A brain-like synchronous tracking control method for dual robotic arms

Abstract

The present invention discloses a brain-like synchronous tracking control method for dual robotic arms, the method comprising: initializing the system configuration to obtain an initialization parameter set; defining a coupling error function for the dual robotic arm system, determining the corresponding Jacobian matrix according to the coupling error function, and determining the differential equation constraint conditions; calculating the adjustment amount of the two joint speeds, integrating the adjusted joint speed signals to obtain the joint angle as the input of the dual robotic arm system, and controlling the movement of the robotic arm; learning to predict the Jacobian matrix of the robotic arm at the next moment according to the input joint angular velocity of the dual robotic arm system and the robotic arm end speed measured by the sensor; and controlling the robotic arm in real time according to the Jacobian matrix of the robotic arm at each moment. The present invention has high portability and wide application scenarios, can reduce the tracking error and synchronization error of the dual robotic arm system, improve the performance of the long-term operation of the control system, and can be widely used in the field of computer technology.

Description

Technical Field

[0001] The present invention relates to the field of computer technology, and in particular to a brain-like synchronous tracking control method for dual robotic arms. Background Art

[0002] Robotic arms have broad potential application prospects in various fields, especially in industrial production, where they can play a huge role, such as reducing the burden of manpower, improving production efficiency, and reducing production costs. Compared with a single robotic arm, a dual robotic arm system has the advantages of a wider operating space, heavier loads, and higher flexibility. Therefore, the coordinated control of a dual robotic arm system is an issue worth studying.

[0003] Similar to human arms, robotic arms are usually composed of multiple rigid links connected by revolute joints or translational joints. The mathematical model of a robotic arm can be divided into a kinematic model and a dynamic model. The kinematic model describes the mapping relationship between the angles of each joint of the robotic arm and the position of a module on the robotic arm (such as the end of the robotic arm) in the task space, while the dynamic model describes the mapping relationship between the torque applied by each joint of the robotic arm and the joint angle. The control of a robotic arm can usually be divided into inverse kinematics control and inverse dynamics control. Inverse kinematics control refers to the calculation of the required joint angles based on the desired posture of the robotic arm, while inverse dynamics control refers to the calculation of the required joint torque based on the desired joint angles.

[0004] At present, the existing technical solutions are generally model-based solutions. However, with the increase in task complexity and robot reconfigurability, it is difficult to obtain the kinematic model parameters of the robot arm in some cases. In addition, long-term work may also cause wear or deformation of the robot arm, which in turn leads to inconsistency between the actual model parameters and the labeled parameters. In the above scenarios, the model parameters of the robot are only partially known or may even be completely unknown, which will cause the performance of existing model-based technologies to degrade or even become completely unapplicable.

[0005] In addition, some existing technologies can also require the dual-arm system to move according to their respective target posture trajectories. When the dual-arm system moves strictly according to the target trajectory, the dual-arm system can be synchronized and tracked, and the ends of the dual-arms will remain relatively still. However, in the actual motion control process of the robotic arm, the actual trajectory of the end of the robotic arm and the target trajectory will inevitably deviate. In this case, there will be a relative displacement between the ends of the dual-arms. The existence of relative displacement may cause damage to the target object operated by the dual-arm system. The above-mentioned existing technologies have not yet considered the problem of relative displacement at the ends of the dual-arms. Summary of the invention

[0006] In view of this, an embodiment of the present invention provides a brain-like synchronous tracking control method for dual robotic arms with high portability and wide application scenarios, which can reduce the tracking error and synchronization error of the dual robotic arm system and improve the long-term operation performance of the control system.

[0007] An aspect of an embodiment of the present invention provides a brain-like synchronous tracking control method for dual robotic arms, comprising:

[0008] Initializing the system configuration to obtain an initialization parameter set, wherein the initialization parameter set includes two joint angles of the dual robotic arms, control system parameters, two Jacobian matrix initial values ​​of the dual robotic arm system, and two target trajectory information of the dual robotic arm system;

[0009] Defining a coupling error function for the dual-manipulator system, determining a corresponding Jacobian matrix according to the coupling error function, and then determining differential equation constraints;

[0010] The two cerebellar models are used to calculate the adjustment of the two joint velocities according to the joint angles and tracking errors of the dual-arm system, and the joint angles are obtained by integrating the adjusted joint velocity signals. The joint angles are used as the input of the dual-arm system to control the corresponding movement of the robotic arms.

[0011] Using the gradient neural dynamics model, the robot arm Jacobian matrix at the next moment is learned based on the input joint angular velocity of the dual robot arm system and the robot arm end velocity measured by the sensor.

[0012] The robotic arm is controlled in real time according to the Jacobian matrix of the robotic arm at each moment.

[0013] Optionally, defining a coupling error function for the dual-manipulator system, determining a corresponding Jacobian matrix according to the coupling error function, and then determining the differential equation constraint conditions include:

[0014] Define the tracking pose error for the dual-arm system and determine the deviation between the target trajectory and the actual trajectory of the robot end measured by the sensor;

[0015] Determine the coupling posture errors of the dual robot arm systems according to the deviations;

[0016] Determine the coupling error function of the dual-manipulator system based on the super-helical algorithm;

[0017] Rewriting the coupling error function to construct a compact coupling error function;

[0018] constructing a quadratic programming scheme according to the coupling error function;

[0019] The quadratic programming scheme is solved to obtain a preliminary optimal joint velocity signal.

[0020] Optionally, constructing a quadratic programming scheme according to the coupling error function includes:

[0021] Design optimization objectives based on differential equation constraints and the robot's physical constraints;

[0022] The synchronous tracking control problem of the dual-manipulator system is modeled as a quadratic programming problem.

[0023] Optionally, the method calculates the adjustment amount of the two joint speeds according to the joint angles and tracking errors of the dual robotic arm system through the two cerebellar models, integrates the adjusted joint speed signals to obtain the joint angles, uses the joint angles as the input of the dual robotic arm system, and controls the corresponding robotic arm movements, including:

[0024] Obtain input vectors of the cerebellum model of the left and right robotic arms of the dual robotic arms at different times;

[0025] Determine, according to the input vector, an update rule for the state vectors of the granule cells in the two cerebellum models;

[0026] Determine the update formula of the state vector of the Purkinje cells of the two cerebellar models at each moment; wherein the state of the Purkinje cells is the weighted sum of the signals of the parallel fibers;

[0027] Acquire the input vectors of the climbing fibers of the two cerebellum models, and update the state vectors of the cerebellar deep nuclei of the two cerebellum models according to the state vector update formula;

[0028] Construct the update rules for the output weights of each of the two cerebellar models;

[0029] The two cerebellar models output compensation amounts for joint velocity respectively, and compensate for the joint velocity, thereby obtaining the final joint velocity signal at each moment.

