Patent Publication Number: US-8984757-B2

Title: Tracking apparatus

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is based upon and claims the benefit of priority from prior Japanese Patent Application No. 2011-154235, filed Jul. 12, 2011, the entire contents of which are incorporated herein by reference. 
     FIELD 
     Embodiments described herein relate generally to tracking apparatuses for causing a target recognition sensor, such as a camera, to track a target that moves in all directions. 
     BACKGROUND 
     In recent years, various systems capable of tracking objects using, for example, an ITV camera, to perform continuous monitoring or obtain detailed information have been commercialized for use in large-scale facilities, such as airports and factories, security equipment employed in electrical power plants or water-supply corporations associated with lifeline, and traffic information support systems, such as ITSs. These tracking systems have a structure contrived to be used not only as ground equipment, but also as systems installed on a moving platform such as a vehicle, ship or airplane. To this end, the structure is made compact and resistance against vibration. More specifically, the tracking systems perform disturbance suppression against vibration and swinging. Further, to enable the tracking systems to sequentially track a plurality of targets, it has come to be important to increase tangential velocity of the systems to cause them to be directed to the targets in a short time. 
     In such a conventional moving object image tracking system as the above, to track a target that moves in all directions, a gimbal structure is often employed. The gimbal structure needs to have at least two axes. In a biaxial gimbal, when a target passes through or near the zenith, it is necessary for its Az axis to instantly shift its orientation from the front to the rear, namely, to instantly rotate through about 180 degrees. However, since there is a limit in motor torque, this operation is difficult to perform, with the result that such a phenomenon as a so-called gimbal lock, in which continuous tracking becomes impossible, will occur. Thus, in the biaxial gimbal structure, the gimbal cannot be oriented toward the zenith or its neighborhood, which makes it difficult to continuously track a target in all directions. 
     To overcome this disadvantage, image tracking systems having a triaxial gimbal structure exist. In the triaxial gimbal structure, the freedom of motion is increased, and motion is divided into Az axis motion and xEL axis motion in order to avoid excessive angular velocity, thereby enabling the gimbal to continuously track a target in all directions within an allowable gimbal rotation range and without gimbal lock. 
     Other types of conventional tracking mechanisms, which employ no gimbal structure, have been proposed. In these mechanisms, a frictional rolling motion mechanism rotates a spherical casing in all directions. 
     Further, a convey apparatus has been proposed as a mechanism for rotating a spherical movable body utilizing friction. In this apparatus, it is difficult to reduce the size, and a control rule for tracking a target is complex. For instance, if the apparatus has a triaxial gimbal structure, the number of driving means, such as motors, increases, which makes reduction of size and cost difficult. Further, since the apparatus is provided with, for example, a camera, the load inertia of the xEL axis is high, which increases the possibility of axial interference between the Az axis and the xEL axis. This is a problem peculiar to the triaxial structure. Although it is possible to reduce the angular velocity of the Az axis using a redundancy axis, the Az axis requires a higher angular velocity than the other axes, the required driving torque will be inevitably increased. 
     In the systems with no conventional gimbal structure, there is no problem of gimbal lock. In this case, however, it is difficult to achieve automation of the systems as moving object image tracking systems. For instance, it is necessary to manually drive a spherical body employed therein by remote control until a target enters the image screen of a camera used therein. Further, these systems do not have any element for acquiring information concerning the orientation of the camera. Because of the above, it is difficult for the systems to realize automatic tracking of targets using information obtained from images of the targets. In addition, in these systems, wireless communication is performed with, for example, the camera in the spherical body, which inevitably limits the operation period of the camera. 
     Moreover, although the above-mentioned conventional mechanism for driving the spherical body is applicable to, for example, a moving apparatus, it cannot easily be applied to moving object image tracking systems. For example, in the mechanism, the spherical body is moved, with a table, installed therein, kept horizontal. This makes it difficult to orient the camera in an arbitrary direction. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram illustrating a tracking apparatus according to a first embodiment; 
         FIG. 2A  is a perspective view illustrating the tracking apparatus shown in  FIG. 1 ,  FIG. 2B  is a front view of the apparatus,  FIG. 2C  is a side view of the apparatus, and  FIG. 2D  is a top plan view of the apparatus; 
         FIG. 3A  shows the respective rotation axes of the first to third gimbals and the movable body incorporated in the tracking apparatus of  FIG. 1 , and  FIG. 3B  shows the respective rotation axes of the first to third gimbals and the movable body; 
         FIG. 4  is a schematic view illustrating the position of the movable body  141  relative to a spherical body  150 ; 
