A method and system for model-free adaptive cooperative control of multiple robots based on neurodynamics

Abstract

The application discloses a kind of multi-robot model-free adaptive cooperative control method and system based on neurodynamics, comprising: the kinematic model of each robot is established including Jacobian matrix to be estimated and unknown disturbance term;Using online learning algorithm based on measurable velocity, the above-mentioned matrix and disturbance term are estimated in real time synchronously;Coupling individual tracking error (single robot actual and expected trajectory deviation) and cooperative error (adjacent robot tracking error difference) comprehensive error model is constructed, and closed-loop error transmission structure is formed;Then according to this, design distributed motion controller, combine online learning result, synchronization error, calculate joint control speed using neurodynamics method to make comprehensive error converge to zero;Finally, the relevant formula is discretized, and the iterative update formula is generated, according to which the instruction is output to drive the robot motion in each control cycle.The method does not need accurate model, and has high robustness, can ensure that multi-robot accurately tracks trajectory and maintains stable formation, and the system has good scalability.

Description

Technical Field

[0001] This invention belongs to the field of robot control technology, and in particular relates to a multi-robot model-free adaptive cooperative control method and system based on neurodynamics. Background Technology

[0002] With the rapid development of robotics technology, multi-robot systems are increasingly being applied in complex scenarios such as industrial automation, intelligent logistics, and disaster relief. Multi-robot collaboration is a core component of this field, referring to multiple robots communicating and cooperating to jointly complete complex tasks that are difficult for a single robot to handle, such as environmental monitoring, search and rescue, and precision agriculture. The sheer number of robots and the complexity of their interactions make these systems more efficient and flexible in handling large-scale tasks and adaptable to dynamically changing environments. However, this also presents significant challenges in areas such as collaborative planning, task allocation, and communication, attracting considerable attention from researchers both domestically and internationally.

[0003] A fundamental problem in the control of multi-robot systems is real-time motion planning: how to enable robots to learn from experience and act collaboratively in real time in dynamically changing and uncertain environments. Traditional control methods, such as centralized or rule-based strategies, often struggle to cope with environmental changes, resource constraints, and communication limitations in real-time applications. Therefore, for dynamic, complex scenarios with unknown or uncertain models, it is necessary to develop collaborative methods capable of adaptive learning and planning. Summary of the Invention

[0004] This invention overcomes the shortcomings of existing technologies and provides a model-free adaptive cooperative control method for multi-robot systems based on neurodynamics, addressing the following problems: 1) The difficulty in achieving high-precision trajectory tracking and stable formation coordination in multi-robot systems under conditions of inaccurate models and unknown external disturbances. 2) To facilitate computer programming and digital processing, a more accurate and stable discrete method is developed to realize multi-robot control.

[0005] The technical solution adopted by this invention to solve its technical problem is:

[0006] A model-free adaptive cooperative control method for multi-robots based on neurodynamics includes the following steps:

[0007] S100: For each robot in a multi-robot system, given the corresponding desired trajectory, establish a kinematic model containing the Jacobian matrix to be estimated and unknown disturbance terms;

[0008] S200: Based on measurable robot end effector speed and joint speed, it uses a gradient descent-driven online learning algorithm to estimate the Jacobian matrix and disturbance terms in real time and synchronously.

[0009] S300: Design a comprehensive error model that couples individual tracking error and cooperative error; where individual tracking error is the deviation between the actual trajectory and the expected trajectory of a single robot, and cooperative error is the difference in individual tracking error between adjacent robots, forming a closed-loop error propagation structure;

[0010] S400: Based on the comprehensive error model, a distributed motion controller is designed for each robot. This controller uses the Jacobian matrix and disturbance term learned online in S200, combined with the synchronization error, and uses the neurodynamics method to calculate the joint control speed that can make the comprehensive error converge to zero.