[0030] Optionally, the method further comprises:

[0031] Multiply the tracking errors of the two manipulators by the pseudo-inverse of the corresponding Jacobian matrix to convert the error in the task space into the error in the joint space;

[0032] The transformed joint space error is used as the training signal for the two cerebellar models.

[0033] Optionally, the use of the gradient neural dynamics model to learn and predict the Jacobian matrix of the robotic arm at the next moment according to the input joint angular velocity of the dual robotic arm system and the robotic arm end velocity measured by the sensor includes:

[0034] The error function is defined according to the end velocities and joint velocities of the dual-manipulator system measured by sensors at each moment;

[0035] According to the error function, the time derivatives of the Jacobian matrices of the two manipulators are designed using the gradient neural dynamics method;

[0036] Predict the Jacobian matrices of the two robotic arms at the next moment.

[0037] Another aspect of the embodiment of the present invention further provides a brain-like synchronous tracking control device for dual robotic arms, comprising:

[0038] The first module is used to initialize the system configuration to obtain an initialization parameter set, wherein the initialization parameter set includes two joint angles of the dual robotic arms, control system parameters, two Jacobian matrix initial values ​​of the dual robotic arm system, and two target trajectory information of the dual robotic arm system;

[0039] The second module is used to define a coupling error function for the dual-manipulator system, determine a corresponding Jacobian matrix according to the coupling error function, and then determine a differential equation constraint condition;

[0040] The third module is used to calculate the adjustment amount of the two joint speeds according to the joint angles and tracking errors of the dual robot arm system through two cerebellar models, integrate the adjusted joint speed signals to obtain the joint angles, use the joint angles as the input of the dual robot arm system, and control the corresponding robot arm movement;

[0041] The fourth module is used to use the gradient neural dynamics model to learn and predict the Jacobian matrix of the robot arm at the next moment based on the input joint angular velocity of the dual robot arm system and the robot arm end velocity measured by the sensor;

[0042] The fifth module is used to control the robot arm in real time according to the Jacobian matrix of the robot arm at each moment.

[0043] Another aspect of an embodiment of the present invention further provides an electronic device, including a processor and a memory;

[0044] The memory is used to store programs;

[0045] The processor executes the program to implement the method described above.

[0046] Another aspect of the embodiments of the present invention further provides a computer-readable storage medium, wherein the storage medium stores a program, and the program is executed by a processor to implement the method described above.

[0047] The embodiment of the present invention also discloses a computer program product or a computer program, which includes a computer instruction stored in a computer-readable storage medium. A processor of a computer device can read the computer instruction from the computer-readable storage medium, and the processor executes the computer instruction, so that the computer device executes the above method.

[0048] The embodiment of the present invention first initializes the system configuration to obtain an initialization parameter set, which includes two joint angles of the dual robotic arm, control system parameters, two Jacobian matrix initial values ​​of the dual robotic arm system, and two target trajectory information of the dual robotic arm system; then, a coupling error function is defined for the dual robotic arm system, and the corresponding Jacobian matrix is ​​determined according to the coupling error function, and then the differential equation constraint is determined; then, two cerebellar models are used to calculate the adjustment of the two joint speeds according to the respective joint angles and tracking errors of the dual robotic arm system, and the joint angles are obtained after the adjusted joint speed signals are integrated, and the joint angles are used as the input of the dual robotic arm system to control the corresponding robotic arm movement; finally, a gradient neural dynamics model is used to learn and predict the Jacobian matrix of the robotic arm at the next moment according to the joint angular velocity of the input dual robotic arm system and the robotic arm end velocity measured by the sensor; and the robotic arm is controlled in real time according to the Jacobian matrix of the robotic arm at each moment. The present invention has high portability and wide application scenarios, can reduce the tracking error and synchronization error of the dual robotic arm system, and improve the performance of the long-term operation of the control system. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0050] Figure 1 A schematic diagram of a dual-manipulator brain-like tracking control system provided by an embodiment of the present invention;

[0051] Figure 2 A flow chart of dual-manipulator brain-like synchronous tracking control provided by an embodiment of the present invention;

[0052] Figure 3 A dual-manipulator synchronous tracking control process based on quadratic programming provided in an embodiment of the present invention;

[0053] Figure 4 A schematic diagram of the structure of a cerebellum model provided by an embodiment of the present invention;

[0054] Figure 5The workflow of the cerebellum model in the control system provided by the embodiment of the present invention;

[0055] Figure 6 The Jacobian matrix prediction process of the dual-manipulator system based on gradient neural dynamics provided in the embodiment of the present invention;

[0056] Figure 7 It is a schematic diagram of controlling the synchronous tracking control of the dual-manipulator system to complete the circular trajectory based on the proposed method;

[0057] Figure 8 It is the comparison between the target trajectory and the actual trajectory of the dual-manipulator system;

[0058] Fig. 9 It is the change of each dual-arm system’s posture error and the change of synchronous posture error;

[0059] Fig.10 Schematic diagram of the change in position error and synchronous position error of the dual-manipulator system when the cerebellum model is not used (Experiment 0) and when the cerebellum model is used to repeat the task 10 times. DETAILED DESCRIPTION

[0060] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0061] In view of the problems existing in the prior art, an embodiment of the present invention provides a brain-like synchronous tracking control method for dual robotic arms, comprising:

[0062] Initializing the system configuration to obtain an initialization parameter set, wherein the initialization parameter set includes two joint angles of the dual robotic arms, control system parameters, two Jacobian matrix initial values ​​of the dual robotic arm system, and two target trajectory information of the dual robotic arm system;

[0063] Defining a coupling error function for the dual-manipulator system, determining a corresponding Jacobian matrix according to the coupling error function, and then determining differential equation constraints;

[0064] The two cerebellar models are used to calculate the adjustment of the two joint velocities according to the joint angles and tracking errors of the dual-arm system, and the joint angles are obtained by integrating the adjusted joint velocity signals. The joint angles are used as the input of the dual-arm system to control the corresponding movement of the robotic arms.

[0065] Using the gradient neural dynamics model, the robot arm Jacobian matrix at the next moment is learned based on the input joint angular velocity of the dual robot arm system and the robot arm end velocity measured by the sensor.

[0066] The robotic arm is controlled in real time according to the Jacobian matrix of the robotic arm at each moment.