         FIG. 5A  is a front view illustrating the position of a wheel,  FIG. 5B  is a top view illustrating the driving direction vector of each wheel,  FIG. 5C  is another top view illustrating a case where the movable body is intended to be driven in the x-direction, and  FIG. 5D  is yet another top view illustrating a case where the movable body is intended to be driven in the y-direction; 
         FIGS. 6A ,  6 B,  6 C and  6 D are perspective views useful in explaining a case where the movable body shifts from a state in which it is oriented upward, to a state in which it is oriented diagonally leftward,  FIG. 6A  shows an initial state,  FIG. 6B  shows a state in which the movable body shifts diagonally leftward,  FIG. 6C  shows a state in which the first and second gimbals rotate in accordance with the diagonally leftward shift of the movable body, and  FIG. 6D  shows a state in which the third gimbal is returned to the center of the rotation range thereof, and the first and second gimbals rotate in their respective directions; 
         FIG. 7  is a view illustrating a tracking error between the field of a camera and a moving object in the first embodiment; 
         FIG. 8  is a block diagram useful in explaining a control system for tracking the moving object; 
         FIG. 9  is a schematic view illustrating a tracking system that emits light to a target; and 
         FIG. 10A  is a perspective view illustrating a tracking apparatus according to a second embodiment, and  FIG. 10B  is a front view of the apparatus of the second embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Tracking apparatuses according to embodiments will be described in detail with reference to the accompanying drawing. In the embodiments, like reference numbers denote like elements, and duplication of description will be avoided. 
     In general, according to the embodiments, a tracking apparatus includes a spherical body, a first gimbal, a second gimbal, a third gimbal, a movable body, three or more spherical driving units, a hold unit, an identifying unit, a first angle sensor, a second angle sensor, a third angle sensor, a fourth angle sensor, a rotation spring driving unit, and a control unit. The first gimbal is supported by a bottom of the spherical body and is configured to rotate about a first gimbal axis extending vertical. The second gimbal is supported by the first gimbal and is configured to rotate about a second gimbal axis perpendicular to the first gimbal axis. The third gimbal is supported by the second gimbal and is configured to rotate about a third gimbal axis perpendicular to the second gimbal axis at an intersection between the first gimbal axis and the second gimbal axis. The movable body is supported by the third gimbal and is configured to rotate about a fourth gimbal axis perpendicular to the third gimbal axis. Three or more spherical driving units are connected to the movable body and are kept in contact with portions of the spherical body to move the movable body in a desired direction. The hold unit connects the third gimbal to the movable body, and holds the spherical driving units pressed against the spherical body. The identifying unit is supported by the movable body and is configured to output position data of a target. The first angle sensor is configured to detect a first rotation angle of the first gimbal relative to the bottom. The second angle sensor is configured to detect a second rotation angle of the second gimbal relative to the first gimbal. The third angle sensor is configured to detect a third rotation angle of the third gimbal relative to the second gimbal. The fourth angle sensor is configured to detect a fourth rotation angle of the movable body relative to the third gimbal. The rotation spring driving unit is configured to return the third gimbal to a center of a rotation range of the third gimbal. The control unit is configured to control the spherical driving units to track the target, using the first to fourth rotation angles. 
     The tracking apparatuses of the embodiments are obtained by applying a moving object image tracking system to a tracking system for emitting light to a moving object. 
     The embodiments have been developed in light of the above-mentioned problem, and aim to provide a tracking apparatus capable of automatically tracking a target in all directions without requiring excessive angular velocity. 
     (First Embodiment) 
     Referring first to  FIG. 1  and  FIGS. 2A and 2B , a tracking apparatus according to a first embodiment will be described.  FIG. 1  is a block diagram illustrating the tracking apparatus.  FIG. 2A  is a perspective view of the tracking apparatus shown in  FIG. 1 , as viewed from a direction of a vector (X, Y, Z)=(1, −1, 1), the Z-axis direction being set as a zenith direction.  FIG. 2B  is a front view of the apparatus, as viewed from the negative Y direction.  FIG. 2C  is a side view of the apparatus, as viewed from the negative X direction.  FIG. 2D  is a top plan view of the apparatus, as viewed from the positive Z direction. The X, Y and Z directions are defined in these figures. 
     The tracking apparatus of the first embodiment comprises first, second and third gimbals  111 ,  121  and  131 , a movable body  141 , a base  101 , first, second, third and fourth angle sensors  112 ,  122 ,  132 ,  142 , a spherical body  150 , wheels  151 ,  152  and  153 , a drive hold unit  155 , a target position identifying unit  161 , a tracking error detecting unit  162 , a control unit  163 , and first, second and third wheel driving units  171 ,  172  and  173 . The combination of each wheel and the corresponding wheel driving unit will hereinafter be referred to as the “spherical driving unit.” 
