JPH05298422A - Motion generating method for articulated structure - Google Patents

Abstract

PURPOSE:To provide a method suitable for the generation of the motion of an articulated structure especially using a key frame in respect of the method for generating the motion of a three-dimensional object. CONSTITUTION:A specified partial structure 102 in a specified section 108 is selected from among the sections 107, 108 determined by the neighboring key frame 101 and the partial structures 102, 103 of the articulated structure, and the data 106 of the joint angle of a joint 104 contained in a selected part is obtained by using dynamical arithmetic operation in the case that the joint torque of the joint 104 is made zero, and processing to multiply joint angular velocity by a real number and the processing to limit the joint angle within a range from a lower limit value 112 to an upper limit value 109 are executed for the obtained data, and the data 105 of the other motion is obtained by interpolating mathematically the joint angle at the key frame 101. Thus, the realistic motion of the articulated structure taking dynamics into consideration can be easily generated from the key frame.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for generating a motion of a three-dimensional object, and more particularly to a method suitable for motion generation using a key frame of an articulated structure.

[0002]

2. Description of the Related Art In the field of computer graphics, when moving a three-dimensional object, dynamics may be considered in order to obtain a realistic movement. In particular, dynamic calculations are often useful when generating the movement of a multi-joint structure having a large number of joints and moving according to changes in the joint angles.

When performing mechanical calculations on articulated structures, joint angles, joint angular velocities, and joint angular accelerations, as discussed in Measurement and Control, 25, 1 (1986), pages 23-29. The inverse dynamics calculation for obtaining the joint torque from the joint and the dynamics calculation for obtaining the joint angular acceleration from the joint angle, the joint angular velocity, and the joint torque are used.

[0004]

In order to obtain a realistic movement, not only the inverse dynamics calculation but also the dynamics calculation is required. However, it was difficult to give a condition that a movement obtained by dynamic calculation has a certain posture at a certain time. Further, in the dynamic calculation, it is necessary to input an unintuitive physical quantity such as a joint torque. Therefore, the motion obtained by the dynamic calculation is more realistic than the motion obtained by using the key frame, but it is difficult to control the detailed motion.

An object of the present invention is to provide a motion generating method capable of easily generating a realistic motion in consideration of dynamics from a key frame in a motion generating process of an articulated structure.

[0006]

In order to achieve the above object, a section defined by adjacent key frames,
A specific partial structure in a specific section is selected from the partial structures of the multi-joint structure, and the motion data of the partial structure in the selected section is joint torque of the joint included in the partial structure. Is calculated by using a dynamics calculation when zero is set, and the obtained data is subjected to a process of multiplying the joint angular velocity by a real number and a process of keeping the joint angle within the range of the lower limit value to the upper limit value, and the selection is made. The data of the movement of the partial structure in the unrestricted section is obtained by mathematically interpolating the joint angle in the key frame of the joint included in the partial structure.

[0007]

By using the dynamic calculation when the joint torque is zero, it is possible to generate the movement when the active joint torque is not applied to the joint, that is, the movement of the multi-joint structure due to inertia. By performing a process of multiplying the joint angular velocity by a real number, the effect of friction acting on the joint can be taken into consideration. By performing the process of keeping the joint angle within the range from the lower limit value to the upper limit value, it is possible to obtain the movement of the joint having the limit in the joint angle. By mathematically interpolating the joint angle, a smooth motion can be obtained in a portion where the dynamic calculation is not used, and the joint angle and the joint angular velocity that are given as initial values when performing the dynamic calculation are calculated by the keyframe. Can be easily adjusted by. As described above, it is possible to easily generate a realistic motion considering dynamics from a key frame.

[0008]

DESCRIPTION OF THE PREFERRED EMBODIMENTS The concept of the processing of the present invention is shown in FIG. 1 and the outline of the processing is shown in FIG.

A key frame (101) consisting of data of each joint angle at a certain time of the multi-joint structure is given.
The interval defined by adjacent keyframes (107,10
A specific partial structure (102) in a specific section (108) is selected from 8) and partial structures (102, 103) included in the multi-joint structure. A motion calculation program (204) for the multi-joint structure is used to calculate the dynamics of the joint angle data (106) of the joint (104) included in the selected partial structure (102) in the selected section (108). Ask for
The joint angle data (105) of the joint (104) included in the unselected substructures (102, 103) in the unselected section (107) is obtained by mathematically interpolating the joint angle in the key frame (101). .. By the program 204, the keyframe data (201) of the articulated structure, which is a set of keyframes (101), and the selected section (10
List of selected substructures (102) in (8) (20)
2) and 1 frame data (203) of the multi-joint structure, which is a set of joint angles at a certain time, are sequentially obtained.