[0067] Optionally, defining a coupling error function for the dual-manipulator system, determining a corresponding Jacobian matrix according to the coupling error function, and then determining the differential equation constraint conditions include:

[0068] Define the tracking pose error for the dual-arm system and determine the deviation between the target trajectory and the actual trajectory of the robot end measured by the sensor;

[0069] Determine the coupling posture errors of the dual robot arm systems according to the deviations;

[0070] Determine the coupling error function of the dual-manipulator system based on the super-helical algorithm;

[0071] Rewriting the coupling error function to construct a compact coupling error function;

[0072] constructing a quadratic programming scheme according to the coupling error function;

[0073] The quadratic programming scheme is solved to obtain a preliminary optimal joint velocity signal.

[0074] Optionally, constructing a quadratic programming scheme according to the coupling error function includes:

[0075] Design optimization objectives based on differential equation constraints and the robot's physical constraints;

[0076] The synchronous tracking control problem of the dual-manipulator system is modeled as a quadratic programming problem.

[0077] Optionally, the method calculates the adjustment amount of the two joint speeds according to the joint angles and tracking errors of the dual robotic arm system through the two cerebellar models, integrates the adjusted joint speed signals to obtain the joint angles, uses the joint angles as the input of the dual robotic arm system, and controls the corresponding robotic arm movements, including:

[0078] Obtain input vectors of the cerebellum model of the left and right robotic arms of the dual robotic arms at different times;

[0079] Determine, according to the input vector, an update rule for the state vectors of the granule cells in the two cerebellum models;

[0080] Determine the update formula of the state vector of the Purkinje cells of the two cerebellar models at each moment; wherein the state of the Purkinje cells is the weighted sum of the signals of the parallel fibers;

[0081] Acquire the input vectors of the climbing fibers of the two cerebellum models, and update the state vectors of the cerebellar deep nuclei of the two cerebellum models according to the state vector update formula;

[0082] Construct the update rules for the output weights of each of the two cerebellar models;

[0083] The two cerebellar models output compensation amounts for joint velocity respectively, and compensate for the joint velocity, thereby obtaining the final joint velocity signal at each moment.

[0084] Optionally, the method further comprises:

[0085] Multiply the tracking errors of the two manipulators by the pseudo-inverse of the corresponding Jacobian matrix to convert the error in the task space into the error in the joint space;

[0086] The transformed joint space error is used as the training signal for the two cerebellar models.

[0087] Optionally, the use of the gradient neural dynamics model to learn and predict the Jacobian matrix of the robotic arm at the next moment according to the input joint angular velocity of the dual robotic arm system and the robotic arm end velocity measured by the sensor includes:

[0088] The error function is defined according to the end velocities and joint velocities of the dual-manipulator system measured by sensors at each moment;

[0089] According to the error function, the time derivatives of the Jacobian matrices of the two manipulators are designed using the gradient neural dynamics method;

[0090] Predict the Jacobian matrices of the two robotic arms at the next moment.

[0091] Another aspect of the embodiment of the present invention further provides a brain-like synchronous tracking control device for dual robotic arms, comprising:

[0092] The first module is used to initialize the system configuration to obtain an initialization parameter set, wherein the initialization parameter set includes two joint angles of the dual robotic arms, control system parameters, two Jacobian matrix initial values ​​of the dual robotic arm system, and two target trajectory information of the dual robotic arm system;

[0093] The second module is used to define a coupling error function for the dual-manipulator system, determine a corresponding Jacobian matrix according to the coupling error function, and then determine a differential equation constraint condition;

[0094] The third module is used to calculate the adjustment amount of the two joint speeds according to the joint angles and tracking errors of the dual robot arm system through two cerebellar models, integrate the adjusted joint speed signals to obtain the joint angles, use the joint angles as the input of the dual robot arm system, and control the corresponding robot arm movement;

[0095] The fourth module is used to use the gradient neural dynamics model to learn and predict the Jacobian matrix of the robot arm at the next moment based on the input joint angular velocity of the dual robot arm system and the robot arm end velocity measured by the sensor;

[0096] The fifth module is used to control the robot arm in real time according to the Jacobian matrix of the robot arm at each moment.

[0097] Another aspect of an embodiment of the present invention further provides an electronic device, including a processor and a memory;

[0098] The memory is used to store programs;

[0099] The processor executes the program to implement the method described above.

[0100] Another aspect of the embodiments of the present invention further provides a computer-readable storage medium, wherein the storage medium stores a program, and the program is executed by a processor to implement the method described above.

[0101] The embodiment of the present invention also discloses a computer program product or a computer program, which includes a computer instruction stored in a computer-readable storage medium. A processor of a computer device can read the computer instruction from the computer-readable storage medium, and the processor executes the computer instruction, so that the computer device executes the above method.

[0102] The specific implementation process of the present invention is described in detail below in conjunction with the accompanying drawings:

[0103] The present invention belongs to the field of artificial intelligence and robotics, and specifically relates to an inverse kinematics coordinated control method for a dual-manipulator system. The present invention aims to solve the problem of synchronous tracking control of the dual-manipulator system.

[0104] Usually, the kinematic model of a robot arm with m joints can be expressed by the following formula:

[0105]

[0106] The input column vector represents the angle value of the m joint angles of the robot at time t, (·) T Represents the transposition operator, vector is a vector of robot arm kinematic parameters (such as connecting rod length, etc.), column vector The vector representing the position and posture of the end of the robot arm in the n-dimensional task space, is a nonlinear mapping function that describes the kinematics of the robot. The kinematic model of the robot can usually also be described at the velocity level. By taking the time derivatives of both sides of formula (1), we can obtain

[0107]

[0108] in represents the partial derivative of the function f(·) with respect to the joint angle θ(t), i.e., the Jacobian matrix of the manipulator, and the column vector Represents the rotation speed of each joint of the robot arm, column vector Represents the movement speed of the end of the robot in the task space. The tracking control problem of the robot (i.e., the inverse kinematics problem of the robot) refers to the control of the robot according to the given target path and posture vector Obtain the required joint angle θ(t), that is

[0109] θ(t)=g(q d (t)), (3)

[0110] The obtained θ(t) is then used to control the robotic arm so that its end follows the target position q d (t) movement, that is, to make the actual position q(t) of the end of the robot tend to the target position q d (t). Since the kinematic mapping function f(·) is nonlinear, it is difficult to directly obtain the mathematical expression of g(·) (i.e., the inverse function of f) by mathematical derivation.

