KR100834508B1 - Torque distribution method of redundant actuated system - Google Patents

Abstract

A method of distributing torque concentrated on a drive shaft to other shafts is provided to use a smaller motor having reduced maximum torque in a given working conditions by distributing the concentrated torque with other shafts based on weighted value as a minimum drive torque obtained from a calculation of a weighted pseudoinverse matrix. A method of uniform torque distribution for a drive shaft includes an input device(10), a robot(20) having an encoder(22) for a drive motor, a subtracter(30), a Jacobian function calculator(40), a PID(Proportional-Integral-Derivate) controller(50), and a weighted pseudoinverse matrix calculator(60).

Description

Torque Distribution method of Redundant Actuated System

1 is a block diagram illustrating a force distribution control algorithm using a weighted pseudomatrix.

2 shows a system modeled in Recurdyn

3 is a block diagram on Simulink of the minimum driving force control algorithm

4 to 8 are graphs showing the torque change of each drive motor through the weight change for the end effector of the 3RRR parallel robot drawing the trajectory of the circular motion.

9 shows a system drive vector of a 3RRR parallel robot.

10 is a graph of change in driving torque when there is no weight

11 is a graph of change in drive torque when the distance between the end effector and each drive shaft is weighted.

12 is a graph of change in driving torque when the inertia matrix is weighted

13 is a graph showing the change in driving torque when the Minimum Norm Torque is weighted

Fig. 14 is a graph comparing the amount of change in driving torque when the inertia matrix is given a weight (single dashed line) and the Minimum Norm Torque is the weight (solid line).

15 is a graph of variation in driving torque in force distribution simulation using a pseudo inverse matrix

16 is a graph showing the change in driving torque of the weighted pseudo-matrix matrix with Minimum Norm Torque as the weight.

Fig. 17 is a graph of variation of drive torque in force distribution simulation using pseudo inverse matrix

18 is a graph of driving torque variation of weighted pseudo-matrix with Minimun Norm as the weight

19 is a graph of the amount of change in driving torque in force distribution simulation using a pseudo inverse matrix

20 is a graph showing the drive torque variation of the weighted pseudo-matrix matrix with Minimum Norm Torque as the weight.

Fig. 21 shows the overall configuration of a 3RRR parallel robot.

22 is a graph of variation in driving torque in force distribution experiment using pseudo inverse matrix

23 is a graph of driving torque variation of weighted pseudo-matrix matrix with Minimum Norm Torque as the weight

Fig. 24 is a graph of variation in driving torque in force distribution experiment using pseudo inverse matrix

25 is a graph of the drive torque variation of the weighted pseudo-matrix matrix with Minimum Norm Torque as the weight.

The present invention relates to a force distribution method of a slack drive system, and more particularly, a slack drive that enables efficient torque distribution between drive shafts by performing a force distribution using a weighted dead matrix and using a minimum drive force as a weight. It relates to the force distribution method of the system.

When the number of drive inputs is greater than the degree of freedom of the system, it is called Redundant Actuated System. Since the number of drive inputs is greater than the degree of system freedom, the drive torque of each drive motor is determined as one when the robot is doing any work. Instead, various methods exist.

Therefore, in the free drive, the optimum solution must be obtained according to the purpose and environment of the robot. The difference between the free drive system and the non-free drive system is that the force distribution can be adjusted.

This redundant drive system has several characteristics that are better than those of a non-redundant drive system. In general, a redundant driving system is used in a parallel robot system rather than a serial robot system, and by using more driving devices, it has the advantage of generating great force, speed, and acceleration in an end effector.

In addition, the use of a marginal drive for the specificity associated with the small work area, which is the biggest disadvantage of the parallel robot system, can eliminate this specificity. In addition, active stiffness is distinguished from non-slack driving. When the robot is affected by disturbance, the amount of impact can be minimized through stiffness control. Since the redundant drive system has one drive shaft more than the non-redundant drive system, the same operation can be performed even when a failure occurs.

