 2 ], 
     (3″) [F ac =A(Rx−R xac ) 2 +B(Ry−R yac ) 2 +C(Rz−R zac ) 2 ], 
     (4″) [F ba =A(Rx−R xba ) 2 +B(Ry−R yba ) 2 +C(Rz−R zba ) 2 ], 
     (5″) [F bb =A(Rx−R xbb ) 2 +B(Ry−R ybb ) 2 +C(Rz−R zbb ) 2 ], 
     (6″) [F bc =A(Rx−R xbc ) 2 +B(Ry−R ybc ) 2 +C(Rz−R zbc ) 2 ], 
     (7″) [F ca =A(Rx−R xca ) 2 +B(Ry−R yca ) 2 +C(Rz−R zca ) 2 ], 
     (8″) [F cb =A(Rx−R xcb ) 2 +B(Ry−R ycb ) 2 +C(Rz−R zcb ) 2 ], and 
     (9″) [F cc =A(Rx−R xcc ) 2 +B(Ry−R ycc ) 2 +C(Rz−R zcc ) 2 ]. 
     By weighting the components whose variations are to be reduced in the above-described steps (1″) to (9″), differences F aa  to F cc  between the attitude angles of the end effector  39  at the next interpolated point in the original path calculated in step S 234  and the attitude angles of the end effector  39  at the next interpolated point in the exception path calculated in step S 233  can be obtained. Thereafter, among the differences F aa  to F cc , the smallest value (the smallest variation) is selected, and the angles of the J1 axis  31  to the J6 axis  36  for the selected candidate are employed as the angles of the axes in the operation for avoiding the singularity. Note that the process performed in step S 236  is an example of the angle selection step, and the main controller  11  that performs the process in the angle selection step corresponds to the angle selecting means. In addition, the main controller  11  stores the angles of the J1 axis  31  to the J6 axis  36  of the selected candidate and the speeds of the J4 axis  34  and the J6 axis  36  in the storage unit  12 . 
     Subsequently, if the flags indicating that the speed reduction process is currently being performed for the J4 axis  34  and the J6 axis  36  are not set, the main controller  11  sets the flags so as to indicate that the speed reduction process is currently being performed for the J4 axis  34  and the J6 axis  36  (step S 237 ). 
     By performing the above-described process (steps S 231  to S 237 ), the next interpolated point P′ i+1  in the exception path that avoids the singularity can be found from the position P i  of the current interpolated point, instead of the next interpolated point P i+1  in the original path that passes through the singularity. 
     A return process (step S 330 ) of the J4 axis  34  and the J6 axis  36  from the speed reduction process subsequently performed by the main controller  11  is described in detail below. 
     An example of the procedure of a return process from the speed reduction process of the articulated robot X corresponding to step S 310  illustrated in  FIG. 5  is described next with reference to  FIG. 6 . 
     As illustrated in  FIG. 8(B) , the main controller  11  calculates, from the next interpolated point P′ i+1  in the exception path that avoids a singularity zone P i  to P i+1 , a difference between the angle at an interpolated point P i+2  after next in the original path that passes through the singularity and the angle at an interpolated point P′ i+2  after next in the exception path that avoids the singularity. If the difference does not exceed a predetermined range, the processing proceeds to P i+3 , where the processing is completed. However, if the difference exceeds the predetermined range, the processing proceeds to P′ i+3 . This processing is repeated as long as the difference exceeds the predetermined range. If finally, the next interpolated point at which the difference is within the predetermined range is found (P′ i+4  to P′ i+5  in this example), the processing proceeds from the interpolated point P′ i+4  to the interpolated point P i+5 , where the processing is completed. Accordingly, the case in which return from the current interpolated point P′ i+4  in the path that avoids the singularity to the next interpolated point P i+5  in the path that passes through the singularity is mainly described next. 
     (Return Process of J6 Axis  36  from Speed Reduction Process) 
     First, the main controller  11  acquires an angle θ 6(i+5)  of the J6 axis  36  at the next interpolated point P i+5  in the system that passes through the singularity calculated in step S 122  and an angle θ′ 6(i+5)  of the J6 axis  36  at the next interpolated point P′ i+5  in the system that avoids the singularity selected in step S 214  (step S 311 ). 
     Subsequently, the main controller  11  determines whether a difference between the angle θ′ 6(i+5)  of the J6 axis  36  of the system that avoid the singularity and the angle θ 6(i+5)  of the J6 axis  36  of the system that passes through the singularity is within the predetermined range (step S 312 ). Note that the predetermined range is determined to be an angle difference value within a range in which if the angle θ′ 6(i+5)  of the J6 axis  36  is replaced with the angle θ 6(i+5)  and the end effector  39  is operated, an adverse effect on the operation, such as vibration, does not occur, in general. That is, the main controller  11  determines whether the interpolated point in the path that avoid the singularity is sufficiently close to an interpolated point in the original path that passes through the singularity and is within a range in which the interpolated point in the path that avoids the singularity is considered to return to the interpolated point in the original path. 
     Accordingly, if the difference value exceeds the predetermined range (NO in step S 312 ), the main controller  11  completes the return process in step S 310 . Thereafter, the processing proceeds to step S 14  (refer to  FIG. 2 ). If the difference value is within a predetermined range (YES in step S 312 ), the main controller  11  calculates the speed when the angle θ′ 6(i+5)  of the J6 axis  36  is replaced with the angle θ 6(i+5)  (step S 313 ). At that time, the speed of the J6 axis  36  is calculated on the basis of the difference between the angle θ 6(i+5)  of the J6 axis  36  at the next interpolated point in the path that passes through the singularity and an angle θ′ 6(i+4)  of the J6 axis  36  at the interpolated point in the path that avoids the singularity. 