A method of using the dynamics calculation will be briefly described. First, the joint angular acceleration when the joint torque of the joint (104) at a certain moment (116) is set to zero is calculated.
The temporary joint angular velocity (113) at the next moment (117) is obtained from the joint angular velocity of 4). Next, the temporary joint angular velocity (1
13) is multiplied by a real value of 0 or more and 1 or less to obtain a corrected joint angular velocity (114) at the next moment (117), and from this and the joint angle (111) of the joint (104), the next moment ( Calculate the temporary joint angle (110) in 117). Temporary joint angle (110)
Is the lower limit (112) to the upper limit (10) of the joint angle of the joint (104)
If it is within the range up to 9), the provisional joint angle (110) is taken as the joint angle at the next moment (117). Temporary joint angle (1
If 10) is outside the range from the lower limit (112) to the upper limit (109), the dynamics are adjusted so that the provisional joint angle (110) matches the lower limit (112) or the upper limit (109). Repeat the calculation using the calculation. By accumulating the data (115) obtained as a result of the above calculation, the joint angle data (106) is obtained.
The list 202 includes real values to be multiplied by the values required when using the dynamics calculation, that is, the lower limit value (112), the upper limit value (109) and the provisional joint angular velocity (113) of the joint angle.

FIG. 3 shows an outline of the processing when the processing shown in FIG. 2 is applied to animation production of a human body model.
First, the motion generation program (204) of the articulated structure is executed, and the key frame data (301) of the human body model corresponding to the data 201 and the list of the selected partial models in the selected section corresponding to the data 202 ( 302) and
One frame data (303) of the human body model corresponding to the data 203 is sequentially obtained. The contents of the data 303 are accumulated as animation data (304) of the human body model by the animation data input program (308). When reproducing the produced animation, the contents of the data 304 are sequentially called by the animation data output program (309), and the obtained one frame data (305) of the human body model and the background data (306) Input to the original object display program (310) to display animation 1
Obtain the frame image (307) and display it.

FIG. 6 shows the configuration of a system for performing the processing shown in FIG. Using this system, it is possible to efficiently create an animation in which a human body model moves realistically. In the storage device (604), the key frame data (301) of the human body model, the list of selected partial models (302) in the selected section, and the background data (306) are used for animation of the human body model. The program (605) converts the animation into one frame image (307). The program 605 includes the program 204, the program 308, the program 309, and the program 310 of FIG.

The details of the processing of the present invention will be described below.

(1) Definition of multi-joint structure The multi-joint structure used in this embodiment is shown in FIG. Joint Jc (4
Let Lc (413) be the link connecting 15) and the joint Je (411, 412) on the tip end side. Also, the joint Jend (4
The part before 05,406) is set as the link Lend (401,402).
The joint Jc (415) has a coordinate system Fc (414) whose origin is Jc.
have. The relative position of Fc (414) with respect to the coordinate system Fb (418) of the joint Jb (419) on the one base side is represented by a 4 × 4 coordinate conversion matrix Mc (416). When the base joint is Jbase (422), Mbase (423) is a coordinate conversion matrix representing the relative position of Fbase (421) with respect to the world coordinate system Fworld (424). The position of Jc (415) represented by Fworld (424) is obtained from these coordinate conversion matrices.

The degree of freedom of each joint of the multi-joint structure used in this embodiment is 1. A joint having two degrees of freedom is considered by replacing two joints with a link having a length of 0 and a mass of 0 connecting them. Similarly, a joint with three degrees of freedom has three joints,
Consider two links that connect them with length 0 and mass 0. It also allows branching from the base toward the tip. That is, for a certain link Lc (413),
There may be a plurality of links Le (407, 408) on one tip side. Therefore, the number of base links Lbase (420) is one, but the number of tip links Lend (401, 402) is one or more.

(2) Inverse dynamics calculation When joint angles, joint angular velocities, and joint angular accelerations of all joints of a multi-joint structure are given at a certain time, the joint torques of all joints are calculated by inverse dynamics calculation. Desired. In this embodiment, a procedure of inverse dynamics calculation using the Newton-Euler method will be described.

