Method and apparatus for representing motion of multiple-jointed object, computer graphic apparatus, and robot controller

Abstract

A bending angle of each joint of a multiple-jointed object is represented with a function expressed independently of a length between joints of the object. Based on the function, contour data is produced for a motion of each joint, which is then displayed on a screen. With this provision, it is unnecessary to generate again functions each time the object is changed in its size. Namely, the functions are independent of the size of the object. Since parameters of the functions can be altered to add characteristics to changes in the bending angles the respective joints, the object is actuated in an action having an emotional expression.

1 . A method of representing a motion of a multiple-jointed object in which an action of each articulation of the object is controlled so as to present the motion thereof on a screen, comprising the steps of: 
 attaining a bending angle of each said joint as a function independent of a length between joints of the object;    obtaining, based on the functions, data of a contour of the object in motion in response to an instruction; and    displaying the contour data on the screen.    
     
     
         2 . A method of representing a motion of a multiple-jointed object in which an action of each articulation of the object is controlled to present the motion thereof on a screen, comprising the steps of: 
 attaining a bending angle of each said joint as a function of time;    obtaining, based on the functions, data of a contour of the object in motion in response to an instruction; and    displaying the contour data on the screen.    
     
     
         3 . A method according to  claim 2  wherein the bending angle of each said joint is attained as a function of a phase difference, time, and an amplitude.  
     
     
         4 . A method of representing a motion of a multiple-jointed object in which an action of each articulation of the object is controlled so as to present the motion thereof on a screen, comprising the steps of: 
 attaining a bending angle of each said joint as a function independent of a length between joints of the object;    obtaining, based on the functions, data of a contour of the object in motion in response to an instruction;    displaying the contour data on a screen,    said step of achieving the display on the screen based the contour data being accomplished by altering values of the parameters of the functions.    
     
     
         5 . A method of representing a motion of a multiple-jointed object in which an action of each articulation of the object is controlled to present the motion thereof on a screen, comprising the steps of: 
 attaining a bending angle of each said joint as a function independent of a length between joints of the object;    specifying in response to an instruction a feature component to the function, the component indicating a change in each said joint in motion;    obtaining, based on the functions, data of a contour of the object in motion in response to an instruction; and    displaying the contour data in association with the feature component on a screen.    
     
     
         6 . A method of representing a motion of a multiple-jointed object in which an action of each articulation of the object is controlled so as to present the motion thereof on a screen, comprising the steps of: 
 attaining a bending angle of each said joint as the following function independent of a length between joints of the object;                      θ   m          (   t   )       =       D   m     +       ∑     n   =   1              A   mn     ·     sin        (       n   ·   t     +     Ψ   mn     -     φ     m   ·   n         )                     (   1   )                         D m : Direct current component    A mn : Amplitude of each frequency component    Ψ mn : Phase    m: Joint number    n: Higher harmonics of order n    Φ m : Phase difference of 1st order higher harmonics between reference joint and m-th joint (Φ m =0 for reference joint)      obtaining, from the function (1), data of a contour of the object in motion in response to an instruction; and    displaying the contour data on the screen.    
     
     
         7 . A method according to  claim 6  further including a step of changing a value of at least either one of the parameters D m , A mn , and Ψ mn  of the function (1), thereby varying the motion of the multiple-articulated object acting based on the function (1).  
     
     
         8 . A method according to  claim 7 , further including the following steps of: 
 establishing a correspondence between a variation range of the value of the parameter and the feature component indicating a change associated with an action of each said joint; and    specifying, in place of the variation range, the feature component, thereby altering the motion of each said joint.    
     
     
         9 . A method according to  claim 8  further including a step of changing a magnitude for the variation range based on the feature component.  
     
     
         10 . A computer graphic apparatus for presenting a motion of a multiple-hinged object on a screen in which an action of each joint of the object is controlled so as to present the motion thereof on the screen, comprising: 
 means for attaining a bending angle of each said joint as a function independent of a length between joints of the object;    means for obtaining, based on the functions, data of a contour of the object in motion in response to an instruction; and    means for displaying the contour data on the screen.    
     
     
         11 . A computer graphic apparatus for presenting a motion of a multiple-jointed object on a screen in which an action of each joint of the object is controlled so as to present the motion thereof on the screen, comprising; 
 means for attaining a bending angle of each said joint as a function of time;    means for obtaining, based on the functions, data of a contour of the object in motion in response to an instruction; and    means for displaying the contour data on the screen.    
     