     Subsequently, the main controller  11  calculates an allowable range of the speed of the J6 axis  36  (step S 314 ). For example, an upper limit and a lower limit are determined by adding and subtracting a predetermined value or a predetermined ratio to and from the value of the speed of the J6 axis  36  at the interpolated point in the path that avoids the singularity. In this manner, the allowable range of the speed can be calculated. Alternatively, the allowable range of the speed of each of the axes may be determined in advance so as to be within a range that does not have an impact on the quality of the workpiece (e.g., the operating condition of the end effector  39 , such as a temperature in the case of welding or a thickness condition of a coating film in the case of coating, or a condition that avoids an abnormal operation of the articulated robot, such as vibration). 
     Subsequently, the main controller  11  determines whether the speed of the J6 axis  36  is within the predetermined allowable range (step S 315 ). Note that the allowable range is determined so as to be a value within a range in which when the end effector  39  is moved, an adverse effect on the operation, such as vibration, does not occur. 
     If the speed of the J6 axis  86  is within the predetermined allowable range (YES in step S 315 ), the main controller  11  changes the next interpolated point from P′ i+5  to P i+5 . In addition, the main controller  11  sets the angle of the J6 axis  36  to θ 6(i+5)  and calculates the angles of the other J1 axis  31  to the J5 axis  35  corresponding to the angle of the J6 axis  36  (step S 316 ). The main controller  11  instructs the storage unit  12  to store the calculated angles of all of the drive shafts, that is, the angles of the J1 axis  31  to the J6 axis  36 . Furthermore, the main controller  11  resets the flag indicating that the speed reduction process for the J6 axis  36  is currently being performed (step S 317 ). 
     However, if the speed of the J6 axis  36  is outside the predetermined allowable range (NO in step S 315 ), the main controller  11  sets the angle of the J6 axis  36  to an angle θ″ 6(i+5) , which is between the angle θ 6(i+5)  and the angle θ′ 6(i+5) , and sets the interpolated point including the angle θ″ 6(i+5)  of the J6 axis  36  to the next interpolated point P″ i+5  (step S 318 ). Thereafter, the main controller  11  calculates the angles of the other J1 axis  31  to the J5 axis  35  corresponding to the angle of the J6 axis  36  (step S 319 ). That is, when replacing the angle θ′ 6(i+5)  of the J6 axis  36  with the angle θ 6(i+5) , the main controller  11  gradually changes the angle of the J6 axis  36  from θ′ 6(i+5)  to θ 6(i+5)  within a predetermined fluctuation range without abruptly changing the angle of the J6 axis  36 . 
     In addition, the main controller  11  instructs the storage unit  12  to store the calculated angles of all of the drive shafts, that is, the angles of the J1 axis  31  to the J6 axis  36 . 
     (Return Process of J4 Axis  34  from Speed Reduction Process) 
     The return process of the J4 axis  34  from the speed reduction process corresponding to step S 320  is similar to the above-described return process of the J6 axis  36  from the speed reduction process (steps S 311  to S 319 ). Accordingly, descriptions of the return process is not repeated. 
     (Return Process of J4 Axis  34 /J6 Axis  36  from Speed Reduction Process) 
     The return process (corresponding to step S 330 ) of the J4 axis  34  and the J6 axis  36  from the speed reduction process is similar to the return process of the J6 axis  36  from the speed reduction process except that the return process is performed for both the J4 axis  34  and the J6 axis  36 . Accordingly, descriptions of the return process is not repeated. 
     By, through the above-described control method, operating the position and attitude of the end effector  39  provided on the manipulator body  30  while preventing a variation of a particular component (one or two of the torch inclination angle Rx, the torch forward tilting angle Ry, and the torch rotation angle Rz) having a large weight for reduction and avoiding a singularity mainly by the main controller  11  of the articulated robot X, a work trajectory that is not significantly deviated from an interpolated point based on the taught point and that allows the speeds of all the axes to be within the allowable range without changing the moving speed of the end effector  39  can be obtained. 
     For example, as illustrated in  FIG. 24 , if a singularity at which the angles of the J4 axis  34  and the J6 axis  36  abruptly change (i.e., the speeds are outside the allowable range) appears at about 0 degrees of the J5 axis  35  rotation, the above-described speed reduction process is performed. Thus, variations of the torch inclination angle Rx and the torch forward tilting angle Ry are reduced, and the angles of the J4 axis  34  and the J6 axis  36  gently vary, as illustrated in  FIG. 9 . In this manner, the speeds of the J4 axis  34  and the J6 axis  36  can be set to values within the allowable range. 
     In addition, as illustrated in  FIG. 10 , if no speed limit is set (an alternate long and short dash line), the speed of the J4 axis  34  abruptly changes in the vicinity of the singularity. However, if the speed limit is simply set (a solid line) or the control method of the present invention is applied (a short dashed line), the speed can be maintained within the allowable range. 
     Note that if, as illustrated in  FIG. 11 , the speed limit is simply set, the attitude fluctuation angles of the torch forward tilting angle and the torch inclination angle significantly vary. 
     However, as illustrated in  FIG. 12 , according to the control method of the present invention, although the torch rotation angle having a small weight assigned thereto (having a speed that need not be limited) significantly varies, variations of the torch inclination angle and the torch inclination angle each having a large weight assigned thereto can be eliminated. 