     In the first embodiment, the spherical body  150  contains the first, second and third gimbals  111 ,  121  and  131 , the movable body  141 , the base  101 , the first, second, third and fourth angle sensors  112 ,  122 ,  132 ,  142 , the wheels  151 ,  152  and  153 , the drive hold unit  155 , the target position identifying unit  161 , the tracking error detecting unit  162 , the control unit  163 , and the first, second and third wheel driving units  171 ,  172  and  173 . The spherical body  150  is formed of a material that enables the target position identifying unit  161  to identify a target. For instance, the spherical body  150  is formed of a transparent material that permits, to pass therethrough, light that can be detected by the target position identifying unit  161 . 
     The first gimbal  111  is supported by the base  101  provided at the bottom of the spherical body  150  so that it can rotate about a first rotation axis  110  which extends vertically and serves as a first gimbal axis. The second gimbal  121  is supported by the first gimbal  111  so that it can rotate about a second rotation axis  120  which is arranged perpendicular to the first rotation axis  110  and is horizontally rotatable. The third gimbal  131  is supported by the second gimbal  121  so that it can rotate about a third rotation axis  130  which is rotatable and perpendicular to the second rotation axis  120 . In  FIG. 1 , the third rotation axis  130  is perpendicular to the sheet of the drawing. 
     Further, a rotary spring driving mechanism  181  is provided in association with the third rotation axis  130 . The spring driving mechanism  181  urges the third gimbal  131  to the center of rotation by its restoring force. For instance, when the third gimbal  131  slightly moves clockwise or counterclockwise about the third rotation axis  130 , the spring driving mechanism  181  rotates the second gimbal  121  and the first gimbal  111  so as to return the third gimbal  131  to the center of rotation. The spring driving mechanism  181  may be coupled to, for example, the shaft of the third gimbal axis, or be incorporated in the third gimbal  131  or the drive hold unit  155 . 
     The base  101  is coupled to the first gimbal  111  to support the first gimbal  111 , the second gimbal  121 , the third gimbal  131 , the movable body  141  and the target position identifying unit  161 , thereby serving as a table for placing the tracking apparatus thereon. 
     The movable body  141  is coupled to the third gimbal  131  via the drive hold unit  155 . The movable body  141  is provided perpendicular to the third rotation axis  130 , and can rotate about a movable axis  140  as a movably supported fourth rotation axis. The movable body  141  is provided with at least three spherical driving units for driving the body  141  itself. The spherical driving units restrict the movement of the third gimbal and the movable body. The spherical driving units comprise wheels (e.g., omni-wheels  151 ,  152  and  153 ) for moving the movable body  141  relative to the spherical body  150 , and the wheel driving units  171 ,  172  and  173  for rotating the wheels.  FIG. 1  and  FIGS. 2A to 2D  show an example case where three omni-wheels  151  to  153  are arranged at regular circumferential intervals of 120 degrees. The “omni-wheel” is a collective term of a wheel (rotary body) that can not only rotate the spherical body as a wheel, but also move in a direction different from the direction of the rotation. The rotation axis of each omni-wheel is connected to the rotation axis of the corresponding wheel driving unit, and the wheel main body of each omni-wheel is rotated by the same. The spherical driving units can rotate the movable body  141  in a desired direction relative to the spherical body  150 . The spherical driving units may incorporate rotary springs for pressing the wheels against the spherical body. 
     The movable body  141  also incorporates the target position identifying unit  161  for outputting target position data. The target position identifying unit  161  is also called as a target identifying sensor, and is, for example, a camera sensor. It identifies a target and obtains image data thereof. 
     The drive hold unit  155  connects the third gimbal  131  to the movable body  141  not only to make the third gimbal  131  and the movable body  141  rotatable relative to each other, but also to keep the wheels of the spherical driving units pressed against the spherical body  150 . This structure enables the movable body  141  to smoothly move along the inner surface of the spherical body  150 . The drive hold unit  155  is provided with, for example, a compression spring, the restoring force of which upwardly urges the movable body  141  in the example of  FIG. 1 , thereby pressing the omni-wheels against the inner surface of the spherical body  150 . Since the omni-wheels are thus pressed against the inner surface of the spherical body  150  with an optimal force by the spring of the drive hold unit  155 , the spherical driving units can transfer the driving forces of the first to third wheel driving units  171  to  173  to the spherical body  150 , using the frictional force between the spherical body  150  and the omni-wheels  151  to  153 . Further, the drive hold unit  155  is, for example, a bearing or an encoder, through which the third gimbal  131  is coupled to the movable body  141 . 