[0111] The synchronous tracking control of the dual-arm system refers to the simultaneous control of two robotic arms (named as robotic arm L and robotic arm R) so that their ends move synchronously according to the target posture, and the ends of the two robotic arms remain relatively stationary during the movement. In the following, the subscript (·) will be used. L and(·) R Respectively represent the variables related to the two robotic arms. Therefore, the kinematics of the two robotic arms can be expressed by the following formulas:

[0112]

[0113]

[0114] At the velocity level, the kinematics of the two manipulators are expressed by the following formulas:

[0115]

[0116]

[0117] The target positions of the two manipulators are denoted as q d,L (t) and q d,R (t). Since the two robotic arms need to move synchronously, the respective target speeds of the two robotic arms are and same.

[0118] Among the existing methods for dual-arm synchronous tracking control, first, the tracking control problem of the robot L can be solved by the following quadratic programming scheme:

[0119]

[0120]

[0121] in represents the identity matrix with diagonal elements of 1, c L =ξ(θ L -θ L (0)), ξ is a parameter greater than 0, θ L (0) represents the initial joint angle vector of the robot arm L. The above quadratic programming scheme is to find a solution that makes the cost function y in (8) satisfy the constraint condition (9). L (t) Minimum joint velocity In the quadratic programming scheme, constraint (9) is designed according to formula (6). The purpose of this constraint is to ensure that the end of the robot arm L follows the target posture q d,L motion; the first term in the cost function (8) is used to minimize the joint velocity of the robot; the second term in the cost function (8) is to complete the repetitive motion task, that is, to ensure that the robot can return to the initial configuration state after completing a periodic task.

[0122] Similarly, the tracking control problem of the robot arm R can be solved by the following quadratic programming scheme:

[0123]

[0124]

[0125] in represents the identity matrix with diagonal elements of 1, c R =ξ(θ R -θ R (0)), ξ is a parameter greater than 0, θ R (0) represents the initial joint angle vector of the robot R. The above quadratic programming scheme is to find a solution that makes the cost function y in (10) satisfy the constraint condition (11). R (t) Minimum joint velocity In the quadratic programming scheme, constraint (11) is designed according to formula (7). The purpose of this constraint is to ensure that the end of the robot arm R follows the target posture q d,R motion; the first term in the cost function (10) is used to minimize the joint velocity of the robot arm; the second term in the cost function (10) is to complete the repetitive motion task.

[0126] Then, unify the above two quadratic programming solutions into one quadratic programming problem

[0127]

[0128]

[0129] in

[0130]

[0131]

[0132] Finally, the commonly used quadratic programming solver is used to solve the unified quadratic programming problem (12)-(13) to obtain the required optimal joint angular velocity signal. Thereby controlling the two robotic arms to complete synchronous tracking control.

[0133] In summary, the existing technology has the following three shortcomings:

[0134] 1. According to the quadratic programming scheme (12)-(13), solving this problem requires the Jacobian matrix J of the dual-manipulator system L and J R According to formulas (1) and (2), the calculation of the Jacobian matrix of the robot requires the kinematic model parameter information of the robot Known. Therefore, the above existing technical solution is a model-based solution. However, with the increase of task complexity and robot reconfigurability, it is difficult to obtain the kinematic model parameters of the robot in some cases. In addition, long-term work may also cause wear or deformation of the robot, which in turn leads to inconsistency between the actual model parameters and the labeled parameters. In the above scenarios, the model parameters of the robot are only partially known or may be completely unknown, which will cause the performance of the existing model-based technology to deteriorate or even be completely inapplicable. Therefore, it is necessary to design a control algorithm (i.e., model-free method) that can learn or estimate the unknown robot model. Although there are some model-free algorithms that can realize the synchronous control of dual-manipulator systems, these algorithms are only applicable to planar robots with low degrees of freedom (2 to 3 joints) and are less practical. In order to realize the synchronous tracking control of dual-manipulator systems with high degrees of freedom (6 or more joints) in 3D space, more advanced model-free control technologies need to be developed.

[0135] 2. The above-mentioned secondary planning schemes (12)-(13) require the dual-arm system to follow their respective target pose trajectories q d,L and q d,R Movement, when the dual robotic arm system moves strictly according to the target trajectory, the dual robotic arm system can be synchronously tracked and controlled, and the ends of the dual robotic arms will remain relatively still. However, in the actual motion control process of the robotic arm, the actual trajectory of the end of the robotic arm and the target trajectory will inevitably deviate. In this case, there will be a relative displacement between the ends of the dual robotic arms. The existence of relative displacement may cause damage to the target object operated by the dual robotic arm system. The above-mentioned existing technologies have not yet considered the problem of relative displacement of the ends of the dual robotic arms.

[0136] 3. Under ideal conditions, the above-mentioned quadratic planning scheme can successfully solve the problem of synchronous motion control of the dual-arm system. However, the robot usually needs to work in a complex dynamic environment (such as an environment with external interference). In this case, the effect of the above-mentioned quadratic planning scheme may not meet the needs. This scheme is a conventional numerical calculation method with a low level of intelligence. Giving the control system the ability to continuously learn can effectively help the robot adapt to complex dynamic environments. How to design a dual-arm synchronous control system with a high level of intelligence and continuous learning ability is also a problem that needs to be solved.

[0137] In view of the shortcomings of the prior art, the present invention has the following three purposes:

[0138] First, the present invention is to design a model-free synchronous tracking control system for a high-degree-of-freedom dual-manipulator system. To this end, the present invention adopts a gradient descent-based method to learn the unknown model of the dual-manipulator system (i.e., the Jacobian matrix J L and JR ). Based on the model information obtained by learning, the present invention adopts a quadratic programming method to solve the tracking control problem of a dual-manipulator system with high degrees of freedom.

[0139] Secondly, the second purpose of the present invention is to solve the problem of relative displacement of the dual-manipulator system to ensure the relative stillness between the dual-manipulator systems. To this end, the present invention defines an error function coupled by tracking error and synchronization error (i.e., relative displacement), applies a superhelical algorithm to the coupled error function to obtain a differential equation, and then uses the obtained differential equation as a constraint condition of the quadratic programming method, thereby ensuring that the tracking error and synchronization error of the dual-manipulator system converge to zero.

[0140] Finally, the third purpose of the present invention is to propose an intelligent control system with learning ability to improve the performance of the control system. Inspired by human limb movement control, the present invention designs a cerebellum model with learning ability to fine-tune the control system, thereby obtaining a brain-like control system with a higher level of intelligence.