     In addition, as illustrated in  FIG. 13(A) , the J1 axis  31  may perform a driving operation in the up-down direction, and the driving direction of the J2 axis  32  may be the same as that of the J3 axis  33 . Alternatively, as illustrated in  FIG. 13(B) , the J1 axis  31  and the J2 axis  32  may perform a driving operation in the right-left direction, and the J3 axis  33  may perform a driving operation in the up-down direction. Note that if a drive shaft performs a driving operation in the up-down direction, the speed may be calculated on the basis of a difference between moving distances of the drive shafts in the up-down direction in addition to the difference between the rotation angles of the motors that move the drive shafts in the up-down direction. 
     While the above description has been made with reference to the technique for, if the speed of an axis exceeds the allowable range, reducing the speed of the axis by increasing an amount of variation of another axis, the angle data on each of the axes may be calculated so that the acceleration is within an allowable range if the amount of variation of the speed (i.e., the acceleration) obtained in the above-described manner exceeds the allowable range. To calculate the angle data, the speed can be replaced with the acceleration, which is the amount of variation of the speed. 
     For example, in step S 123 , the main controller  11  calculates the acceleration instead of the speed. In step S 131 , the main controller  11  calculates the allowable range of the acceleration. In step S 132 , the main controller  11  determines whether the acceleration calculated in step S 123  is outside the allowable range of the acceleration calculated in step S 131 . Thereafter, if the acceleration is outside the allowable range, the main controller  11  calculates data on the angle of each of the axes so that the acceleration is within the allowable range. At that time, the above-described predetermined values D and G used in the calculation of the candidates of the acceleration are, for example, the absolute values of a variation of acceleration that is known to have jerk within a predetermined allowable range. Note that since the calculation can be performed by simply replacing the speed with the acceleration and replacing the acceleration with the jerk (jolt) in the above-described calculation, description of the calculation is not repeated. 
     First Embodiment 
     In a first embodiment, a method for controlling an articulated robot X that differs from that in the above-described embodiment is described. 
     If the articulated robot X is controlled using the method according to the above-described embodiment, control is performed so that even when the angle of the sign of the angle of the J5 axis  35  at the work start point is opposite to that at the work end point, the angle of the J5 axis  35  does not pass through 0°. Accordingly, the angle of the J5 axis  35  at the work end point is offset from an original target value. In such a case, for example, as illustrated in  FIG. 15 , the angles of the other J4 axis  34  and the J6 axis  36  may abruptly vary or exceed the operating limit angle (e.g., ±180°). 
     In addition, for the articulated robot X, two solutions of the inverse kinematics problem are obtained from one attitude data. For example, as illustrated in  FIG. 15 , if the amount of change in the angle of the J6 axis  36  abruptly increases or decreases, a different solution of the J6 axis  36  gets close to the current angle of the J6 axis  36 . Therefore, in the first embodiment, the configuration that prevents abrupt change in the J4 axis  34  and the J6 axis  36  by using two solutions of the inverse kinematics problem is described. 
       FIG. 14  is a flowchart illustrating another method for controlling the articulated robot X. Note that the same numbering will be used in referring to a procedure as is utilized above in describing the above-described embodiment illustrated in  FIG. 2  and, thus, detailed description of the procedure is not repeated. 
     First, like the above-described configuration, in the configuration of the first embodiment, the main controller  11  obtains, as the angles of the J1 axis  31  to the J6 axis  36  for moving the end effector  39  to the next interpolated point, a solution to the inverse kinematics problem in which the sign of the angle of the J5 axis  35  is the same as that at the work start point (S 12 ) until it is determined in step S 13  that the speed reduction process is needed (No in step S 13 ). Note that in step S 12 , the speeds corresponding to the calculated J4 axis  34  to the J6 axis  36  are also calculated. 
     In addition, in the subsequent step S 14 , the main controller  11  controls the drive instructing unit  13  and reads, from the storage unit  12 , the solution in the form of the angles of the J1 axis  31  to the J6 axis  36  for moving the end effector  39  to the next interpolated point so that the angle of the J5 axis  35  has a sign that is the same as the sign of the angle of the J5 axis  35  at the work start point. Thereafter, the main controller  11  outputs the angles to the actuators of the drive shafts of the manipulator body  30 . In this manner, each of the J1 axis  31  to the J6 axis  36  operates by regarding, as a target value, the solution in which the angle of the J5 axis  35  has a sign that is the same as the sign of the angle of the J5 axis  35  at the work start point (Yes in S 15 ) until the end effector  39  moves to the position and attitude at the work end point (No in S 15 ). 
     (Steps S 411  to S 412 ) 
     However, if, in step S 13 , it is determined that the speed reduction process is needed (Yes in S 13 ), the main controller  11 , in the subsequent step S 411 , calculates the angles of the J1 axis  31  to the J6 axis  36  and the speeds of the J4 axis  34  to the J6 axis  36  at the next interpolated point as in step S 12 . Note that in step S 411 , the speeds corresponding to the calculated J4 axis  34  to the J6 axis  36  are also calculated. 