     The first, second, third and fourth rotation axes  110 ,  120 ,  130  and  140  are provided with first, second, third and fourth angle sensors  112 ,  122 ,  132  and  142 , respectively. The first angle sensor  112  detects the rotation angle of the first gimbal  111 . The second angle sensor  122  detects the rotation angle of the second gimbal  121  relative to the first gimbal  111 . The third angle sensor  132  detects the rotation angle of the third gimbal  131  relative to the second gimbal  121 . The fourth angle sensor  142  detects the rotation angle of the movable body  141  relative to the third gimbal  131 . The fourth angle sensor  142  is, for example, an encoder. 
     The tracking error detecting unit  162  processes image data acquired from the target position identifying unit  161  to detect tracking error values. In general, the tracking error detecting unit  162  converts the image data into monochrome image data by digitization, thereby extracting the characterizing point of a target from the image data to identify the position of the target in the viewing field of the camera and to regard the two-directional amounts (ΔX, ΔY) of the target deviated from the center of the viewing field as tracking error detection values. The process time including the above image processing is a sampling time required for obtaining the tracking error detection values that will be described later with reference to  FIG. 7 . 
     The control unit  163  acquires data concerning the aforementioned four angles from the first, second, third and fourth angle sensors  112 ,  122 ,  132  and  142 , respectively, thereby identifying the orientation of the target position identifying unit  161 , and instructing the first, second and third wheel driving units  171 ,  172  and  173  to make, zero, the tracking error detection values acquired from the tracking error detecting unit  162  to drive the wheels  151 ,  152  and  153 . In other words, the control unit  163  calculates virtual position data associated with the same coordinate system as that of the target position identifying unit  161 , using the four angles, and controls the spherical driving units to make the virtual position data coincide with the position data output from the target position identifying unit  161 . 
     Referring then to  FIGS. 3A and 3B , a rough description will be given of the first, second, third and fourth rotation axes  110 ,  120 ,  130  and  140  of the first, second, third and fourth gimbals  111 ,  121  and  131  and the movable body  141 , which are set with respect to the spherical body  150 .  FIG. 3A  shows a case where the target position identifying unit  161  is oriented horizontally, and  FIG. 3B  shows a case where the target position identifying unit  161  is oriented vertically (i.e., oriented toward the zenith).  FIG. 3A  shows the respective rotation axes of the first to third gimbals and the movable body incorporated in the tracking apparatus of  FIG. 1 , these rotation axes being assumed when the target position recognition unit of the apparatus is oriented horizontally.  FIG. 3B  shows the respective rotation axes of the first to third gimbals and the movable body, assumed when the target position recognition unit is oriented toward the zenith.  FIGS. 2A to 2D  show a case where the movable body  141  is oriented upward, i.e., the target position identifying unit  161  is oriented toward the zenith. 
     With reference to the coordinate system Σ 0  of the spherical body  150 , the first, second, third and fourth rotation axes  110 ,  120 ,  130  and  140  of the first, second, third and fourth gimbals  111 ,  121  and  131  and the movable body  141  are set. The angle sensors are provided in association with these rotation axes. The first angle sensor  112  detects the rotation angle θ 1  of the first gimbal  111  relative to the spherical body  150 . The second angle sensor  122  detects the rotation angle θ 2  of the second gimbal  121  relative to the first gimbal  111 . The third angle sensor  132  detects the rotation angle θ 3  of the third gimbal  131  relative to the second gimbal  121 . The fourth angle sensor  142  detects the rotation angle θ 4  of the movable body  141  relative to the third gimbal  131 . Further, the aforementioned rotary spring driving mechanism  181  is provided in association with the third rotation axis  130 . This mechanism has a restoring force for returning, to the center of the rotation range, the third gimbal  131  that can be externally rotated. In other words, the mechanism returns the third gimbal  131  to its initial position assumed when no external force is exerted on the gimbal  131 . 
     Referring to  FIG. 4 , a description will be given of the position of the movable body  141  relative to the spherical body  150 . 
     The rotation axes have the same intersection, and are therefore associated, only in rotation transform, with the coordinate system Σc of a camera that serves as the target position identifying unit  161  and is provided on the movable body  141 . Accordingly, the movable body  141  is positioned on a spherical coordinate system associated with the spherical body  150 . 
     Referring then to  FIGS. 5A to 5D , the relationship between the spherical body  150 , the omni-wheels and driving directional vectors will be described. 
       FIG. 5A  is a front view corresponding to  FIG. 2B , and  FIG. 5B  is a top view corresponding to  FIG. 2D .  FIG. 5B  shows a state in which the movable body  141  is oriented upward, and the coordinate system Σ 0  of the spherical body  150  coincides with that Σc of the camera. A description will now be given of an instance where, for example, the spherical body  150  has a radius of R, and three omni-wheels i (i=1 to 3) are attached to the spherical body at an attachment angle of φ with respect to the z 0  axis extending toward the zenith, and arranged at regular circumferential intervals of 120 degrees. The coordinates P i  (i=1 to 3) of contacts between the spherical body  150  and each wheel i are given by
 