The amount required for calculation is defined as follows.
Let θc be the joint angle of Jc. Let τc be the joint torque of Jc. Let mc be the mass of Lc. Let ωc be a 3 × 1 vector representing the rotation speed of Jc. Let zc be a 3 × 1 vector representing the axis of rotation of Jc. Let vc be a 3 × 1 vector representing the translational velocity of Jc. Let uc be a 3 × 1 vector representing the translational velocity of the center of gravity of Lc. rc is 3 from Jb to Jc
X1 vector. sc is 3 from Jc to the center of gravity of Lc
X1 vector. Let fc be a 3 × 1 vector representing the force acting from Lc to Le. fend represents a force that acts on Lend from the outside. Let nc be a 3 × 1 vector representing the moment acting from Lc to Le. nend is Lend
Represents the moment acting from the outside. Let Ac be a 3 × 3 transformation matrix for rotation from Fc to Fworld. Ac
Matches a 3 × 3 submatrix of rotations of the product of Mbase to Mc. Let Ic be the 3 × 3 inertial tensor around the center of gravity of Lc represented by Fc. Let a be a 3 × 1 vector representing the value obtained by subtracting the acceleration of gravity from the acceleration of the base. Let E be the total number of Jends, that is, the total number of Lends.
Let Kf be a 3 × E matrix consisting of E column vectors representing forces. The i-th column vector of Kf represents the force externally acting on the i-th Lend. Let Kn be a 3 × E matrix consisting of E column vectors representing moments. I of Kn
The th column vector represents the moment that acts externally on the i th Lend. Let N be the total number of joints, ie the total number of links. Θ, where N is the i-th component θi
1 vector. Let T be N, where i is the i-th component
X1 vector.

The link Lc has a radius wc, a height hc, and a y of Fc.
When represented by a cylinder of uniform density with the axis as the axis of rotation, the component Iij at the i-th row and the j-th column of the inertia tensor Ic of Lc is as follows.

[0019]

[Equation 1] I11 = (mc · hc ² + 3mc · wc ² ) / 12 (Equation 1)

[0020]

[Equation 2] I22 = (mc · wc ² ) / 2 (Equation 2)

[0021]

[Equation 3] I33 = (mc · hc ² + 3mc · wc ² ) / 12 (Equation 3)

[0022]

## EQU4 ## I12 = I13 = I21 = I23 = I31 = I32 = 0 (Equation 4) The inverse dynamics calculation is performed by the following procedure. In the equation below, 'is the first derivative in time, and is the 2 in time.
Represents the second derivative, and ^ represents the transposition.

(1) In ωbase, ωbase ', vbase', the number 5
The initial value shown in is given.

[0024]

[Expression 5] ωbase = 0, ωbase ′ = 0, vbase ′ = a (Equation 5) [mathematical formula-see original document] An offset corresponding to the gravity acceleration is given vertically upward with respect to vbase '.

(2) From the base toward the tip, the calculations of the equations 6 to 9 are repeated.

[0026]

[Equation 6] ωc = ωb + zcθc ′ (Equation 6)

[0027]

## EQU7 ## ωc '= ωb' + zcθc "+ ωb × zcθc '(Equation 7)

[0028]

(8) vc '= ωb' × rc + ωb × (ωb × rc) + vb '(Equation 8)

[0029]

Mathematical Expression 9 uc ′ = ωc ′ × sc + ωc × (ωc × sc) + vc ′ (Equation 9) (3) In the i-th fend and the i-th nend, the equation 10
The initial values shown in are given (1 ≦ i ≦ E).

[0030]

Fend = Kf · ei ^, nend = Kn · ei ^ (Equation 10) In Equation 10, ei is an E × 1 unit vector in which the i-th component is 1 and the others are 0. ..

(4) From the tip to the base, number 11
To the calculation of Equation 13 are repeated.

[0032]

Mathematical Expression 11 fc = mcuc '+ Σfe (Expression 11)

[0033]

Mathematical Expression 12 nc = AcIcAc ^ ωc '+ ωc × (AcIcAc ^ ωc) + sc × mcuc' + Σ ((re × fe) + ne) (Equation 12)

[0034]

[Equation 13] τc = zc ^ · nc (Equation 13) T is obtained by the above procedure. This calculation is performed by the function Dinv
Is expressed as

[0035]

[Equation 14] T = Dinv (Θ, Θ ', Θ ", a, Kf, Kn) (Equation 14) (3) Dynamic calculation Joint angles and joints of all joints of the multi-joint structure at a certain time Given the angular velocity and the joint torque, the joint angular accelerations of all the joints can be obtained by the dynamic calculation.
The dynamic calculation is performed by using the inverse dynamic calculation.