     However, at that time, among two solutions of the inverse kinematics problem obtained in the form of the angles of the J1 axis  31  to the J6 axis  36  for moving the end effector  39  to the next interpolated point, the main controller  11  calculates a solution to the inverse kinematics problem in which the sign of the angle of the J5 axis  35  is opposite to that at the work start point (a different solution). Let θ41, θ51, and θ61 denote the angles of the J4 axis  34 , the J5 axis  35 , and the J6 axis  36 , respectively, serving as one of the two solutions of the inverse kinematics problem, and let θ41′, θ51′, and θ61′ denote the angles of the J4 axis  34 , the J5 axis  35 , and the J6 axis  36 , respectively, serving as the other solution. Then, the angles have the following relationship: θ41−θ41′=±π, θ51+θ′=0, and θ61−θ61′=±π. For example, if (θ41, θ51, θ61)=(90°, 75°, 0°), then (θ41′, θ51′, θ61′)=(−90°, −75 °, 180°). 
     As described above, according to the first embodiment, if the speeds of the J4 axis  34  and the J6 axis  36  are within the allowable range, the main controller  11  employs the solution in which the sign of the angle of the J5 axis  35  at the next interpolated point is the same as that at the work start point. However, if the speeds of the J4 axis  34  and the J6 axis  36  are outside the allowable range, the main controller  11  employs the solution in which the sign of the angle of the angle of the J5 axis  35  at the next interpolated point is opposite to that at the work start point. Note that this process is an example of the angle calculation step, and the main controller  11  that performs the process in the angle calculation step corresponds to the angle calculating means. 
     Thereafter, in the subsequent step S 412 , as in step S 13 , the main controller  11  determines whether the speed reduction process is necessary, that is, whether the speeds of the J4 axis  34  and the J6 axis  36  calculated in step S 412  are within the allowable range or whether the speed reduction process is currently being performed for the J4 axis  34  and the J6 axis  36 . 
     If it is determined that the speed reduction process is necessary (Yes in step S 412 ), the processing proceeds to step S 413 . However, it is determined that the speed reduction process is not necessary (No in step S 412 ), the processing proceeds to step S 414 . 
     (Step S 413 ) 
     In step S 413 , as in step S 20  illustrated in  FIG. 5 , the speed reduction process is performed in order to reduce the speed of one or both of the J4 axis  34  and the J6 axis  36 . Note that at that time, since the main controller  11  employs one of two solutions of the inverse kinematics problem in which the sign of the J5 axis  35  is opposite to that at the work start point in the form of the angles of the J1 axis  31  to the J6 axis  36  for moving the end effector  39  to the next interpolated point, the J1 axis  31  to the J6 axis  36  operate using the solution as the target values. Also note that the process performed in step S 413  is similar to the process performed in step S 20  except for the angles of the J4 axis  34  and the J6 axis  36 . Accordingly, description of the process performed in step S 413  is not repeated. 
     (Steps S 414  to S 415 ) 
     In addition, in step S 414 , as in step S 14 , the main controller  11  controls the drive instructing unit  13  and reads, from the storage unit  12 , the angles of the J1 axis  31  to the J6 axis  36  for moving the end effector  39  to the next interpolated point. Thereafter, the main controller  11  outputs the angles to the actuators of the drive shafts of the manipulator body  30 . At that time, the angles of the J1 axis  31  to the J6 axis  86  are the target values calculated in step S 411  or S 413  as a solution in which the angle of the J5 axis  35  has a sign that is the same as the sign of the angle of the J5 axis  35  at the work start point. Accordingly, the angle of the J5 axis  35  is changed while passing through an angle of 0°. 
     Thereafter, each of the J1 axis  31  to the J6 axis  36  operates by regarding, as a target value, the solution in which the angle of the J5 axis  35  has a sign that is the same as the sign of the angle of the J5 axis  35  at the work start point (No in S 415 ) until the end effector  39  moves to the position and attitude at the work end point (Yes in S 415 ). 
       FIG. 15  illustrates an example of the result of the operation performed by the J4 axis, J5 axis, and J6 axis in the original path that passes through a singularity when the sign of the angle of the J5 axis  35  at the work start point is opposite to that at the work end point (when the sign changes from plus to minus or from minus to plus), that is, the angle passes through 0°. In the example illustrated in  FIG. 15 , control is performed so that the angle of the J5 axis  35  does not pass through 0° and, thus, the angle of the J5 axis  35  at the work end point is positive. Accordingly, it can be seen that the amounts of change in the angles of the other J4 axis  34  and J6 axis  36  are increased. 
     In contrast,  FIG. 16  illustrates an example of the result when the method for controlling the articulated robot X according to the first embodiment and, at that time, the sign of the angle of the J5 axis  35  at the work start point is opposite to that at the work end point. The example illustrated in  FIG. 16  indicates that, by causing the J5 axis  35  to pass through 0°, the amounts of change in the angles of the other J4 axis  34  and the J6 axis  36  can be reduced. 
       FIG. 17  illustrates a change in the attitude data of the end effector  39  occurring when the same speed operation is performed without employing the method for controlling the articulated robot X according to the first embodiment.  FIG. 18  illustrates a change in the attitude data of the end effector  39  occurring when the method for controlling the articulated robot X according to the first embodiment is employed. Note that in  FIGS. 17 and 18 , the ordinate represents an amount of variation of the attitude data of the end effector  39  at the original interpolated point, and the abscissa represents a time. 
     As illustrated in  FIG. 17 , when the control method according to the first embodiment is not employed, variations of the inclination angle and the forward tilting angle are large. However, as illustrated in  FIG. 18 , when the control method according to the first embodiment is employed and if the weights of the inclination angle and the forward tilting angle (the amount of reduction in the variation) are set to large values, variations of the inclination angle and the forward tilting angle can be reduced at the expense of the accuracy of the rotation angle, which is unnecessary for welding operations. 