     
         12 . An apparatus according to  claim 11  wherein the bending angle of each said joint is attained as a function of a phase difference, time, and an amplitude.  
     
     
         13 . A computer graphic apparatus for presenting a motion of a multiple-articulated object on a screen in which an action of each joint of the object is controlled so as to present the motion thereof on the screen, comprising; 
 means for attaining a bending angle of each said joint as a function independent of a length between joints of the object;    means for obtaining, based on the functions, data of a contour of the object in motion in response to an instruction;    means for displaying the contour data on a screen, and    means for altering values of the parameters of the functions, thereby changing the display on the screen based on the contour data.    
     
     
         14 . A computer graphic apparatus for presenting a motion of a multiple-hinged object on a screen in which an action of each joint of the object is controlled so as to present the motion thereof on the screen, comprising; 
 means for attaining a bending angle of each said joint as a function independent of a length between joints of the object;    means for specifying in response to an instruction a feature component to the functions, the component indicating a change in each said joint in motion;    means for obtaining, based on the functions, data of a contour of the object in motion in response to an instruction; and    means for displaying the contour data in association with the feature component on a screen.    
     
     
         15 . A computer graphic apparatus for presenting a motion of a multiple-hinged object on a screen in which an action of each joint of the object is controlled so as to present the motion thereof on the screen, comprising; 
 store means for storing therein a bending angle of each said joint as the following function independent of a length between joints of the object;                      θ   m          (   t   )       =       D   m     +       ∑     n   =   1              A   mn     ·     sin        (       n   ·   t     +     Ψ   mn     -     φ     m   ·   n         )                     (   1   )                         D m : Direct current component    A mn : Amplitude of each frequency component    Ψ mn : Phase    m: Joint number    n: Higher harmonics of order n    Φ m : Phase difference of 1st order higher harmonics between reference joint and m-th joint (Φ m =0 for reference joint)      means for obtaining, based on the function (1), data of a contour of the object in motion in response to an instruction; and    means for displaying the contour data on the screen.    
     
     
         16 . A computer graphic apparatus for presenting a motion of a multiple-hinged object on a screen in which an action of each joint of the object is controlled so as to present the motion thereof on the screen, comprising; 
 store means for storing therein a bending angle of each said joint as the following function independent of a length between joints of the object;                      θ   m          (   t   )       =       (       D   m     +     d   m       )     +       ∑     n   =   1            [         (       A   mn     +     a   mn       )     ·   sin          {       n   ·   t     +     (       Ψ   mn     +     Ψ   mn       )     -       φ   mn     ·   n       }       ]                 (   2   )                         D m : Direct current component    A mn : Amplitude of each frequency component    Ψ mn : Phase    m: Joint number    n: Higher harmonics of order n    Φ m : Phase difference of 1st order higher harmonics between reference joint and m-th joint (Φ=0 for reference joint)    d m : Direct current component of qualification component    a mn : Qualification component of each frequency component    ψ mn : Phase component of qualification component      means for setting and for changing values of d mn , a mn , and ψ mn ;    means for obtaining, based on the function (2), data of a contour of the object in motion in response to an instruction; and    means for displaying the contour data on the screen.    
     
     
         17 . An apparatus according to  claim 16  further including: 
 a table for storing therein preset/change values respectively of d m , a mn , and ψ mn  of the function (2) and feature components indicating a change of each said joint in motion with correspondences established therebetween; and  
 means for referencing said table based on a specification of the feature components, thereby determining the preset/change values of d m , a mn , and ψ mn .  
 