The relationship shown in Expression 15 is established between Θ ″ in Expression 14 and T.

[0037]

## EQU15 ## H.theta. "= TB (Equation 15) H is an inertial matrix and B is a bias vector.
It is one vector and is obtained by Equation 16.

[0038]

## EQU16 ## B = Dinv (.THETA., .THETA. ', 0, a, Kf, Kn) (Equation 16) H is an N.times.N matrix, and its i-th column vector Hi is obtained by Eq. ≦ i ≦ N).

[0039]

## EQU17 ## Hi = Dinv (Θ, 0, ei, 0,0,0) (Equation 17) In Equation 17, ei is an N × 1 unit in which the ith component is 1 and the others are 0. Is a vector. Letting the i-th component of B be bi, bi represents the joint torque of Ji when the influence of the joint angular acceleration is ignored. Further, Hi represents the joint torque of Ji when the influences of the joint angular velocity, the gravity, the acceleration of the base, and the external force are ignored and the joint angular acceleration of Ji is set to 1 and the other joint angular accelerations are set to 0.

(4) Method of using dynamics calculation If the bias vector B and the inertia matrix H are obtained, Θ ″ can be obtained from T. However, T is not an intuitive value. Therefore, in the present invention, Equation 15 is solved by using T as a zero vector, and a motion is generated using the obtained Θ ″. The motion obtained at this time is a motion when no active joint torque is applied to the joint, that is, a motion of the multi-joint structure due to inertia and is realistic. The calculation using the dynamics calculation is performed on the joint (104) included in the selected partial structure P (102) in the selected section (108) by the procedure shown in FIG. 5 and the following. However, a sufficiently short fixed time interval is Δt, a current time (116) of interest is tc, and a next instant time (117)
Be td = tc + Δt.

(1) Assume that the joint angle Θc and joint angular velocity Θc 'of P at time tc are given (50
1).

(2) Joint torque T of P at time tc
Is a zero vector (502).

(3) The bias vector B of P at time tc is obtained from Θc and Θc 'using Equation 16 (50
3).

(4) From Θc, the inertia matrix H of P at time tc is obtained by using the equation (17) (504).

(5) Substituting T, H, and B into Equation 15, the joint angular acceleration Θc ″ of P at time tc is obtained (505).

(6) From Θc ′ and Θc ″, the provisional joint angular velocity Θt ′ of P at time td is calculated using equation 18 (506).

[0047]

[Formula 18] Θt ′ = Θc ′ + Θc ″ · Δt (Equation 18) (7) From the list 202, a real value that is to be multiplied by the joint angular velocity of P in the currently focused section is extracted, and this is represented by Θt ′. The corrected joint angular velocity Θm ′ of P at time td is obtained by multiplying each component (507), provided that when returning from the process 514 to the process 507 through the process 506, The value corresponding to the corrected component is not multiplied by the real value.The real value by which each component of Θt 'is multiplied may be different from each other, but is set to a value of 0 or more and 1 or less. Does not move at all.The joint corresponding to the component multiplied by 1 moves without any friction.

(8) From Θc and Θm ′, the provisional joint angle Θt of P at time td is calculated using equation 19 (508).

[0049]

Θt = Θc + Θm ′ · Δt (Equation 19) (9) From the list 202, the lower limit value and the upper limit value of the joint angle of P in the currently focused section are extracted (50
9).

(10) When all the components of Θt are within the range from the corresponding lower limit value to the upper limit value (510 is YES
If so, Θt is set as the joint angle Θd of P at time td, and the process proceeds to the next time (returns to 515 via 511). When the last time of the section of interest is reached (51
If 5 is YES), the process ends.

(11) If there is a component out of the range from the corresponding lower limit value to the upper limit value among the components of Θt (510
If NO, then match the corresponding value to the lower or upper limit, whichever is closer (512). From the corrected Θt, Θc ″ is recalculated using Equation 20 (513).