 P   1   =[R ·sin φ 0  R ·cos φ]
 
 P   2 =└−½· R ·sin φ {square root over (3)}/2· R ·sin φ  R ·cos φ┘
 
 P   2 =└−½· R ·sin φ −{square root over (3)}/2· R ·sin φ  R ·cos φ┘  [1]
 
     Further, the driving-directional vector s i  (i=1 to 3) of each contact is given by
 
s 1 =[0 −1 0]
 
 s   2 =└√{square root over (3)}/2 ½ 0┘
 
 s   3 =└√{square root over (3)}/2 ½ 0┘  [2]
 
     Using these relationships, the relationship between the angular velocity ω j  (j=x, y, z), expressed by └ω x  ω y  ω z ┘, of the movable body  141  about the axes (x, y, z) of the camera coordinate system, and the circumferential velocity vsi (i=1 to 3) of each wheel i is given by 
     
       
         
           
             
               
                 
                   
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     From this equation, the rotational speed of the motor, used to detect the angular velocity of the movable body  141  on the coordinate system of the camera provided on the movable body  141 , can be determined. 
     For instance, to rotate the movable body  141  in the x-direction, angular velocity ω y  about the axis y is applied to the movable body  141 . At this time, from the equation [3], vsi (i=1 to 3) is given by
 
( vs 1,  vs 2,  vs 3)=(0, √{square root over (3)}/2 cos φ, −√{square root over (3)}/2 cos φ)
 
     In this case, the wheels ( 152  and  153 ) are rotated so that the motor rotational direction corresponding to vector s 2  is opposite to the motor rotational velocity corresponding to vector s 1 , as is shown in  FIG. 5C . 
     Further, to rotate the movable body  141  in the y-direction, angular velocity  ω x about the axis x is applied to the movable body  141 . At this time, from the equation [3], vsi (i=1 to 3) is given by
 
( vs 1,  vs 2,  vs 3)=(cos φ, −½ cos φ, −½ cos φ)
 
     In this case, the wheels ( 151 ,  152  and  153 ) are rotated so that the motor rotational direction corresponding to vector s 2  is opposite to the motor rotational velocity corresponding to vector s 1 , and the absolute value of vectors s 2  and s 3  is half that of vector s 1 , as is shown in  FIG. 5D . 
     Referring then to  FIGS. 6A to 6D , a description will be given of changes in the attitudes of the gimbals assumed when the movable body  141  is driven by the spherical driving units along the inner surface of the spherical body  150 . 
       FIGS. 6A to 6D  show a case where the movable body  141  shifts from an upward oriented state to a rearward oriented state, i.e., a diagonally leftward oriented state ((X, Y, Z)=(−1, 1, 0)). As in  FIG. 2B , the frontward direction is set as the negative Y direction.  FIG. 6A  shows an initial state where if the movable body  141  is upward oriented, the third gimbal  131  is also upward oriented. When the movable body  141  starts to be moved diagonally leftward by the operations of the spherical driving units, the first to third gimbals coupled to the movable body  141  are driven in accordance with the motion of the movable body  141 , as is shown in  FIG. 6B . At this time, the third gimbal  131  closest to the movable body  141  initially rotates. When the diagonally leftward motion of the movable body  141  advances as shown in  FIG. 6C , the first and second gimbals also rotate about their respective axes. At this time, the rotation spring associated with the third rotation axis  130  is driven to produce a restoration force for returning the third rotation axis  130  to the center of its rotation range. This restoration force is distributed to the first and second gimbals  111  and  121  to rotate them. When the motion of the movable body  141  further advances as shown in  FIG. 6D , a state is assumed in which the third gimbal  131  is returned to the center of the rotation range, and only the first and second gimbals  111  and  121  can rotate (in accordance with the motion of the movable body  141 ). As described above, the tracking apparatus of the first embodiment has a passive redundancy caused by driving the rotation spring in association with the third rotation axis  130 . This feature enables the first to third gimbals to be driven by the motion of the movable body  141  even when the third gimbal  131  is oriented toward the zenith or its vicinity. 
     Referring to  FIG. 7 , the relationship between the viewing field of a camera image and a target will be described. 
     When a target is captured within the viewing field of a camera as the target position identifying unit  161  on the movable body  141 , using the coordinate system Σc of the camera, tracking error detection values (ΔX, ΔY) as the amounts deviated from the center of the camera are acquired. In general, the tracking error detection values are acquired by calculating the center of gravity associated with a characterizing point obtained from image information. 
     Referring to  FIG. 8 , a tracking control system according to the first embodiment will be described.  FIG. 8  is a block diagram illustrating the tracking control system for tracking a moving target. 
     When the movable body  141  is driven on the inner surface of the spherical body  150  by the spherical driving units, the target position identifying unit  161  on the movable body  141  is swung to acquire image data including a target, thereby acquiring tracking error detection values (ΔX, ΔY) as position data concerning the target. Further, in accordance with the swing motion of the movable body  141 , the first to third gimbals  111  to  131  are driven. At this time, since the gimbals  111 ,  121  and  131  and the movable body  141  are provided with the first, second, third and fourth angle sensors  112 ,  122 ,  132  and  142 , angle data (Θ 1 , θ 2 , θ 3  and θ 4 ) indicating the attitude of the movable body  141  is obtained. 
     Based on the tracking error detection values and the angle data, the control unit  163  generates angular velocity instructions for driving the spherical driving units. 
     To control the movable body  141  so as to make the target position identifying unit  161  track a target, it is necessary to cause the coordinate system of the camera to coincide with that of the driving directional vector, and to perform tracking control for generating angular velocities that reduce tracking errors. Assuming that the tracking error detection values (ΔX, ΔY) are inputs, and tracking gain K C  as a tracking proportional gain is a constant, angular velocity instruction ω jr  (j=x, y, z) for the movable body  141  is given by 
     