     
     
         18 . A computer graphic apparatus for presenting a motion of a multiple-hinged object on a screen in which an action of each joint of the object is controlled so as to present the motion thereof on the screen, comprising; 
 store means for storing therein a bending angle of each said joint as the following function independent of a length between joints of the object;                            θ   m          (   t   )       =                  (       D   m     +       α   m     ·     d   m         )     +         β   m     _     ·       ∑     n   =   1            [       (       A   mn     +       α   m     ·     a   mn         )     ·                                      sin        {       n   ·   t     +     (       Ψ   mn     +       α   m     ·     ψ   mn         )     -     φ     mn   ·   n         }       ]                 (   3   )                         D m : Direct current component    A mn : Aplitude of each frequency component    Ψ mn : Phase    m: Joint number    n: Higher harmonics of order n    Φ m : Phase difference of 1st order higher harmonics between reference joint and m-th joint (Φ m =0 for reference joint)    d m : Direct current component of qualification component    a mn : Qualification component of each frequency component    ψ mn : Phase component of qualification component    α m , β m : Magnitude      means for setting and for changing values of the magnitudes α m  and β m ;    means for attaining a value of the function (3) for each said joint;    means for obtaining, based on the function (3), data of a contour of the object in motion in response to an instruction; and    means for displaying the contour data on the screen.    
     
     
         19 . A computer graphic apparatus for presenting a motion of a multiple-hinged object on a screen in which an action of each joint of the object is controlled so as to present the motion thereof on the screen, comprising; 
 store means for storing therein a bending angle of each said joint as the following function independent of a length between joints of the object;                            θ   m          (   t   )       =                  (       D   m     +       ∑   i            α     m                 i       ·     d     m                 i             )     +       β   m     ·       ∑     n   =   1            [       (       A   mn     +       ∑   i            α     m                 i       ·     a   mni           )     ·                                      sin        {       n   ·   t     +     (       Ψ   mn     +       ∑   i            α   mi     ·     ψ   mni           )     -     φ     mn   ·   n         }       ]                 (   4   )                         D m : Direct current component    A mn : Amplitude of each frequency component    Ψ mn : Phase    m: Joint number    n: Higher harmonics of order n    Φ m : Phase difference of 1st order higher harmonics between reference joint and m-th joint (Φ m =0 for reference joint)    d mi : Direct current components of respective kinds of qualification components    a mi : Qualification components of different kinds for each frequency component    ψ mi : Phase components of respective kinds of qualification components    α mi : Magnitude of each qualification component    β m : Magnitude of amplitude      means for setting and for changing values of α mi  and β mi ;    means for setting and for changing values of d mi , a mni , and Φ mni ;    means for attaining a value of the function (4) for each said joint;    means for obtaining, based on the function (4), data of a contour of the object in motion in response to an instruction; and    means for displaying the contour data on the screen.    
     
     
         20 . An apparatus according to  claim 19  further including: 
 a table for storing therein preset and change values of d mi , a mni , and Φ mni  (i varies for each feature component) of the function (4) and the feature component denoting a change of each said joint in motion with correspondences established therebetween; and  
 means for referencing said table depending on a specification of the feature component, thereby determining the values of d mi , a mni , and Φ mni .  
 
     
     
         21 . A robot motion control method in which operational instructions are supplied to a multiple-articulated robot so as to actuate the robot in a desired motion, comprising the steps of: 
 attaining a bending angle of each joint of the robot as a function independent of a length between joints thereof;    obtaining positional data of each said joint based on the function;    creating an operational instruction for the robot depending on the positional data; and    driving the robot based on the operational instruction.    
     
     
         22 . A robot motion control apparatus in which operational instructions are supplied to a multiple-articulated robot so as to actuate the robot in a desired motion, comprising: 
 store means for storing therein a bending angle of each joint of the robot as a function independent of a length between joints thereof;    means for obtaining positional data of each said joint based on the function;    means for generating an operational instruction for the robot depending on the positional data; and    means for driving the robot based on the operational instruction.    
     
     
         23 . An apparatus for representing a motion of a multiple-jointed object in which an action of each joint of the object is controlled so as to present the motion thereof on a screen, comprising: 
 store means for storing therein a plurality of primary functions of time designating actions of respective joints of the object;    select means for selecting, from the plural primary functions of time, a plurality of primary functions of time;    computation means for achieving, based on the selected primary functions of time, a computation of at least a secondary function of time; and    output means for outputting, based on the secondary function of time, a motion of the multiple-jointed object.    
     
     
         24 . An apparatus according to  claim 23  wherein said computation means achieves, based on a mean value of the selected plural primary functions of time, the computation of at least a secondary function of time.  
     
     
         25 . An apparatus according to  claim 24  wherein the mean value is obtained by applying magnitudes to the respective primary functions of time.  
     
     
         26 . An apparatus according to  claim 23  wherein said output means is display means.  
     