[0052]

## EQU20 ## .THETA.c "= ((. THETA.t-.THETA.c) /. DELTA.t-.THETA.c ') /. DELTA.t (Equation 20) (12) Among the recalculated components of .THETA.c", the corrected component of .THETA.t , Of the components of T given in (2), which do not correspond to the corrected component of Θt, are substituted into Equation 15 to obtain all the components of the joint angular acceleration Θc ″ of P at time tc. , Return to (6) (return to 506 via 514).

(5) Mathematical Interpolation of Joint Angle The joint angle data of the joint (104) included in the unselected substructures (102, 103) in the unselected section (107).
(105) sets the joint angle in the keyframe (101) to 3
It is determined by interpolation using the next spline or the like. As a result, smooth motion can be obtained in the portion not using the dynamics calculation, and the joint angle and the joint angular velocity at the first time of the section in which the dynamics calculation is performed can be easily adjusted by changing the key frame. The result of the change is
Joint angle data obtained by using dynamics calculation (106)
Reflected in.

As described above, the realistic movement considering the dynamics can be generated from the key frame without inputting the unintuitive value of the joint torque. By using the method of the present invention, the realistic movement of the multi-joint structure can be easily obtained.

[0055]

According to the present invention, it is possible to easily generate a realistic motion of an articulated structure in consideration of dynamics from a key frame.

[Brief description of drawings]

FIG. 1 is a conceptual diagram of processing of the present invention.

FIG. 2 is a schematic diagram of processing of the present invention.

FIG. 3 is a schematic diagram of processing when the processing of the present invention is applied to animation production of a human body model.

FIG. 4 is a diagram showing an articulated structure.

FIG. 5 is a diagram showing a calculation algorithm using dynamic calculation.

FIG. 6 is a system configuration diagram when the processing of the present invention is applied to animation production of a human body model.

[Explanation of symbols]

101 ... Key frame at a certain time of the multi-joint structure, 102 ... Partial structure included in the multi-joint structure, 10
3 ... Other partial structure included in multi-joint structure, 104 ...
Joints included in 102, 105 ... Section 10 of joint 104
7, joint angle data 106, joint angle data in the section 108 of the joint 104, 107 ... section defined by the adjacent key frame 101, 108 ... other section defined by the adjacent key frame 101,
109 ... Upper limit of joint angle of joint 104 in section 108, 110 ... Provisional joint angle of joint 104 at time 117, 111 ... Joint angle of joint 104 at time 116,
112 ... Lower limit value of joint angle section 108 of joint 104, 113 ... Temporary joint angular velocity of joint 104 at time 117, 114 ... Corrected joint angular velocity of joint 104 at time 117, 115 ... Configure joint angle data 106 Data, 116 ... Time at one moment, 117 ... Time at the next moment, 201 ... Key frame data of articulated structure,
202 ... List of selected partial structures in the selected section, 203 ... Data of one frame of multi-joint structure, 204 ... Motion generation program of multi-joint structure

Claims (2)

[Claims] 1. In a motion generation process of a multi-joint structure having one or more joints, a key frame consisting of data of a joint angle at a certain time of the multi-joint structure is given, and a section defined by adjacent key frames. And a partial structure of the multi-joint structure, the specific partial structure in the specific section is selected, and the movement data of the partial structure in the selected section is used as the partial structure. Obtained by using a dynamic calculation when the joint torque of the joint included in the body is set to zero, and the motion data of the partial structure in the unselected section is calculated as the motion data of the joint included in the partial structure in the section. A method for generating a motion of a multi-joint structure, which is characterized by mathematically interpolating a joint angle in a key frame. 2. A method of using the dynamics calculation, wherein a joint angular acceleration of a joint included in the selected partial structure is set to zero, and the joint angular acceleration is calculated. From the joint angular velocity of the joint, the provisional joint angular velocity of the joint at the next moment is obtained, and the product of the provisional joint angular velocity and a real value of 0 or more and 1 or less is the corrected joint angular velocity of the joint at the next moment, The provisional joint angle of the joint at the next moment is obtained from the corrected joint angular velocity and the joint angle of the joint, and the provisional joint angle is within the range from the lower limit value to the upper limit value of the joint angle of the joint. In this case, the provisional joint angle is set as the joint angle of the joint at the next moment, and when the provisional joint angle is outside the range from the lower limit value to the upper limit value, the provisional joint angle is set to the lower limit value or The calculation using the dynamics calculation is repeated so as to match the upper limit value. Operation method of generating multi-joint structure of claim 1, wherein the determination of the joint angle at the moment of the joint included in partial structures below.