     Second Embodiment 
     In addition, as described in the above embodiment, when control is performed for the articulated robot X so that the angle of the J5 axis  35  does not pass through a singularity at which the angle is close to 0° between the work start point and the work end point and if the sign of the angle of the J5 axis  35  at the work start point is opposite to that at the work end point, the angle of the J5 axis  35  at the work end point differs from a desired angle. 
     In contrast, as noted in the above-described first embodiment, when control is performed for the articulated robot X so that the angle of the J5 axis  35  passes through an angle of about 0° between the work start point and the work end point and if the sign of the angle of the J5 axis  35  at the work start point is the same as that at the work end point, the angle of the J5 axis  35  at the work end point differs from a desired angle. 
     In these cases, for example, wires connected to the J1 axis  31  to the J6 axis  36  and the end effector  39  of the articulated robot X may get tangled, or the J4 axis  34  to the J6 axis  36  may exceed their drive limiting points in the subsequent operation, which is problematic. 
     Accordingly, the control method according to the above-described embodiment and the control method according to the first embodiment can be switched in accordance with whether the signs of the angles of the J5 axis  35  of the first articulated drive system at the work start point and the work end point are the same or different from each other. 
       FIG. 19  is a flowchart illustrating a method for controlling the articulated robot X according to a second embodiment. Note that the same numbering will be used in referring to a procedure as is utilized above in describing the above-described embodiment and the first embodiment and, thus, detailed description of the procedure is not repeated. 
     More specifically, between “Yes” in step S 13  and each of step S 20  and step S 411 , the main controller  11  performs a process for determining whether the signs of the angles of the J5 axis  35  of the first articulated drive system at the work start point and the work end point are the same or different from each other (Yes in step S 511 ). 
     If the signs of the angles of the J5 axis  35  of the first articulated drive system at the work start point and the work end point are the same (Yes in step S 511 ), the processing performed by the main controller  11  proceeds to step S 20 . In this case, the solution to the inverse kinematics problem in which the sign of the angle of the J5 axis  35  of the first articulated drive system is the same as that at the work start point is employed. 
     However, the signs of the angles of the J5 axis  35  of the first articulated drive system at the work start point and the work end point are opposite to each other (No in step S 511 ), the processing performed by the main controller  11  proceeds to step S 411 . In this case, the solution to the inverse kinematics problem in which the sign of the angle of the J5 axis  35  of the first articulated drive system is opposite to that at the work start point is employed. That is, in the case where the signs of the angles of the J5 axis  35  of the first articulated drive system at the work start point and the work end point are opposite to each other, when the angle of the J5 axis  35  moves close to 0° and if the speeds of the J4 axis  34  and the J6 axis  36  are within the allowable range, the solution to the inverse kinematics problem in which the sign of the angle of the J5 axis  35  of the first articulated drive system is the same as that at the work start point is employed. However, when the angle of the J5 axis  35  moves close to 0° and if the speeds of the J4 axis  34  and the J6 axis  36  are outside the allowable range, the solution to the inverse kinematics problem in which the sign of the angle of the J5 axis  35  of the first articulated drive system is opposite to that at the work start point is employed. Such a process is an example of the angle calculation step, and the main controller  11  that performs the process corresponds to the angle calculating means. 
     In this manner, the sign of the angle of the J5 axis  35  at the taught work end point is the same as the taught sign. Accordingly, for example, the wires connected to the J1 axis  31  to the J6 axis  36  and the end effector  39  can be prevented from getting tangled. In addition, the J4 axis  34  to the J6 axis  36  are prevented from exceeding their drive limiting points. 
     Third Embodiment 
     While the above description has been made with reference to the end effector  39  of the articulated robot X having a single work point, an articulated robot X 1  including an end effector  39 A having two work points may be controlled, as illustrated in  FIG. 20 . 
     The articulated robot X 1  includes the end effector  39 A, and the configurations other than the end effector  39 A are the same as those of the articulated robot X. In addition, the control of the articulated robot X 1  is the same as that of the articulated robot X except for the processes performed in steps S 215  and S 216  illustrated in  FIG. 5  (including steps S 225 , S 226 , S 235  and S 236 ). Hereinafter, descriptions of the processes and configurations of the articulated robot X 1  that are the same as those of the articulated robot X are not repeated. 
     The configurations of the articulated robot X 1  that differ from those of the articulated robot X illustrated in  FIG. 1  are described first. 
     The end effector  39 A is attached to the top end of the manipulator body  30  (the top end of the J6 axis  86 ). The end effector  39 A is an effector having two work points that have an effect on a workpiece. Examples of the work point include a welding device (a torch), a painting device, a tool, a gripper, and a sensor. Note that a torch having two work points is referred to as a “tandem torch”. 
     Subsequently, the processes performed in steps S 215  and S 216  of the speed reduction process that differ from those of the embodiments of the present invention are mainly described next with reference to the flowchart illustrated in  FIG. 5 . 
     First, the main controller  11  performs step S 201 . In this case, the speed of the J6 axis  36  is outside the allowable range, or a flag indicating that the speed reduction process for the J6 axis  36  is currently being performed is set (“J6 axis outside range” in step S 201 ). The main controller  11  further performs steps S 211  to S 214 . 