Looking at the existing studies on the spare drive as described above, in the case of the non-free drive manipulator and the free drive manipulator compared to the maximum load capacity, the maximum speed, the maximum acceleration in the end effector work by the free drive Performance Improvement (Sang-Heon Lee, Byung-Joo Lee, Kyun Yun-Keun, 'Performance Analysis and Optimal Design of Driving Human Body Robot Module', Journal of the Korean Society of Mechanical Engineers, Vol.19, No.1, pp.181-192, 1995 (Sungbok Kim, 'Operational quality analysis of parallel manipulators with actuation redundancy', IEEE International Conference on Robotics and Automation, pp2651-2656, 1997), Jacobian's singular values Indexes to determine the degree of failure of robot joints based on the A study on the performance of a free-running robot that withstands faults by presenting a heavy-duty actuator (Lee Byung-ju, Kim Hee-guk, Kim Dong-gu, 'Analysis of the performance of free-running / freedom robots that can withstand failure', pp.2927-) 2938, 1995).

And, a study on the force distribution technique of slack drive system using weighted pseudo inverse matrix (Park, Dong-il, Kim Soo-hyun, Kwak Yun-geun, 'A study on the force distribution method of slack driving using weighted pseudo-matrix', Korean Society of Mechanical Engineers, 2002) (DONG IL PARK, 'Torque distribution using a weighted pseudoinverse in a redundantly actuated mechanism', Advanced Robotics, Vol. 17, pp807-820, 2003), and applying weights to inertia matrices to derive results by applying them to two-degree-of-freedom parallel robots. On the other hand, there has been a study on the dynamic controller based on the kinematically decomposed modeling of the redundant drive manipulator.

And, as described above, since the number of driving inputs in the redundant driving system is greater than the system degree of freedom, the torques applied to the driving inputs when the robot does any work are not determined as one, but exist in various ways. This is because Jacobian is not a square matrix. In general, when the number of drive inputs and the degree of freedom of the system are the same, the Jacobian appears as a square matrix, so the forces corresponding to each drive input are determined to be one. More often, Jacobian does not appear square. In order to invert the Jacobian matrix, a pseudo inverse is used, and there are various forces corresponding to the driving inputs.

Therefore, different driving inputs can be used to perform the same work. Therefore, the driving input suitable for the purpose and environment of the robot should be determined.

As such, there are many force distribution techniques for determining the driving input. The most common method is the method using the minimum norm torque (S.Kock, W. Schumacher, 'A Parallel xy Manipulator with Actuation Redundancy for High-Speed and Active-stiffness Applications', IEEE International Conference on Robotics and Automation, 1998) (DONG IL PARK, 'Torque distribution using a weighted pseudoinverse in a redundantly actuated mechanism', Advanced Robotics, Vol. 17, pp807-820, 2003).

The disadvantage of the method using the minimum driving force is that the theory uses only the minimum torque applied to the motor, so that one shaft takes a lot of torque and the other shaft takes a lot of torque.

However, in parallel robots, the forces acting on the respective driving inputs need to be balanced, not biased to one side, and even when a large amount of force is applied to one side or almost no force on one side, It's not an efficient use.

An object of the present invention for solving the above problems is to perform a force distribution by using a weighted ministry matrix, and by using the minimum driving force as the weight, it is possible to reduce the torque of the drive shaft that takes the maximum drive torque by efficient torque distribution between the drive shafts The purpose is to reduce the maximum torque of the motor, so that smaller motors can be used in the same working environment, thereby achieving economic benefits.

Features of the present invention for achieving the above object

By re-distributing the drive torque output from the controller to which the general control algorithm is applied in the controller to which the weighted ministry matrix control algorithm is applied, redistributing the drive torque to the drive shaft to distribute the maximum torque intensively on one axis to each axis. Will lower the maximum torque.

The force distribution method of the redundant drive system according to the present invention utilizes a force distribution control algorithm by introducing a weight matrix to more freely control the torque of each drive motor to a desired size.

Kinematically, in nonsingular configurations, the weighted pseudoinverse matrix ((J ^T ) ^{W +} ) is given by Equation 1 below.

In the above, J represents Jacobian which is a relation between the speed of the end point of the robot and the drive motor speed of each drive shaft, J ^T represents the Jacobian matrix determined according to the attitude and motion of the robot, W represents the weight matrix, The general solution at this time is represented by Equation 2.

와 같으며, τ_AW는 가중치를 거쳐 새로운 구동토크를 나타내고, F_C는 엔드 이펙터에서의 힘과 토크를 나타낸다.Where the weight matrix W is

Τ _AW represents the new drive torque by weight, and F _C represents the force and torque at the end effector.

Equation (3) by substituting equation (3) into equation (2) is the same as equation (4).