       
         
           
             
               
                 
                   
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                               Y 
                             
                           
                         
                         
                           
                             
                               Δ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               X 
                             
                           
                         
                         
                           
                             0 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   [ 
                   4 
                   ] 
                 
               
             
           
         
       
     
     Further, it is necessary to orient the movable body  141  toward a target where the target position identifying unit  161  does not catch the target. Assuming that the position vector of the target is (eT_x, eT_y, eT_z), the relationship between the position vector of the target (eT_x, eT_y, eT_z) and the angles (θ r1 , θ r2 ) of the target on an easily designated spherical coordinate system is expressed by the following equations [5]: 
     
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           eT_x 
                           = 
                           
                             cos 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 θ 
                                 
                                   r 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                               
                               · 
                               cos 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               θ 
                               
                                 r 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           eT_y 
                           = 
                           
                             cos 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 θ 
                                 
                                   r 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                               
                               · 
                               sin 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               θ 
                               
                                 r 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           eT_z 
                           = 
                           
                             sin 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               θ 
                               
                                 r 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   5 
                   ] 
                 
               
             
           
         
       
     
     Since the tracking apparatus of the first embodiment comprises angle sensors corresponding to the gimbals, the orientation of the movable body  141  can be detected. Assume here that angle data corresponding to the first, second and third gimbals  111 ,  121  and  131  and the movable body  141  are set to θ 1 , θ 2 , θ 3  and θ 4 , respectively. The position vector of the target in the coordinate system Σ 0  of the spherical body  150  is the sum of the visual axis vector from the origin of the coordinate system Σ 0  to the origin of the coordinate system Σc of the camera, and the virtual tracking error vector (dltX, dltY) of the target position in the virtual camera coordinate system Σc associated with the virtual gimbals. The coordinate transform matrices  0 R 1 ,  1 R 2 ,  2 R 3 ,  3 R 4 ,  4 R c  corresponding to the rotation axes are expressed by the following equations [6]: 
     
       
         
           
             
               
                 
                   
                     
                       R 
                       1 
                         
                         
                         
                       0 
                     
                     = 
                     
                       [ 
                       
                         
                           
                             
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ1 
                             
                           
                           
                             
                               
                                 - 
                                 sin 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                           
                             0 
                           
                         
                         
                           
                             
                               sin 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                           
                             
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             1 
                           
                         
                       
                       ] 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       R 
                       2 
                         
                         
                         
                       1 
                     
                     = 
                     
                       
                         [ 
                         
                           
                             
                               1 
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               1 
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 - 
                                 1 
                               
                             
                             
                               0 
                             
                           
                         
                         ] 
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             
                               
                                 cos 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 θ2 
                               
                             
                             
                               
                                 
                                   - 
                                   sin 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 θ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 sin 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 θ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                             
                               
                                 cos 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 θ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               1 
                             
                           
                         
                         ] 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       R 
                       3 
                         
                         
                         
                       2 
                     
                     = 
                     
                       
                         [ 
                         
                           
                             
                               1 
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               
                                 - 
                                 1 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               1 
                             
                             
                               0 
                             
                           
                         
                         ] 
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             
                               
                                 cos 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 θ3 
                               
                             
                             
                               
                                 
                                   - 
                                   sin 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 θ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 3 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 sin 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 θ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 3 
                               
                             
                             
                               
                                 cos 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 θ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 3 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               1 
                             
                           
                         
                         ] 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       R 
                       4 
                         
                         
                         
                       3 
                     
                     = 
                     
                       
                         [ 
                         
                           
                             
                               1 
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               1 
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 - 
                                 1 
                               
                             
                             
                               0 
                             
                           
                         
                         ] 
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               1 
                             
                           
                           
                             
                               0 
                             
                             
                               1 
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 - 
                                 1 
                               
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                         
                         ] 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       R 
                       c 
                         
                         
                         
                       4 
                     
                     = 
                     
                       [ 
                       
                         
                           
                             
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ4 
                             
                           
                           
                             
                               
                                 - 
                                 sin 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               4 
                             
                           
                           
                             0 
                           
                         
                         
                           
                             
                               sin 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               4 
                             
                           
                           
                             
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               4 
                             
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             1 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   [ 
                   6 
                   ] 
                 
               
             
           
         
       
     
     The transform matrix from the coordinate system Σ 0  of the spherical body  150  to the camera coordinate system Σc is given by
 
 0 R c = 0 R 1   1 R 2   2 R 3   3 R 4   4 R c   [7]
 
     From the above relationships, the relationship between the inner product of the position vector of the target and the attitude of the tracking mechanism, and the position vector of the target is given by 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             dot_eT 
                             ⁢ 
                             _eX 
                           
                         
                       
                       
                         
                           
                             dot_eT 
                             ⁢ 
                             _eY 
                           
                         
                       
                       
                         
                           
                             dot_eT 
                             ⁢ 
                             _eE 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           R 
                           c 
                             