     Subsequently, in step S 215 , the main controller  11  acquires information (weight information) regarding a component for which the variation thereof needs to be reduced from among the components (torch inclination angle Rx, torch forward tilting angle Ry, torch rotation angle Rz) of data defining the attitude of the end effector  39 A in the weld line coordinate system Σline converted in step S 213 . At that time, according to the third embodiment, the end effector  39 A is the welding torch having two work points. Because of the nature of a welding task using a welding torch, the rotation angle about the axis of the torch and the advance rate of the torch are important. Thus, according to the first embodiment, the standard setting is determined in advance so that the torch rotation angle Rz is a component having a large weight (i.e., components having a value to be reduced), and the torch forward tilting angle Ry is a component having a small weight (i.e., a component having a value that is not reduced). 
     Subsequently, in step S 216 , the main controller  11  selects, from among a plurality of calculated candidates for the next interpolated point, a candidate having the smallest variation of a particular component (one or two of the torch inclination angle Rx, the torch forward tilting angle Ry, and the torch rotation angle Rz) having a large weight for reduction obtained in step S 215 . For example, when variation of the torch rotation angle Rz is reduced and if variation of the torch forward tilting angle Ry is allowed, the weighting coefficients are set so that A=0.2, B=0, and C=1 (i.e., the particular components are the torch inclination angle and the torch rotation angle) or A=0, B=0, and C=1 (i.e., the particular component is the torch rotation angle). Thereafter, the following operations (1″) to (3″) are performed for the candidates in the above-described operations (1′) to (3′) performed in step S 213 , respectively: 
     (1″) [F a =A(Rx−R xa ) 2 +B(Ry−R ya ) 2 +C(Rz−R za ) 2 ], 
     (2″) [F b =A(Rx−R xb ) 2 +B(Ry−R yb ) 2 +C(Rz−R zb ) 2 ], and 
     (3″) [F c =A(Rx−R xc ) 2 +B(Ry−R yc ) 2 +C(Rz−R zc ) 2 ]. 
     Through the above-described operations (1″) to (3″), a difference between the attitude angle of the end effector  39 A at the next interpolated point in the path that passes through the singularity and the attitude angle of the end effector  39 A at the next interpolated point in the path that avoids the singularity can be obtained for each of the candidates. Thereafter among Fa to Fc, the smallest value (the smallest variation) is selected, and the angles of the J1 axis  31  to the J6 axis  36  of the selected candidate are employed as the angles of the axes in the operation for avoiding the singularity. 
     Subsequently, the main controller  11  performs step S 217  and the subsequent steps. Note that as in the embodiment, instead of performing steps S 211  to S 216 , the main controller  11  performs steps S 221  to S 226  or steps S 231  to S 236  for each of the drive shafts that are determined to have a speed outside the allowable range. 
     Through the above-described control method, by activating the position and attitude of the end effector  39 A provided in the manipulator body  30  while reducing variation of the torch inclination angle Rx and the torch rotation angle Rz each having a large weight for reduction and avoiding the singularity mainly by the main controller  11  of the articulated robot X 1 , a work trajectory that is not significantly deviated from the interpolated points based on the taught points and that allows the speeds of all the axes to be within the allowable range without changing the moving speed of the end effector  39 A can be obtained. 
     In addition, if, as illustrated in  FIG. 21 , the control method according to the first embodiment is applied, the torch forward tilting angle Ry having a small weight for reduction significantly varies. However, the attitude fluctuation angle of the torch rotation angle Rz having a large weight for reduction can be reduced. 
     Fourth Embodiment 
     While the above description has been made with reference to the control method of the manipulator body  30  including three axes, that is, the J1 axis  31  to the J3 axis  33  as drive shafts of the second articulated drive system of the articulated robot X, the control method can be applied to a manipulator including four or more drive shafts of the second articulated drive system. Note that hereinafter, descriptions of the configurations and processes of an articulated robot X 2  that are the same as those of the articulated robot X are not repeated. 
     The configurations of the articulated robot X 2  illustrated in  FIG. 22  that differ from those of the articulated robot X illustrated in  FIG. 1  are described first. 
     As illustrated in  FIG. 22 , the articulated robot X 1  includes the control unit  10 , the operation unit  21 , and a manipulator body  30 A. The manipulator body  30 A includes three drive shafts of the first articulated drive system, that is, the J4 axis  34 , the J5 axis  35 , and the J6 axis  36 , and four drive shafts of the second articulated drive system, that is, the J1 axis  31 , the J2 axis  32 , the J3 axis  33 , and a J7 axis  37 . 
     Like the J1 axis  31  to the J6 axis  36 , the J7 axis  37  is driven by, for example, an electric motor. In response to an instruction received from the drive instructing unit  13 , the J7 axis  37  is driven to rotate in the positive and negative directions. Through rotational drive of a plurality of axes in conjunction with one another, the motion of a wrist and an arm of a human can be realized. Among the plurality of axes, the four axes of the second articulated drive system including the J7 axis  37  simulate the motion of a human arm and move the position of the end effector  39 . 
     The processes that differ from those according to the embodiment of the present invention are described next with reference to the flowcharts illustrated in  FIGS. 2 to 6 . 