[0141] like Figure 1 As shown in FIG. 1 , it is a schematic diagram of the brain-like synchronous tracking control of the dual-manipulator system proposed in the present invention. The input of the control system is the target trajectory defined by the user, and the output of the control system is the joint angle value that can be used to control the movement of the dual-manipulator system. The operation flow chart of the entire system is shown in FIG. Figure 2 As shown, it includes the following steps:

[0142] A. Initialize the robot arm joint angle θ at time t0=0 L (t0) and θ R (t0), control system related parameters (including the convergence parameters of the gradient neural dynamics model, the superhelical algorithm parameters and the cerebellum model parameters) and the initial value of the Jacobian matrix J of the dual manipulator system L (t0) and J R (t0), input the predefined target trajectory information q of the dual robotic arm system d,L (t) and q d,R (t).

[0143] B. Define the nth moment (t n ), which is composed of the tracking error between the actual position of the robot measured by the sensor and the target position and the synchronization error between the dual robot systems. The superhelical algorithm is applied to the coupling error function, and the Jacobian matrix learned using the gradient neural dynamics model is substituted into it to obtain the differential equation constraints. Considering the obtained constraints and the physical constraints of the robot and designing the optimization objectives, the synchronous tracking control problem of the dual robot system is modeled as a quadratic programming problem, and the preliminary joint velocity signals are obtained by solving the problem. and

[0144] C. The two cerebellar models calculate the adjustment of the joint speeds of the two robotic arms according to the joint angles and tracking errors of the dual robotic arm system. and The adjusted joint velocity signal and Integrate separately, and get the joint angle θ L (t n ) and θ R (t n ) can be used as the input of the dual-arm system to control the movement of the robotic arms. At the same time, the tracking errors of the two robotic arms are multiplied by the pseudo-inverse of the corresponding Jacobian matrix to convert the error in the task space into the error in the joint space. The converted joint space errors can be used as training signals for the two cerebellum models.

[0145] D. Using the gradient neural dynamics model according to t n The joint angular velocity of the dual-arm system at each moment And the end speed of the robot arm measured by the sensor Learn to predict the next time t n+1 Jacobian matrix J of the robot arm L (t n+1 ), J R (t n+1 ).

[0146] After completing step D, repeat steps B to D until the entire tracking control task is completed.

[0147] The synchronous tracking control system and control method of this embodiment are further described in detail below:

[0148] In order to realize the synchronous tracking control of the dual-manipulator system, the present invention invents a Figure 1 The model-free control system shown in Figure 1 is Figure 2 As shown, the execution of the invented control system includes the following steps.

[0149] A. Take the dual-arm system composed of two LBR iiwa 7 R800s (number of joint angles m = 7) as an example. First, initialize the joint angle θ of the robot L at time t0 = 0. L (t0)=[π / 6,π / 4,π / 2,π / 2,-π / 4,-π / 6,π / 2] T Radians and joint angles θ of the robot arm R R (t0)=[-π / 6,π / 4,π / 2,-π / 2,π / 4,π / 6,π / 2] TThe parameter of the gradient neural dynamics model is set to λ = 0.5, and the parameter of the coupling error is set to k s =0.2, the parameters of the supercoil algorithm are set to l1=0.1, l2=0.0001, and p=0.99. The parameters of the cerebellum model mainly include the number of granule cells N=400, the dynamic change speed of granule cells k g =0.5, granulocyte state leakage rate k l =0.6, and the learning rate of the output weight η = 0.0001. The above parameters will be defined in the further technical solution. Taking the robot L as an example, in order to initialize its Jacobian matrix, it is necessary to give a sufficiently small increment Δθ to the angle of the jth joint angle (j = 1, 2, ..., 7) L,j , thereby changing the state of the joint angle and measuring the posture change vector Δq at the end of the robot arm L L , so the (i,j)th element of the Jacobian matrix of the robot L is initialized to

[0150]

[0151] where Δq L,i Indicates the amount of posture change Δq L Therefore, according to the posture change Δq L All elements of and the angle increment Δθ of the j-th joint angle L,j , we can determine all the elements in the jth column of the initial value of the Jacobian matrix. Similarly, repeating the above process for all joints of the robot L (j = 1, 2, ..., 7) can determine the Jacobian matrix J L Similarly, the (i,j)th element of the Jacobian matrix of the robot R is initialized to

[0152]

[0153] where Δθ R,j represents the increment of the angle of the jth joint angle of the robot arm R, Δq R Indicates the resulting change in the terminal posture.

[0154] Taking the circular trajectory as an example, the target trajectory of the dual-arm system is defined as follows:

[0155]

[0156] Where T d =40 seconds indicates the task duration; q d,L (t0) = [x L,0 ,y L,0 ,z L,0 ,α L,0,β L,0 ,γ L,0 ,κ L,0 ] T represents the initial position of the end of the robot arm L measured by the sensor, where the first three items represent the position, and the last four items are the robot end posture (i.e., direction) expressed by quaternion; q d,R (t0) = [x R,0 ,y R,0 ,z R,0 ,α R,0 ,β R,0 ,γ R,0 ,κ R,0 ] T Represents the initial position of the end of the robot arm R.

[0157] B. Define the nth moment (t n )’s coupling error function∈ L and ∈ R , which is composed of the tracking error between the actual and target poses of the robot and the synchronization error between the dual robot systems. The superhelical algorithm is applied to the coupling error function, and the Jacobian matrix learned using the gradient neural dynamics model is substituted into it to obtain the differential equation constraints. Considering the obtained constraints and the physical constraints of the robot and designing the optimization objectives, the synchronous tracking control problem of the dual robot system is modeled as a quadratic programming problem, and the preliminary joint velocity signals are obtained by solving the problem. and

[0158] C. The two cerebellar models calculate the adjustment of the joint speeds of the two robotic arms according to the joint angles and tracking errors of the dual robotic arm system. and The adjusted joint velocity signal and Integrate separately, and get the joint angle θ L (t n ) and θ R (t n ) can be used as the input of the dual-arm system to control the movement of the robotic arms. At the same time, the tracking errors of the two robotic arms are multiplied by the pseudo-inverse of the corresponding Jacobian matrix to convert the error in the task space into the error in the joint space. The converted joint space errors can be used as training signals for the two cerebellum models.

[0159] D. Using the gradient neural dynamics model according to t n The joint angular velocity of the dual-arm system at each moment And the end speed of the robot arm measured by the sensor Learn to predict the next time tn+1 Jacobian matrix J of the dual-manipulator system L (t n+1 ), J R (t n+1 ).