     
         27 . An apparatus for representing a motion of a multiple-jointed object in which a route of a movement of the object is created, comprising: 
 input means for inputting therefrom information designating a first position of the movement of the object, information denoting at least either one of a speed of the object and a direction of the movement thereof at the first point, information indicating a last position of the movement of the object, and information denoting at least either one of a speed of the object and a direction of the movement thereof at the last point; and    computation means for achieving computations, based on the four kinds of information, to attain information designating a path of the movement of the object from the first position to the last position.    
     
     
         28 . An apparatus according to  claim 27  further including display means for displaying the information designating a path of the movement of the object from the first position to the last position.  
     
     
         29 . An apparatus according to  claim 28  wherein said display means displays the information designating a first position of the movement of the object and the information indicating a last position of the movement of the object.  
     
     
         30 . An apparatus according to  claim 28  wherein said display means displays the information denoting at least either one of a speed of the object and a direction of the movement thereof at the first point and the information denoting at least either one of a speed of the object and a direction of the movement thereof at the last point.  
     
     
         31 . An apparatus according to  claim 27  wherein the information denoting at least either one of a speed of the object and a direction of the movement thereof at the first point and the information denoting at least either one of a speed of the object and a direction of the movement thereof at the last point are vector information.  
     
     
         32 . An apparatus for representing a motion of a multiple-jointed object in which a route of a movement of the object is created, comprising: 
 input means for inputting therefrom information. associated with a position of the object in the movement and information designating a direction of the movement of the object; and    computation means for achieving computations, based on the information associated with a position of the object in the movement and the information indicating a direction of the movement of the object, to attain information designating a path of the movement of the object being moved.    
     
     
         33 . An apparatus according to  claim 32  further including store means for storing therein the information associated with a position of the object in the movement and the information of a direction of the movement of the object.  
     
     
         34 . An apparatus according to  claim 32  wherein the information denoting a direction of the movement of the object is information indicating a direction of the object in the movement relative to a desired point in a coordinate system or to another multiple-jointed obejct.  
     
     
         35 . An apparatus according to  claim 32  wherein the information denoting a direction of the movement of the object is information indicating a direction of the object in the movement relative to a desired line in a coordinate system.  
     
     
         36 . An apparatus according to  claim 32  wherein the information denoting a direction of the movement of the object is information indicating a direction of the object in the movement relative to a desired plane in a coordinate system.  
     
     
         37 . An apparatus according to  claim 32  wherein the information denoting a direction of the movement of the object is information indicating a direction of the object in the movement relative to a preceding direction of the movement of the object.  
     
     
         38 . A motion representing apparatus for representing with functions of time an action of each joint of a multiple-jointed object, comprising: 
 means for specifying transit points of the object;    path generate means for generating a path along which the object moves between specified transit points; and    output means for outputting a motion of the object passing a specified transit point.    
     
     
         39 . A motion representing apparatus for representing with functions of time an action of each joint of a multiple-jointed object comprising: 
 means for specifying transit points of the object;    path generate means for generating a path along which the object moves between specified transit points; and    output means for outputting a motion of the object passing a point in the proximity of a specified transit point.    
     
     
         40 . An apparatus according to  claim 38  further including means for drawing a curved line between the specified transit points and for allowing the object to move along the curved line between the specified transit points.  
     
     
         41 . An apparatus according to  claim 38  further including: 
 means for drawing a curved line between the specified transit points to allow the object to move along the curved line between the specified transit points;  
 means operative, when the object moves along the generated curved line, for minimizing a stride width of a foot of the object on a side of a radius of curvature and for increasing a stride width of a foot thereof on a side opposite thereto of a radius of curvature depending on a radius of curvature of the curved line where the object is moving; and  
 means for preventing each said foot from slipping on a tangential plane of the curved line, thereby controlling the object to move along the curved line without causing any foot slip.  
 
     
     
         42 . A motion representing apparatus for representing with functions of time an action of each joint of a multiple-jointed object comprising: 
 means operative, when the object moves along a curve, for detecting or computing a radius of curvature of the curve;    means for detecting or computing a speed of the movement of the object;    means for computing a centrifugal force based on the radius of curvature and the speed; and    means for correcting the functions of time, thereby establishing an equilibrium state between the centrifugal force and a gravity applied onto the object.    
     