                             
                             
                           0 
                         
                         ) 
                       
                       
                         - 
                         1 
                       
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             eT_x 
                           
                         
                         
                           
                             eT_y 
                           
                         
                         
                           
                             eT_z 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   [ 
                   8 
                   ] 
                 
               
             
           
         
       
     
     where dot_eT_eX represents the inner product of the position vector eT of the target and the horizontal unit vector eX of the camera associated with the gimbals, dot_eT_eY represents the inner product of the position vector eT of the target and the vertical unit vector eY of the camera associated with the gimbals, and dot_eT_eE represents the inner product of the position vector eT of the target and the unit vector eE of the visual axis vector of the camera associated with the gimbals. Further, |eT|=|eE|=1. 
     Accordingly, the virtual tracking error values (dltX, dltY) of the target position in the virtual camera coordinate system Σc associated with the virtual gimbals are given by
 
 dltX =dot —   eT   —   eX /dot —   eT   —   eE  
 
 dltY =dot —   eT   —   eY /dot —   eT   —   eE   [9]
 
     By substituting the virtual tracking error values (dltX, dltY) for the inputs (ΔX, ΔY) of the equation [4] to thereby apply the angular velocity generation rule expressed by the equation [4], orientation toward the position of the target can be realized. 
     Referring then to  FIG. 9 , a description will be given of a tracking system employed in the first embodiment for applying light to a target. 
       FIG. 9  is a view illustrating a light guiding system  902  provided inside the first, second and third gimbals  111 ,  121  and  131 , and the movable body  141 .  FIG. 9  is a front view similar to  FIG. 2B .  FIG. 9  is a schematic sectional view of the spherical body  150 , the first, second and third gimbals  111 ,  121  and  131 , and the movable body  141 . Inside the first, second and third gimbals  111 ,  121  and  131 , there are provided mirrors  901 , a light guiding path and a light source  903 , which form a coude optical system, and the light guiding path extends through the movable body  141  to guide the light emitted from the light source  903 . In the example of  FIG. 9 , the first gimbal  111  has three mirrors  901 , and the third gimbal  131  has one mirror  901 , and the light guiding path is indicated by the thick broken line. The light guiding path is formed of, for example, a hollow member, or a transparent material for permitting desired light to pass. 
     When the gimbals are rotated in accordance with the swing motion of the movable body  141 , the mirrors  901  rotate in accordance with the attitudes of the gimbals. By guiding light from the base  110  side through the coude optical system, the light can be applied to a target regardless of the attitude of the movable body  141 . Although in the optical system of the first embodiment, light is emitted from the center of the movable body  141 , the optical axis of the movable body  141  can be changed by forming another light guiding path in the body. Further, if the optical system is provided in a reverse manner, the tracking apparatus may be modified such that light is guided from the movable body  141  and received by a target position identifying unit (such as a camera) provided on, for example, the base, instead of on the movable body  141 . 
     In the above-described first embodiment, since a target is tracked using the spherical driving units, the problem of gimbal lock can be avoided, and since each driving axis does not require a high angular velocity, the whole apparatus can be made compact and light. Further, since the orientation of the camera can be detected using the gimbal mechanism driven in accordance with the swing motion of the movable body with, for example, a camera placed thereon, the camera serving as a target identifying sensor is permitted to automatically track the target in all directions. 
     Further, since the target identifying sensor formed of, for example, the camera is provided on the movable body, the position of the target detected from an image obtained by the camera is on the same coordinate system as that of the driving directional vector of the movable body, thereby simplifying the image tracking control rule. 
     Yet further, the orientation of the camera and the attitude of the movable body can be detected by the driven gimbal mechanism and the four angle sensors. By calculating a virtual tracking error obtained by the camera on the movable body with respect to a target position vector of an arbitrary direction, the camera can be oriented in an arbitrary direction. 
     Furthermore, by providing a coude optical system in the gimbal mechanism and the movable body coupled thereto, light can be applied to the target automatically tracked. 
     (Second Embodiment) 
     Referring to  FIGS. 10A and 10B , a description will be given of a tracking apparatus according to a second embodiment.  FIGS. 10A and 10B  schematically illustrate the tracking apparatus of the second embodiment.  FIG. 10A  is a perspective view obtained in the direction defined by vector (X, Y, Z)=(1, −1, 1), with the positive Z-direction set as the zenith direction.  FIG. 10B  is a front view obtained in the negative Y-direction. The tracking apparatus of the second embodiment differs from that of the first embodiment in that in the former, the movable body  141  is movable over the outer surface of a spherical body with the wheels of the movable body  141  kept in contact with the outer surface. 