[0160] After completing step D, repeat steps B to D until the entire tracking control task is completed.

[0161] Based on the above technical solution, the dual-manipulator system is controlled to complete the synchronous tracking control task of the circular trajectory. The mathematical operations in the above process can be completed by the MATLAB software in the host computer, and then the solved joint control signal is transmitted to the robot. First, Figure 7 As shown, it is a schematic diagram of the dual-manipulator system completing a circular trajectory synchronous tracking control. It can be seen that after the end of the robot arm completes the docking, it moves synchronously along the circular target trajectory, and the end posture remains unchanged during the movement. Figure 8 It is a comparison between the target trajectory and the actual trajectory of the dual robotic arm system. It can be seen that the actual trajectory of the end of the robotic arm coincides with the target trajectory. Fig. 9 It is the change of the position error and the synchronous position error of the dual-arm system. It can be seen that the position tracking error and position synchronization error of the dual-arm system are both in the order of millimeters, and the posture error is also small enough. In addition, in order to reflect the learning ability of the cerebellum model proposed in the present invention, multiple repeated experiments can be carried out. Fig.10 As shown, in experiment 0, only the quadratic programming scheme is used without the cerebellum model. In this case, the average tracking error of the robot arm L is about 1 mm, the average tracking error of the robot arm R is about 1.5 mm, and the average synchronization error of the dual robot arms is about 1.2 mm. In contrast, the dual robot arm system repeats the tracking task 10 times (experiments 1-10) when the cerebellum model is used. On the one hand, in the first experiment, due to the regulatory effect of the cerebellum model, the tracking error and synchronization error of the robot arm are both reduced compared to the case where the cerebellum model is not used. On the other hand, due to the learning ability of the cerebellum, in repeated experiments 1-10, the tracking error and synchronization error of the dual robot arm system gradually decreased to less than 1 mm. The above results not only reflect the effectiveness of the dual robot arm model-free synchronous tracking control scheme proposed in the present invention, but also reflect the learning ability of the cerebellum model designed by the present invention and its regulatory effect on the control system.

[0162] Furthermore, for the core innovation step B, Figure 3 As shown, the specific plan is as follows:

[0163] B1: First, at the nth moment, the tracking posture error is defined for the dual-arm system, that is, the deviation between the target trajectory and the actual trajectory of the robot end measured by the sensor

[0164]

[0165] At the same time, the synchronization error of the dual-manipulator system can be defined as

[0166] ε=e L -e R . (20)

[0167] B2: Therefore, the coupled posture errors of the dual-arm system can be defined as

[0168]

[0169] Among them, k s is the weight parameter of the coupling pose error.

[0170] B3: Apply the superhelical algorithm to the coupling error function. The definition of the superhelical algorithm is as follows

[0171]

[0172] Where l1, l2 and p are the parameters of the superhelix algorithm, s1 and s2 are the state variables of the algorithm, and Represent the time derivatives of s1 and s2 respectively, and sign(·) is the sign function. The sign function returns a vector indicating the positive and negative of each element of the input vector. For example, if the i-th element of the input vector is greater than 0, the i-th element of the vector returned by the sign function is 1; if the i-th element of the input vector is less than 0, the i-th element of the vector returned by the sign function is -1; if the i-th element of the input vector is equal to 0, the i-th element of the vector returned by the sign function is 0. Then substitute the coupling error functions of the dual-manipulator system into the superhelical algorithm, that is, use ∈ L and ∈ R Substituting s1 respectively, we can get

[0173]

[0174] B4: For simplicity, the above equations (23) can be rewritten into the following compact form:

[0175]

[0176] in

[0177]

[0178]

[0179]

[0180] B5: Design the following quadratic programming scheme at the nth moment

[0181]

[0182]

[0183]

[0184] Θ - ≤Θ≤Θ - (31)

[0185] Among them, W q ∈ represents the identity matrix with diagonal elements set to 1 and other elements set to 0. vector and Respectively represent the lower and upper limits of the joint speed of the dual-manipulator system, and the vector Θ - and θ - Respectively represent the lower and upper limits of the joint angles of the dual-arm system. The above quadratic programming scheme is to find a solution that makes the cost function y(t n )Minimum joint speed of dual-arm system In the quadratic programming scheme, constraint (29) is obtained from the compact differential equation (24) in step B4. The purpose of this constraint is to ensure that the end of the dual-arm system moves synchronously according to the target posture; constraints (30) and (31) require that the obtained joint velocity solution satisfies the physical limit constraints of the robot. The cost function y(t n ) is used to minimize the joint velocity of the robot; the cost function y(t n ) is to complete a repetitive motion task.

[0186] B6: Use a commonly used solver (such as the quadprog function in MATLAB) to solve the quadratic programming solutions (28) to (31) and obtain t n Initial optimal joint velocity signal at all times

[0187] Furthermore: The core innovation point, step C, is mainly to use the learning ability of the cerebellum model to compensate for the preliminary joint velocity signal obtained in step B, so as to obtain a better joint velocity solution to improve the intelligence level of the control system. Biological studies have shown that people mainly rely on the cerebellum to manage motor functions. It receives sensory information from muscles, limbs, joints, skin, etc. through the nervous system of the cerebellar cortex, and senses feedback information, and then integrates the obtained information into a specific area - the "memory" for memory. When needed, the information stored in these memories is taken out as instructions to drive and coordinate muscle movements - control signals. When there is a difference between the sensed information and the feedback information, it is adjusted through association to achieve the purpose of motion control. Inspired by the above biological mechanisms, the present invention will design a cerebellum model to assist in the coordinated tracking control of a dual robotic arm system. Figure 4 As shown in the figure, the cerebellum model mainly includes Mossyfiber (MF), granular cell (GC), Purkinje cell (PC), and deep cerebellar nuclei (DCN). The afferent unit is responsible for transmitting the input signal to the granular cell, and the granular cell is responsible for encoding the input signal to update its own state. The state signal of the granular cell is transmitted through the parallel fiber (PF) and transmitted to the Purkinje cell after weighted operation. The climbing fiber (CF) is used to receive training signals to train the weights between the parallel fiber and the Purkinje cell. Purkinje cells, afferent units and climbing fibers transmit excitatory and inhibitory signals to the deep cerebellar nuclei through synapses. The state of the deep cerebellar nuclei is the output of the cerebellum model. As shown in the figure, the cerebellum model mainly includes Mossyfiber (MF), granular cell (GC), Purkinje cell (PC), and deep cerebellar nuclei (DCN). Figure 1 As shown, the present invention provides a cerebellum model for each of the two robotic arms. Figure 5 As shown, the two cerebellum models corresponding to the dual-manipulator system in the present invention are at t n The workflow at this moment is as follows:

[0188] C1: at t n At this moment, the input vectors of the cerebellum model corresponding to the robot arm L and the robot arm R are and

[0189] C2: State vectors of granule cells in two cerebellar models and The update rules are as follows:

[0190]

[0191]

[0192] where k g represents the dynamic change rate of granulocytes, k l Granulocyte state leak rate, matrix and Represent the input weights between the afferent units and granule cells of the two cerebellar models, respectively, and the matrices and Represent the internal weights between the granular cells of the two cerebellar models. The input weight matrix and the internal connection weight matrix are randomly initialized to values ​​between [-1, 1] and remain unchanged during the model operation. N ] T Represents the output activation function of granulocytes, usually using the sigmoid activation function:

[0193]

[0194] Next, parallel fibers in two cerebellar models and Used to convey the state of granulocytes, i.e.

[0195]

[0196]

[0197] C3: The state of the Purkinje cell is the weighted sum of the signals of the parallel fibers, so the Purkinje cells of the two cerebellar models are n The state vector at time and The update formulas are:

[0198]

[0199]

[0200] The matrix and are the output weights between the parallel fibers and Purkinje cells of the two cerebellar models, and their initialization values ​​are all 0, tanh(·)=tanh1,tanh2,…,tanh N ] T is the hyperbolic tangent activation function, which is defined as:

[0201]

[0202] C4: The input vectors of the climbing fibers of the two cerebellar models are and in The operator represents the pseudo-inverse operation of the matrix. The afferent units and climbing fibers in the cerebellum model send excitatory signals to the deep cerebellar nuclei through synapses, while the Purkinje cells send inhibitory signals to the deep cerebellar nuclei through synapses. Therefore, the state vectors of the deep cerebellar nuclei of the two cerebellum models are and In t n Updated to

[0203]

[0204]

[0205] where the vector and Represents the synaptic plasticity between the afferent units and the deep cerebellar nuclei in the two cerebellar models, respectively. The matrices and represents the synaptic plasticity between climbing fibers and deep cerebellar nuclei in the two cerebellar models, respectively. The matrices and They represent the synaptic plasticity between Purkinje cells and deep cerebellar nuclei in the two cerebellum models. The initial values ​​of the matrices and vectors representing synaptic plasticity are all 0.

[0206] C5: Output weights need to be trained during the operation of the cerebellum-like model and The update rules for the output weights of the two cerebellum models are as follows

[0207]

[0208]

[0209] Where η represents the output weight learning rate. At the same time, the matrix and vector related to synaptic plasticity need to be updated during the training process. The change in the synaptic plasticity vector between the afferent unit (MF) and the deep cerebellar nucleus (DCN) of the two cerebellar models is as follows:

[0210]

[0211]

[0212] Where, the subscript i=1,2…,m represents the i-th element of the corresponding vector, LTP max =1×10 -6 stands for Long term potentiation (LTP), LTD max =1×10 -3represents the maximum long-term depression (LTD), k d =2 represents the decay rate. The changes in the synaptic plasticity matrix between the Purkinje cells (PC) and the deep cerebellar nuclei (DCN) of the two cerebellar models are as follows:

[0213]

[0214]

[0215] Wherein, the subscript i=1,2…,m represents the i-th element of the corresponding vector or the (i,i)-th element of the corresponding matrix. max =1×10 -3 stands for maximum long-term potentiation, LTD max =1×10 -3 represents the maximum long-term inhibition, k d =2 represents the decay rate. The changes in the synaptic plasticity matrix between the climbing fibers (CF) and the deep cerebellar nuclei (DCN) of the two cerebellar models are as follows:

[0216]

[0217]

[0218] Wherein, the subscript i=1,2…,m represents the i-th element of the corresponding vector or the (i,i)-th element of the corresponding matrix. MTP max =1×10 -4 Modulating term potentiation (MTP), MTD max =1×10 -4 represents the maximum modulation term depression (MTD), k d =2 represents the attenuation rate.

[0219] C6: The two cerebellum models output compensation for joint velocity respectively And compensate the joint velocity obtained in step B to get t n The final joint velocity signal at the moment

[0220]

[0221]

[0222] The joint velocity signals are integrated over time to obtain t n The joint angle signal θ at time L(t n ) and θ R (t n ), and use the joint angle signals to control the movements of robot arms L and R respectively.

[0223] Further, for the core innovation step D, as Figure 6 The specific plan is as follows

[0224] D1: First, according to t n The end velocities and joint velocities of the dual-arm system measured by the sensors at each moment are defined as the following error functions:

[0225]

[0226]

[0227] Where ‖·‖2 represents the bi-norm of the vector (i.e., the sum of the squares of the elements in the vector), and Respectively represent the actual speed of the two robot arms at their respective ends, J L and J R represents the learned t n The Jacobian matrix at time instant. and They can be regarded as the estimated end velocities of the two robotic arms respectively.

[0228] D2: Using the gradient neural dynamics method, design the time derivatives of the Jacobian matrices of the two manipulators

[0229]

[0230]

[0231] Where λ represents the parameter of gradient neural dynamics. The above design formula first calculates the partial derivative of the error function with respect to the Jacobian matrix, and then designs the update direction of the Jacobian matrix along the negative gradient direction (i.e., the direction in which the error decreases).

[0232] D3: Finally, predict the Jacobian matrix of each of the two robotic arms at the next moment

[0233]

[0234]

[0235] Where Δt = 0.1 seconds represents the time sampling interval. The predicted Jacobian matrix will be used for the control of the dual-manipulator system at the next moment.

[0236] In summary, the present invention specifically introduces the principle, function and implementation method of the proposed dual-arm system synchronous tracking control scheme. First, this embodiment can realize the control of the robotic arm when the model of the dual-arm system is unknown, thereby solving the challenges brought by model uncertainty or unknown models, avoiding the complex process of modeling the robotic arm, and the control scheme has good portability for robotic arms of different types and structures (including robotic arms with low degrees of freedom and high degrees of freedom). Secondly, this embodiment can realize synchronous control during the collaboration of the dual-arm system, thereby expanding the application scenarios of the robotic arm. Finally, the cerebellum model proposed in this embodiment has the ability of continuous learning, which can reduce the tracking error and synchronization error of the dual-arm system and improve the long-term operation performance of the control system.