     According to the embodiment, angles (θ 1 , θ 2 , θ 3 , θ 4 , θ 5 , θ 6 ) of the J1 axis  31  to the J6 axis  36  are calculated from the position and attitude P i (X i , Y i , Z i , α i , β i , γ i ) of an interpolated point as the solution to an inverse kinematics problem, and the position and attitude P i (X i , Y i , Z i , α i , β i , γ i ) are calculated from angles (θ 1 , θ 2 , θ 3 , θ 4 , θ 5 , θ 6 ) of the J1 axis  31  to the J6 axis  36  as the solution to a forward kinematics problem. In contrast, according to the fourth embodiment, angles (θ 1 , θ 2 , θ 3 , θ 4 , θ 5 , θ 6 , θ 7 ) of the J1 axis  31  to the J7 axis  37  are calculated from the position and attitude P i (X i , Y i , Z i , α i , β i , γ i ) of an interpolated point as the solution to an inverse kinematics problem, and the position and attitude P i (X i , Y i , Z i , α i , β i , γ i ) are calculated from angles (θ 1 , θ 2 , θ 3 , θ 4 , θ 5 , θ 6 , θ 7 ) of the J1 axis  31  to the J7 axis  37  as the solution to a forward kinematics problem. As described above, the numbers of variables of angle differ from each other (i.e., 6 and 7). 
     In step S 122 , by calculating the solution to the inverse kinematics problem, the main controller  11  obtains the angles (θ 1 , θ 2 , θ 3 , θ 4 , θ 5 , θ 6 , θ 7 ) of the J1 axis  31  to the J7 axis  37  from the position and attitude P i+1 (X i+1 , Y i+1 , Z i+1 , α i+1 , β i+1 , γ i+1 ) at the next interpolated point and stores the obtained angles in the storage unit  12 . 
     Subsequently, the processes that are the same as those in step S 123  and the subsequent steps are performed. At that time, it is determined that the speed reduction process is necessary (YES in S 13 ), and the speed of the J6 axis  36  is outside the allowable range or a flag indicating that the speed reduction process of the J6 axis  36  is being performed is set (“J6 axis outside range” in step S 201 ) is set. In addition, in step S 211 , the candidates of the angle of the J6 axis  36  are calculated. 
     Subsequently, in step S 212 , the main controller  11  calculates the angles of the other J1 axis  31  to J5 axis  35  and J7 axis  87  corresponding to each of the calculated candidates of the angle of the J6 axis  36  at the next interpolated point. For example, as illustrated in the following operations (1) to (3), by using the position (X i+1 , Y i+1 , Z i+1 ) of the end effector  39  at the next interpolated point P i+1  calculated in step S 122  and the angles (θ 4 , θ 5 ) of the J4 axis  34  and the J5 axis  35  of the first articulated drive system, the main controller  11  recalculates the angles (θ 1 , θ 2 , θ 3 , θ 7 ) of the J1 axis  31  to the J3 axis  33  and the J7 axis  37  of the second articulated drive system for each of the candidates (θ 6a , θ 6b , θ 6c ) of the angle of the J6 axis  36 . 
     (1) Calculating [θ 1a , θ 2a , θ 3a , θ 4 , θ 5 , θ 6a , θ 7 ] from [X i+1 , Y i+1 , Z i+1 , θ 4 , θ 5 , θ 6a ] for the candidate θ 6a . 
     (2) Calculating [θ 1b , θ 2b , θ 3b , θ 4 , θ 5 , θ 6b , θ 7 ] from [X i+1 , Y i+1 , Z i+1 , θ 4 , θ 5 , θ 6b ] for the candidate θ 6b . 
     (3) Calculating [θ 1c , θ 2c , θ 3c , θ 4 , θ 5 , θ 6c , θ 7 ] from [X i+1 , Y i+1 , Z i+1 , θ 4 , θ 5 , θ 6c ] for the candidate θ 6c . 
     Subsequently, in step S 213 , the main controller  11  calculates the components of data (torch inclination angle Rx, torch forward tilting angle Ry, torch rotation angle Rz) defining the attitude of the end effector  39  in the weld line coordinate system at the next interpolated point in the calculated system that avoids a singularity. For example, the main controller  11  performs the following operations for the candidates θ 6a  to θ 6c  in the above-described operations (1) to (3): 
     (1′) Calculating [R xa , R ya , R za ] from [θ 1a , θ 2a , θ 3a , θ 4a , θ 5 , θ 6a , θ 7 ], 
     (2′) Calculating [R xb , R yb , R zb ] from [θ 1b , θ 2b , θ 3b , θ 4b , θ 5 , θ 6b , θ 7 ], and 
     (3′) Calculating [R xc , R yc , R zc ] from [θ 1c , θ 2c , θ 3c , θ 4c , θ 5 , θ 6c , θ 7 ]. 
     Subsequently, in step S 214 , the main controller  11  calculates the components of data (torch inclination angle Rx, torch forward tilting angle Ry, torch rotation angle Rz) defining the attitude of the end effector  39  in the weld line coordinate system at the next interpolated point P i+1  in the calculated system that passes through the singularity. 
     Subsequently, the main controller  11  performs the processes in step S 215  and the subsequent steps. Note that as in the embodiment, instead of performing steps S 211  to S 216 , the main controller  11  performs steps S 221  to S 226  or steps S 231  to S 236  for each of the drive shafts that are determined to have a speed outside the allowable range. 
     Through the above-described control method, by activating the position and attitude of the end effector  39  provided in the manipulator body  30 A with four axes of the second articulated drive system while reducing variation of the component (any one of the torch inclination angle Rx, the torch forward tilting angle Ry, and the torch rotation angle Rz) having a large weight for reduction and avoiding the singularity mainly by the main controller  11  of the articulated robot X 2 , a work trajectory that is not significantly deviated from the interpolated points based on the taught points and that allows the speeds of all the axes to be within the allowable range without changing the moving speed of the end effector  39  can be obtained. 