는 의사역행렬을 이용한 힘 분배에서 나온 구동토크 τ_A이다. 따라서, 수학식 4를 다시 표현을 하면 수학식 5와 같다.From the stomach

Is the driving torque τ _A derived from the force distribution using the pseudo inverse matrix. Therefore, Equation 4 is expressed as Equation 5 again.

As a result, the drive torque τ _A derived from the force distribution control of the pseudo inverse matrix is weighted and the force is distributed to the new drive torque τ _AW .

The force distribution control algorithm using the weighted inverse matrix is shown in FIG.

In FIG. 1, a position (out1, out2) of an end point to be moved by the robot 20 is input through the input means 10 including the keyboard, and an input reference (Reference, out1, out2 or x _R ) value and the robot ( The output position value (x _feedback ) of the end point of the robot obtained by inserting the output rotational displacement value (q _feedback ) from the encoder 22 of the drive motor constituting the motor into the static kinematic equation of the free-running 3RRR parallel robot 20 and Subtracted through the subtractor 30, the subtracted value and the output rotational displacement value (q _feedback ) are inputted to the Jacobian function calculating unit 40, and the PID controller 50 calculates the drive torque of each drive shaft. The output drive torque τ _A is calculated by the weighted stationary matrix calculation unit 60 to obtain a redistribution value τ _AW of the drive torque, and the output is transmitted to the robot to drive the robot.

In the PID controller 50, the P controller controls the feedback control signal to be linearly proportional to the error of the system (error = x _reference -x _feedback ), and the I controller controls the normal state even if the error signal is zero at the control input. In the case that the control output does not reach the target position because it is not 0, the controller uses the I controller to reach the target position. Controller used to converge to a value).

The change in output torque of the driving input for the change in weight will be described below.

In order to check the torque variation of the drive input against the change in weight, the system was modeled and simulated using RecurDyn (hereinafter referred to as RecurDyn), which is a multibody dynamics analysis program. Since the RecurDyn dynamics analysis program supports Simulink from Matlab, the control algorithm is programmed with Simulink and linked with RecurDyn.

2 is a view of a system modeled in RecurDyn. It is composed of 3RRR type parallel robot and the driver is attached at the end.

The length of each link is 700mm and the distance between the end driver and the driver is set to 1400mm. The joint frictional force applied to each joint was set to zero. The direction of gravity was set in the direction opposite the axis of rotation of the actuator (-Z axis).

The input method of the drive shaft is possible to input angle, angular velocity, angular acceleration and torque, but in the present invention, since the input of the drive shaft is torque, the input method of the drive shaft is set to torque input.

Figure 3 is a block diagram on Simulink of the minimum driving force control algorithm, the controller used a PD controller.

In order to analyze the influence of the weights, the torque change was observed by changing three weight variables for the three drive inputs of the redundant 3RRR parallel robot on Simulink in Matlab.

The graphs of FIGS. 4 to 8 show torque changes of the respective driving motors through weight changes for the end effector of the 3RRR parallel robot drawing the trajectory of the circular motion.

4 is a graph of torque change of each of the drive motors when no weight is applied, and FIG. 5 is a graph of torque change of the drive motors when the weight is given to the drive shaft A1, and FIG. 6 is a drive motor when the weight is given to the drive shaft A2. 7 is a torque change graph of FIG. 7 and FIG. 7 is a torque change graph of each drive motor when a weight is given to the drive shaft A3, and FIG. 8 is a torque change graph of each drive motor when a weight is applied to all of the drive shafts A1, A2 and A3. .

In analyzing the graphs of FIGS. 4 to 8, as the weight increases, the corresponding drive torque value decreases, and other torque values tend to increase.

As shown in FIG. 5, as the weight increases, the magnitude of the torque value of the drive shaft A1 gradually decreases, and eventually the torque value converges to zero. In the graphs of FIGS. 6 and 7, as the respective weights increase, the magnitude of the corresponding drive torque value gradually decreases, and eventually the torque value converges to zero. When the weight of each drive shaft is increased at the same time, as shown in the graph result of FIG.

As the weight increases, the torque value corresponding to the weight tends to gradually decrease, eventually converging to a value of zero. Torque values that do not correspond to weights tend to increase, but not necessarily increase.

As shown in FIG. 8, when the weights are increased together, a graph of a slight increase or decrease in torque change is shown in FIG. 4 without weighting. In other words, we knew about the result of weight on torque value, but we could conclude that each weight is not independently determined and that three weights should be related at the same time. The weighting method will be described below in which weight can be selected to effectively reduce the maximum driving torque.