[0237] In some selectable embodiments, the function / operation mentioned in the block diagram may not occur in the order mentioned in the operation diagram. For example, depending on the function / operation involved, the two boxes shown in succession can actually be executed substantially simultaneously or the boxes can sometimes be executed in reverse order. In addition, the embodiment presented and described in the flow chart of the present invention is provided by way of example, for the purpose of providing a more comprehensive understanding of technology. The disclosed method is not limited to the operation and logic flow presented herein. Selectable embodiments are expected, wherein the order of various operations is changed and the sub-operation of a part for which is described as a larger operation is performed independently.

[0238] In addition, although the present invention is described in the context of functional modules, it should be understood that, unless otherwise specified, one or more of the functions and / or features described may be integrated into a single physical device and / or software module, or one or more functions and / or features may be implemented in separate physical devices or software modules. It is also understood that a detailed discussion of the actual implementation of each module is unnecessary for understanding the present invention. More specifically, in view of the properties, functions, and internal relationships of the various functional modules in the device disclosed herein, the actual implementation of the module will be understood within the conventional skills of the engineer. Therefore, those skilled in the art can implement the present invention set forth in the claims without excessive experimentation using ordinary techniques. It is also understood that the specific concepts disclosed are merely illustrative and are not intended to limit the scope of the present invention, which is determined by the full scope of the appended claims and their equivalents.

[0239] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc., which can store program codes.

[0240] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, device or apparatus (such as a computer-based system, a system including a processor, or other system that can fetch instructions from an instruction execution system, device or apparatus and execute instructions), or in conjunction with such instruction execution systems, devices or apparatuses. For the purposes of this specification, "computer-readable medium" can be any device that can contain, store, communicate, propagate or transmit a program for use by an instruction execution system, device or apparatus, or in conjunction with such instruction execution systems, devices or apparatuses.

[0241] More specific examples of computer-readable media (a non-exhaustive list) include the following: an electrical connection with one or more wires (electronic device), a portable computer disk case (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disk read-only memory (CDROM). In addition, the computer-readable medium may even be a paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, deciphering or, if necessary, processing in another suitable manner, and then stored in a computer memory.

[0242] It should be understood that the various parts of the present invention can be implemented by hardware, software, firmware or a combination thereof. In the above-mentioned embodiments, a plurality of steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0243] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "examples", "specific examples", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0244] Although the embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the claims and their equivalents.

[0245] The above is a specific description of the preferred implementation of the present invention, but the present invention is not limited to the described embodiments. Those skilled in the art may make various equivalent modifications or substitutions without violating the spirit of the present invention. These equivalent modifications or substitutions are all included in the scope defined by the claims of this application.

Claims

1. A brain-like synchronous tracking control method for dual robotic arms, characterized in that: include: Initializing the system configuration to obtain an initialization parameter set, wherein the initialization parameter set includes two joint angles of the dual robotic arms, control system parameters, two Jacobian matrix initial values ​​of the dual robotic arm system, and two target trajectory information of the dual robotic arm system; Defining a coupling error function for the dual-manipulator system, determining a corresponding Jacobian matrix according to the coupling error function, and then determining differential equation constraints; The two cerebellar models are used to calculate the adjustment of the two joint velocities according to the joint angles and tracking errors of the dual-arm system, and the joint angles are obtained by integrating the adjusted joint velocity signals. The joint angles are used as the input of the dual-arm system to control the corresponding movement of the robotic arms. Using the gradient neural dynamics model, the robot arm Jacobian matrix at the next moment is learned based on the input joint angular velocity of the dual robot arm system and the robot arm end velocity measured by the sensor. According to the Jacobian matrix of the robot arm at each moment, the robot arm is controlled in real time; Defining a coupling error function for the dual-manipulator system, determining a corresponding Jacobian matrix according to the coupling error function, and then determining differential equation constraints, includes: Define the tracking pose error for the dual-arm system and determine the deviation between the target trajectory and the actual trajectory of the robot end measured by the sensor; Determine the coupling posture errors of the dual robot arm systems according to the deviations; Determine the coupling error function of the dual-manipulator system based on the super-helical algorithm; Rewriting the coupling error function to construct a compact coupling error function; constructing a quadratic programming scheme according to the coupling error function; Solving the quadratic programming scheme to obtain a preliminary optimal joint velocity signal; The constructing of a quadratic programming scheme according to the coupling error function comprises: Design optimization objectives based on differential equation constraints and the robot's physical constraints; The synchronous tracking control problem of the dual-manipulator system is modeled as a quadratic programming problem; The method calculates the adjustment amount of the two joint speeds according to the joint angles and tracking errors of the dual-arm system through the two cerebellar models, integrates the adjusted joint speed signals to obtain the joint angles, uses the joint angles as the input of the dual-arm system, and controls the corresponding movement of the robotic arms, including: Obtain input vectors of the cerebellum model of the left and right robotic arms of the dual robotic arms at different times; Determine, according to the input vector, an update rule for the state vectors of the granule cells in the two cerebellum models; Determine the update formula of the state vector of the Purkinje cells of the two cerebellar models at each moment; wherein the state of the Purkinje cells is the weighted sum of the signals of the parallel fibers; Acquire the input vectors of the climbing fibers of the two cerebellum models, and update the state vectors of the cerebellar deep nuclei of the two cerebellum models according to the state vector update formula; Construct the update rules for the output weights of each of the two cerebellar models; The two cerebellar models output compensation amounts for joint velocity respectively, and compensate for the joint velocity, thereby obtaining the final joint velocity signal at each moment; The method further comprises: Multiply the tracking errors of the two manipulators by the pseudo-inverse of the corresponding Jacobian matrix to convert the error in the task space into the error in the joint space; The transformed joint space error is used as the training signal for the two cerebellum models; The gradient neural dynamics model is used to learn and predict the Jacobian matrix of the robotic arm at the next moment according to the input joint angular velocity of the dual robotic arm system and the robotic arm end velocity measured by the sensor, including: The error function is defined according to the end velocities and joint velocities of the dual-manipulator system measured by sensors at each moment; According to the error function, the time derivatives of the Jacobian matrices of the two manipulators are designed using the gradient neural dynamics method; Predict the Jacobian matrices of the two robotic arms at the next moment.

2. An electronic device, characterized in that: including a processor and a memory; The memory is used to store programs; The processor executes the program to implement the method according to claim 1.

3. A computer-readable storage medium, characterized in that: The storage medium stores a program, and the program is executed by a processor to implement the method according to claim 1.

4. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the method according to claim 1 is implemented.

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