     In addition to the movable body  141 , the tracking apparatus of the second embodiment comprises a spherical body  1001 , a cover  1002 , a drive hold unit  1003 , first, second and third gimbals  111 ,  121  and  131 , a base  101 , first, second, third and fourth angle sensors  112 ,  122 ,  132  and  142 , wheels  151 ,  152  and  153 , a target position identifying unit  161 , a tracking error detecting unit  162 , a control unit  163 , and first, second and third wheel driving units  171 ,  172  and  173 . Although  FIGS. 10A and 10B  do not show all components, elements similar to those shown in  FIG. 1  are incorporated in the tracking apparatus of the second embodiment. A description will now be given of only different elements. 
     The movable body  141  is provided outside the spherical body  1001 , and is kept in contact with the outer surface of the spherical body  1001  via the wheels  151 ,  152  and  153 . The movable body  141  is movable over the outer surface of the spherical body  1001 . As in the first embodiment, the spherical driving units and the target position identifying unit  161  are attached to the movable body  141 . The first, second and third gimbals  111 ,  121  and  131  are provided inside the spherical body  1001 , and operate in the same way as in the first embodiment. The movable body  141  is connected to the third gimbal via the drive hold unit  1003 . A rotary spring driving mechanism  181  is provided in associated with the third rotation axis  130 , as in the first embodiment. The rotary spring driving mechanism  181  returns the third gimbal  131  to the center of the rotation range thereof. The drive hold unit  1003  urges the spherical driving units of the third gimbal  131  against the spherical body  1001 . The drive hold unit  1003  connects the movable body  141  to the third gimbal  131  to permit the movable body  141  and the third gimbal  131  to freely rotate relative to each other. 
     The movable body  141  is connected to the third gimbal  131  via the drive hold unit  1003 . The movable body  141  is provided perpendicular to the third rotation axis  130 , and can rotate about a movable axis  140  as a movably supported fourth rotation axis. The movable body  141  includes, for example, a permanent magnet section, and the drive hold unit  1003  includes, for example, a coil. In this case, when a current is passed through the coil, the magnet serves as an electromagnet to connect the movable body  141  to the third gimbal  131 , and also to enable the drive hold unit  1003  to support the movable body  141  so that the movable body  141  can rotate about the movable axis  140 . Further, the movable body  141  is stuck to the spherical body  1001  by the attraction force of the electromagnet, thereby pressing the omni-wheels against the spherical body  1001 . 
     Since thus the omni-wheels are pressed against the spherical body  1001  with an appropriate force by the electromagnet of the drive hold unit  1003 , the spherical driving units can transfer the driving forces of the wheel driving units to the spherical body  1001  using the frictional forces between the spherical body  1001  and the omni-wheels. 
     In the second embodiment, since the movable body  141  exists outside the spherical body  1001 , the rotation angle of the movable body  141  about the movable axis  140  may be detected by a method different from that of the first embodiment. For instance, the fourth angle sensor  142  may be formed of, for example, an optical encoder. In this case, the rotation angle of the movable body  141  with respect to the third gimbal  131  is optically detected by permitting light through the spherical body  1001 . 
     Further, the cover  1002  has a size sufficient to cover the movable body  141 , the target position identifying unit  161 , the spherical driving units, the spherical body  1001  and the base  101 , and is formed of a material that permits the target position identifying unit  161  to identify a target. For example, the cover  1002  is formed of a transparent material that permits the light to be detected by the target position identifying unit  161 . 
     The second embodiment constructed as the above can provide the same advantage as the first embodiment. Since the gimbals are provided inside the spherical body and the movable body and the spherical driving units are provided outside the spherical body, the gimbals, and the movable body and spherical driving units, can be subjected to maintenance work individually. Further, since the gimbals are provided inside the spherical body and the movable body and the spherical driving units are provided outside the spherical body, the wiring of driving units (such as motors) included in the spherical driving units is prevented from being entangled with the gimbals. In contrast, in the first embodiment, since the gimbals, the movable body and the spherical driving units are provided inside the spherical body, the wiring, for example, is prevented from projecting therefrom. 
     Yet further, since in the embodiments, target tracking is possible without causing a great angular velocity about a particular rotation axis, the embodiments are applicable to a device, such as an image monitoring device, for tracking a moving object. In addition, since in the embodiments, light guiding is possible while the tracking apparatus is oriented in all directions, the embodiments are applicable to a device, such as a laser peening apparatus, a three-dimensional processor, and a video image display device, which are oriented to a light emission system. Also, since in the embodiments, the light or radiation received by the movable body  141  can be transmitted to a fixed section, such as the base, the embodiments are applicable to a device for orienting a light collective solar panel or a receiving antenna. 
     The embodiments are not limited to the above-described embodiments, but can be modified in various ways without departing from its scope. For instance, the embodiments are not limited to a triaxial gimbal structure, but can be easily modified to have such a redundancy as to couple the movable body  141  to a bi-axial gimbal structure via an elastic material. 
     While certain embodiments have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the inventions. Indeed, the novel embodiments described herein may be embodied in a variety of other forms; furthermore, various omissions, substitutions and changes in the form of the embodiments described herein may be made without departing from the spirit of the inventions. The accompanying claims and their equivalents are intended to cover such forms or modifications as would fall within the scope and spirit of the inventions.