As in the weight analysis described above, it was found that the weight cannot be arbitrarily selected when the weight is selected for the driving torque. That is, three weights should be related to each other at the same time. Here, there can be several variables related to the three drive shafts.

The first and easiest thing to think about is the weight of the distance from the end effector to each drive shaft. As the end effector moves, the length of the drive shaft increases or decreases. Rather than shrinking or stretching each one, it is a related variable in which the length of one side increases and the length of the other decreases as the end effector moves. The distance from the end effector to each drive shaft can be easily obtained. If the coordinate values in the end effector are Xc and Yc, respectively, the weights of the equations are as shown in Equation 6.

In the above description, X _A1 , X _A2 , X _A3 , Y _A1 , Y _A2 , and Y _A3 are coordinate values of the respective driving shafts A1, A2, and A3.

The second weighted variable is the Inertia Matrix corresponding to each leg. In FIG. 9, when the mass of each link is m1 and m2, the inertia matrix of the leg corresponding to the drive shaft A1 of the redundant 3RRR parallel robot is expressed by Equation 7 below.

In the above inertia matrix, 1-norm, the size of the inertia matrix, was selected as the weight.

Therefore, when the inertia matrix is applied as the weight, each weight is expressed by the following Equation 8.

The third doctor yeokhaengryeolreul leave as using power distribution scheme _mA1 τ, τ _mA2, τ _mA3 respectively, the drive motor of the drive shaft in a determined, the weight in case of applying the Minimum Norm Troque by weight is shown in the following equation (9).

In the simulation of the 3RRR parallel robot, the driving torque change to which each weight is applied is as follows.

FIG. 10 is a graph showing a change in driving torque when no weight is applied, FIG. 11 is a graph showing a change in driving torque when the distance between an end effector and each drive shaft is weighted, and FIG. 12 is a weighted inertia matrix. Fig. 13 is a graph showing the change in driving torque when Fig. 13 is a graph of the change in driving torque when the Minimum Norm Torque is the weight, and Fig. 14 is the weight of the Minimum Norm Torque when the inertia matrix is a weight (single dashed line). It is a comparative graph of the drive torque change amount when given by (solid line).

When comparing the weights, the driving torque change when the distance was given as a weight showed that the maximum driving torque was slightly changed than the driving torque without applying the weight, but the driving torque of other driving shafts tended to be larger. . In the graph of the drive torque variation when Minimum Norm Troque is given as the weight, it can be seen that the maximum drive torque applied to the drive shaft is the smallest among the three weights. The torque change graph of FIGS. 10 to 13 is summarized in Table 1 below.

Maximum (Nm) Minimum (Nm) If no weight 23.1 -12.5 Distance weighting case 22.5 -20.5 Inertia matrix weighting case 21.27 -14.12 Minimum driving force weight 17.80 -19.20

Referring to the comparison graph of the drive torque change in FIG. 14, when the minimum norm torque is given as a weight as shown by the solid line, it can be seen that the smaller maximum torque is applied at the portion where the maximum torque is applied. Comparing the drive torque applied to the drive shaft other than the drive shaft that takes the maximum torque, the torque change is greater when the minimum norm torque is given as the weight.

Looking at the comparison graph above, it can be seen that the torque distribution is achieved by lowering the maximum driving torque more effectively when Minimum Norm Torque is weighted.

On the other hand, various force distribution algorithms can be used for the marginal driving. The driving torque applied to each drive shaft can be adjusted according to the working environment and purpose of the robot.

In the general redundant drive system, a method of minimizing the norm of the drive torque vector of the drive shaft is used to minimize the drive torque applied to each drive shaft. In the method of minimizing the norm of the torque vector, a large drive torque is applied to some drive shafts, and a relatively small drive torque is applied to other drive shafts. Therefore, it is possible to obtain a gain of reducing the maximum drive torque applied to the drive motor by redistributing the drive torque of the drive shaft that takes the large drive torque to the drive motor that takes the small drive drive torque. This allows the use of smaller capacity motors to perform the same task, thereby contributing to the economical efficiency and miniaturization of the system when redundant drive is used, to reduce the maximum drive torque on the drive shaft to verify this. For this purpose, we perform a force distribution simulation using a weighted pseudomatrix with a weighted minimum norm torque, and in order to prove this, a force distribution simulation using a pseudo inverse matrix and a weighted distribution matrix with a weighted minimum norm torque is performed. Experiment

The simulation runs over three cases.