     As described above, the control method according to the fourth embodiment is useful for controlling a manipulator having a plurality of joint shafts for which the angles (θ 4 , θ 5 , θ 6 ) of the shafts of the first articulated drive system can be obtained from the position and attitude (X i , Y i , Z i , α i , β i , γ i ) at the interpolated point P i  as the solution to the inverse kinematics problem and, in addition, the angles (θ 1 , θ 2 , θ 3 , θ 7 ) of the shafts of the second articulated drive system can be obtained from the position and angles (X i , Y i , Z i , θ 4 , θ 5 , θ 6 ) of the shafts of the first articulated drive system at the interpolated point P i  as the solution to the inverse kinematics problem. 
     Accordingly, the control method can be applied to not only articulated robots having the above-described 6-axis or 7-axis manipulator but articulated robots having 8 or more-axis manipulators. 
     Fifth Embodiment 
     In addition, the control unit  10  of the articulated robot X can be realized without using a dedicated system, that is, by using a widely used computer system Y connected to a network illustrated in  FIG. 29 . The widely used computer system Y illustrated in  FIG. 29  includes, for example, the main controller  11 , the storage unit  12 , an external storage unit  103 , an input/output unit  104 , a display unit  105 , a transceiver  106 , and an internal bus  109 . The main controller  11  includes a CPU (Central Processing Unit), and the storage unit  12  includes, for example, a RAM (Random Access Memory). The main controller  11  executes a program stored in the storage unit  12  to realize the control unit  10 , which is the control apparatus of the articulated robot X. 
     For example, by storing a program that executes the above-described process in a computer-readable recording medium (e.g., a flexible disk, a CD-ROM, or a DVD-ROM), distributing the recording medium, and installing the program in a computer, the control unit  10  of the articulated robot X that executes the above-described process may be configured. Alternatively, the program may be stored in a storage unit of a server apparatus in a communication network, such as the Internet. Thereafter, a widely used computer, for example, may download the program. In this manner, the control unit  10  of the articulated robot X may be configured. 
     Although the invention has been described by reference to specific embodiments, it should be understood that numerous modifications and combinations needed due to the design and other factors may be made within the spirit and scope of the inventive concepts described. 
     In the above-described embodiments, for example, a singularity avoidance process for avoiding the singularity of the J5 axis  35  is performed so that one of or both of the speeds of the J4 axis  34  and the J6 axis  36  of the first articulated drive system are not outside the allowable range. At that time, the articulated robot may include means for externally announcing that the singularity avoidance process is being performed. 
     More specifically, when, as illustrated in  FIG. 5 , the speed reduction process is performed in order to avoid the singularity, the message “Singularity Avoidance ON” indicating that a singularity avoidance process is being performed may be displayed on a display screen M of the operation unit  21  (a teach pendant), as illustrated in  FIG. 30 . However, the displayed information is not limited to the message “Singularity is being avoided”. Any type of information that indicates that a singularity avoidance process is being performed can be used. 
     By displaying information indicating that a singularity avoidance process is being performed, an operator can recognize whether the manipulator body  30  is in a singularity avoidance mode (an avoidance welding mode) or in a non-singularity avoidance mode (a normal welding mode) during a welding operation. Accordingly, if, for example, quality inspection is performed after a workpiece (a material) is welded, the operator can carefully watch a portion welded in the avoidance welding mode and inspect the weld quality. Thereafter, the operator can change the weld condition for welding in the avoidance welding mode on the basis of the result of inspection as needed. In addition, for example, the operator can monitor the motion of the whole manipulator body  30  in the avoidance welding mode by eye. Thereafter, the operator can change the operation performed by the manipulator body  30  when the manipulator body  30  is activated for, for example, the next welding operation. 
     Note that in addition to displaying the message “Singularity Avoidance ON”, identification of the processing program (e.g., the program number of a reproducing program) may be displayed on the display screen M. Alternatively, a period of time during which the processing program is being executed (a reproduction time) or the type of motion of the end effector  39  (e.g., “linear movement”) may be displayed on the display screen M. Furthermore, the previously taught torch information (e.g., the torch inclination angle, the torch forward tilting angle, and the torch rotation angle) and the current torch information may be displayed on the display screen M. 
     In this manner, the operator can recognize the detailed status of the manipulator body  30  in the singularity avoidance mode. 
     While the above-described example has been described with reference to the display screen M displaying information indicating that a singularity avoidance process is being performed, the information indicating that a singularity avoidance process is being performed may be provided using sound from, for example, a speaker. Alternatively, the information may be provided using a lighted lamp or a blinking lamp. Still alternatively, the information indicating that a singularity avoidance process is being performed may be displayed on an external display unit other than the teach pendant  21  of the articulated robot. 
     In addition, a time of “Singularity Avoidance ON” may be stored in the storage unit  12  of the control unit  10 . Thereafter, the time log of the singularity avoidance mode may be displayed on the display screen M of the operation unit  21  (the teach pendant) after the welding operation is completed so that the operator can recognize the time log of the singularity avoidance mode. 
     REFERENCE SIGNS LIST 
     
         
         
           
             X, X 1 , X 2  articulated robot 
               10  control unit 
               11  main controller 
               12  storage unit 
               13  drive instructing unit 
               21  operation unit 
               30 ,  30 A manipulator body 
               31  J1 axis 
               32  J2 axis 
               33  J3 axis 
               34  J4 axis 
               35  J5 axis 
               36  J6 axis 
               37  J7 axis 
               39 ,  39 A end effector