     
         43 . An apparatus according to  claim 42  further including means for altering information related to the gravity.  
     
     
         44 . A motion representing apparatus for representing with functions of time an action of each joint of a multiple-jointed object, comprising: 
 means for specifying a plurality of points in a space;    means for inputting therefrom information related to a number of steps; and    output means for outputting the motion of the object moving with a specified number of steps between a plurality of specified number of positions.    
     
     
         45 . A motion representing apparatus for representing with functions of time an action of each joint of a multiple-jointed object, comprising: 
 means for specifying a plurality of points of time;    means for inputting therefrom information related to a number of steps; and    output means for outputting the motion of the object moving with a specified number of steps between a plurality of specified number of points of time.    
     
     
         46 . A motion representing apparatus for representing with functions of time an action of each joint of a multiple-jointed object comprising, output means for outputting the motion of the object which takes a specified posture at a specified position during the movement.  
     
     
         47 . A motion representing apparatus for representing with functions of time an action of each joint of a multiple-jointed object comprising, output means for outputting the motion of the object which takes a specified posture at a specified point of time during the movement.  
     
     
         48 . A motion representing apparatus for representing with functions of time an action of each joint of a multiple-jointed object, comprising: 
 means for representing with the functions of time the motion of the object in a specified space;    means for achieving an interpolation on a function of time representing the motion of the object in a space assigned with a function of time representing a motion between specified spaces, the interpolation being conducted by use of a distance between the spaces, thereby generating a function of time representing the motion of the object at an intermediate point; and    output means for outputting a motion of the object, the motion changing in a specified interval in substantially a continuous manner.    
     
     
         49 . A motion representing apparatus for representing with functions of time an action of each joint of a multiple-jointed object, comprising: 
 means for representing with the functions of time a motion of the object in a specified point of time;    means for achieving an interpolation on a function of time representing a motion of the object at a point of time assinged with a function of time representing a motion between specified points of time, the interpolation being conducted by use of a period of time between the points of time, thereby generating a function of time representing the motion of the object at an intermediate point of time; and    output means for outputting a motion of the object, the motion changing in a specified interval in substantially a continuous manner.    
     
     
         50 . A motion representing apparatus for representing with functions of time and by use of a key frame method an action of each joint of a multiple-jointed object, comprising: 
 means for separating from the representation of functions of time actions of particular joints of the object, thereby creating the actions of the separated joints in the key frame method; and    means for combining a representation of functions of time with a representation obtained by the key frame method, thereby processing a motion of the object.    
     
     
         51 . An apparatus according to  claim 50  further including means for transforming the motions produced in the key frame method into functions of time and for memorizing therein the functions of time.  
     
     
         52 . A motion representing apparatus for representing with functions of time and by use of a key frame method an action of each joint of a multiple-jointed object, comprising: 
 means for measuring an action of said each joint of the object;    means for transforming the measured action of said each joint into a function of time; and    output means for outputting a motion of the object depending on the function of time.    
     
     
         53 . An apparatus according to  claim 52  wherein said transformation means corrects the measured action of said each joint of the object and then transforms the corrected action into a function of time.  
     
     
         54 . A motion representing apparatus for representing with functions of time an action of each joint of a multiple-jointed object, wherein actions of respective joints of the object are generated in a key frame method and then the obtained actions are transformed into functions of time, thereby outputting a motion of the object.  
     
     
         55 . A motion representing apparatus for representing with functions of time an action of each joint of a multiple-jointed object, wherein when a motion of the object is selected, functions of time are created for all of said joints by use of a group of functions of time representing an identical action, thereby producing a motion of the object.  
     
     
         56 . A motion representing apparatus for representing with functions of time an action of each joint of a multiple-jointed object, wherein when a motion of the object is selected, functions of time are created for all of said joints by use of a group of functions of time representing an identical action and/or different actions, thereby generating a motion of the object.  
     
     
         57 . A computer graphic system achieving computer graphics comprising: 
 a motion representing apparatus according to claim  23 ; and    a display for displaying the motion of the multiple-articulated object.    
     
     
         58 . A robot control system comprising: 
 a motion representing apparatus according to claim  23 ; and    a robot being driven in association with the motion of the object.    
     
     
         59 . An apparatus according to  claim 23  wherein the primary functions of time are components of a function of time.