The first case is the trajectory of a circle with a radius of 70 mm around (0,0). This is the case when the force at the end effector is given as (-14.4, -14.4).

15 and 16 are graphs showing the change amount of the drive torque of the force distribution simulation using the pseudo inverse matrix and the change amount of the drive torque of the weighted dead matrix with the minimum norm torque applied.

The second case is the trajectory of a circle with a radius of 70 mm around (120,0). This is the case when the force at the end effector is given as (20,0).

17 and 18 are graphs showing the change amount of the drive torque of the force distribution simulation using the pseudo inverse matrix and the change amount of the drive torque of the weighted ministry matrix with Minimun Norm as the weight.

The third case is the trajectory of a circle with a radius of 70 mm around (120,0). This is the case when the force at the end effector is given as (0, -20).

19 and 20 are graphs showing the change amount of the drive torque of the force distribution simulation using the pseudo inverse matrix and the change amount of the drive torque of the weighted dead matrix with the minimum norm torque as the weight.

In the first case, the maximum torque of -19.45 [Nm] is needed for the application of pseudo inverse force distribution, while the maximum torque of 15.04 [Nm] is required for the force distribution using weighted inverse matrix. It can be seen that the driving torque of the driving shafts other than the driving shaft that takes the maximum torque increases from 10.36 [Nm] to 15.04 [Nm] when the force distribution is applied using the weighted inverse matrix. As the torque distribution is applied toward the lower driving torque with less driving torque, the maximum driving torque is reduced by about 23%.

In the second case, the maximum driving torque of 22.42 [Nm] is required for the application of pseudo inverse matrix, and the maximum driving torque of -18.84 [Nm] is needed for the force distribution result using the weighted inverse matrix. As in the first case, when the pseudo inverse force distribution is applied, the torque of the drive shaft that takes the maximum drive torque is distributed to the other drive shafts, which reduces the overall drive torque by about 16%.

In the third case, torque is distributed to the drive shaft that requires relatively little torque of the drive shaft, which reduces the maximum drive torque of about 22%. The above results are summarized in table 2 as the reduction of the maximum drive torque.

Driving force (Nm) Weighted Ministry Matrix (Nm) % Reduction case 1 19.45 15.04 23 case 2 22.42 18.84 16 case 3 17.62 13.69 22

The simulation results show that the maximum torque applied to the drive shaft is reduced by about 16-23% when the force distribution using the weighted pseudo inverse matrix is weighted by applying the minimum norm torque to the maximum torque applied to the drive shaft. appear. The drive torque of the drive shaft with large drive torque is distributed to the drive shaft with small force distribution when the force is distributed using the weighted inverse matrix, and the overall effect of balancing the torque load on each drive shaft can be seen.

We will see below that the results of the above simulations yield similar results by applying weighted dead-space matrix force distribution to the 3RRR parallel robot. When the force distribution using the pseudo inverse matrix and the weight distribution using the weighted inverse matrix with the minimum norm torque are applied to the 3RRR parallel robot, the driving torque values applied to the driving motor are compared.

The overall configuration of the 3RRR parallel robot used in this experiment is shown in FIG. 21.

The 3RRR parallel robot is composed of four main components. The first is a 3RRR parallel robot body connected to the servo motor and the reducer. The second is a servo motor and motor drive system. The third is a motion control that reads the encoder values attached to the motor and sends a drive command to the drive. It is a board. Finally, it consists of a computer running a control program.

The 3RRR parallel robot consists of three legs, and each leg is connected by two link structures. Each link is connected by a rotary joint, and the structure where the three legs meet is connected by the rotary joint. The link is made of aluminum to minimize link weight. In the case of a rotary joint, a double row angular contact ball bearing was selected to minimize the vertical movement of the joint and to withstand the axial load. Each link is 200mm long. All links are designed to be the same length.

The drive was based on the HC-MFS23 model, an AC servo motor produced by Mitsubishi. The reducer used the CFS25B model produced by the harmonic drive. Mitsubishi's MR-J2-20A model was used as the servo amplifier to drive the servo motor. The servo amplifier offers three control modes: position control, speed control and torque control. In the experiment, torque control mode was used, and torque control mode can generate torque proportional to the input voltage in the servo motor. The encoder attached to the motor is capable of 10000 pulses per revolution according to the setting of the servo amplifier. In this experiment, it was set to 8000 pulses per revolution.

Motion Control Board used ACS Motion Control's SPIIPLUS PCI4R0 model. The model is capable of four analog outputs with an output voltage range of -10V to + 10V. The feedback signal can be a digital encoder or a sin-cos encoder. The control board features a PCI slot as well as a control computer, as well as a general control board, and can be used separately from the control computer for LAN and RS232 communication.

In the following, the force distribution control experiment using the pseudo inverse matrix and the force distribution control experiment using the weighted inverse matrix will be performed as in the simulation, and the maximum torque values of the drive shafts will be compared.

Experiments were performed on the case where the end effector draws the circle trajectories at various positions.

The first path is the trajectory of a circle with a radius of 50 mm around (0,0).

22 and 23 are graphs showing the change amount of the drive torque of the force distribution experiment using the pseudo inverse matrix and the change amount of the drive torque of the weighted dead matrix with the minimum norm torque as the weight.

The second path is to draw the trajectory of a circle with a radius of 50mm around (0,50). FIG. 24 and FIG. 25 are graphs showing changes in the drive torque of the force distribution experiment using the pseudo inverse matrix and the drive torque change graph of the weighted dead zone matrix to which the minimum norm torque is applied as a weight.

Drive shaft A1 Drive shaft A2 Drive shaft A3 Pseudo inverse matrix (Nm) max 11.21 10.51 11.60 min -4.10 -2.57 -4.07 Weighted Ministry Matrix (Nm) max 7.61 7.29 7.34 min -7.52 -6.81 -7.08

Drive shaft A1 Drive shaft A2 Drive shaft A3 Pseudo inverse matrix (Nm) max 12.69 12.83 10.47 min -4.89 -4.05 -3.96 Weighted Ministry Matrix (Nm) max 7.07 7.84 8.79 min -7.91 -6.44 -7.47

In Tables 3 and 4, it can be seen that the torque of 10-13 [Nm] is applied when the force distribution control using the pseudo inverse matrix is applied as a whole. In the case of the force distribution control using the weighted pseudo inverse, the torque of 6.5-9 [Nm] can be seen. Here, look at the change in the maximum torque applied to the drive shaft when applying each force distribution control as shown in Table 5.

Driving force (Nm) Weighted Ministry Matrix (Nm) % Reduction case 1 11.60 7.61 33 case 2 12.83 8.79 27

From Table 5, it can be seen that the force distribution control using the weighted inverse matrix is more efficient in the force distribution of the driving torque than the force distribution control using the pseudo inverse matrix. Force distribution using the weighted minus matrix with weighted Minimum Norm Torque is distributed evenly to each motor through redistribution, which can reduce the maximum torque applied to the motor by about 25-33%. I could.

Therefore, Minimum Norm Torque was selected as the weight to reduce the maximum value of the driving input. As a result, the small torque is slightly increased among the drive inputs, but the large torque value is decreased, and the torque distribution of the entire system is achieved, thereby reducing the maximum torque of the used driver.

 It can be concluded that a motor with a 25-36% smaller capacity of the drive motor of a redundant 3RRR parallel robot can be used, which can also contribute to the economy and miniaturization of the system.

Claims (2)

Inputting a position (out1, out2) of the end point to which the free driving system is to move through an input means including a keyboard, The output position value (x _feedback ) of the end point of the robot obtained by inserting the output rotational displacement value (q _feedback ) from the encoder 22 of the drive motor constituting the slack drive system into the static kinematic equation of the slack drive system and the input step Subtracting the input end point position of the robot through the subtractor 30, Inputting the subtracted value and the output rotational displacement value (q _feedback ) to the Jacobian function calculating unit 40 to perform the operation; Receiving the value calculated by the Jacobian function calculating unit 40 and calculating and outputting the drive torque of each drive shaft in the PID controller 50; Computing the output drive torque (τ _A ) in the weighted stationary matrix calculation unit 60 to obtain the redistribution value (τ _AW ) of the drive torque, and transfers this output to the free drive system to drive the free drive system. The force distribution method of a marginal drive system characterized by the above-mentioned. The method of claim 1, wherein the weighted ministry matrix calculation unit (60) uses a minimum driving force as a weight.

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