[0011] S500: Discretizes the continuous-time formula of the online learning algorithm and the distributed motion controller to form an iterative update formula that can run on a digital computer. Based on the discretized update formula, it calculates and outputs joint control commands in each control cycle to drive the robot joint movement, thereby achieving accurate tracking of the desired trajectory and stable formation coordination among multiple robots.

[0012] Preferably, S100 includes:

[0013] S110: For a single robotic arm, based on the positive kinematics of the robotic arm, the relationship between the joint angles and the end effector position is established as follows:

[0014] (1)

[0015] in, It is the end effector of the robotic arm. The actual location in the dimensional task space. It is a mapping function determined by the mathematical model of the robotic arm, given a desired target trajectory. In order for the robotic arm to track the target's motion trajectory, it is necessary to find a suitable joint angle vector for the robot. ,make sure Able to converge ;

[0016] S120: Differentiate both sides of formula (1) and introduce an unknown disturbance term, namely the velocity disturbance term. ,get:

[0017] (2)

[0018] in, It is the Jacobian matrix of the robotic arm, the value of which is obtained by considering the joint angles of the robotic arm at any given time. Seeking, It is the task space dimension. It's the number of joints. It is the joint angular velocity vector, which is the joint angle. Regarding time The derivative of , They are , Regarding time The derivative of represents the actual end effector speed and the expected end effector speed.

[0019] Preferably, S200 includes:

[0020] S210: For the system's... A robotic arm, based on the real-time measurable actual speed of the end effector. and joint angular velocity Define the velocity prediction residual vector :

[0021] (3)

[0022] in, For the first The velocity prediction error vector of the robotic arm For the first Online estimates of the Jacobian matrix for each robotic arm. For the first Online estimates of the speed disturbance term of the robotic arm. The first one obtained by the sensor measurement The actual speed of the end effector of the robotic arm is required to enable the robotic arm to track the target's motion trajectory. and Converging to the true value, i.e. ;

[0023] S220: Define speed prediction error index :

[0024] (4)

[0025] in, For the first Speed ​​prediction error index of a robotic arm The square of the Euclidean norm;

[0026] In order to obtain and The update rate is determined using a gradient descent-based update algorithm, employing the following online learning algorithm:

[0027] (5)

[0028] (6)

[0029] in, The learning rate for the Jacobian matrix estimate. The learning rate for the estimated velocity disturbance term. For the first Update rate of the Jacobian matrix estimate of each robotic arm For the first Update rate of the estimated speed disturbance term of the robotic arm The partial derivative of the velocity prediction error index with respect to the Jacobian matrix estimate is given by... The partial derivative of the speed prediction error index with respect to the estimated value of the speed disturbance term. For the first The joint angle vectors of the robotic arm, For the first The joint angular velocity vectors of the robotic arm, For the first Speed ​​interference error of the robotic arm;

[0030] Further obtain Update value at time and :

[0031] (7)

[0032] (8)

[0033] in, For the first A robotic arm at any time The Jacobian matrix estimate, For the time step, take , For the first A robotic arm at any time Estimates of the speed disturbance term.

[0034] Preferably, S300 includes:

[0035] S310: Define the first The individual tracking error of each robot is:

[0036] (9)

[0037] in, For the first Individual tracking error of the robot It is the end effector of the robotic arm. Dimensional task space The actual location at any given time. For the end effector of the robotic arm Dimensional task space The position of the expected trajectory at any given moment;

[0038] S320: This defines a robot by arranging its members in a chain-like queue, forming a circular structure. Compared to the previous robot Cooperative error between them:

[0039] (10)

[0040] The first robot and the... The coordination error between robots is defined as:

[0041] (11)

[0042] in, For the first The coordination error between the current robot and the previous robot For the first Individual tracking error of each robot and The first The actual and desired positions of the robots. For the individual tracking error of the first robot, For the first Individual tracking error of each robot and These are the actual position and the desired position of the first robot, respectively. and The first The actual and desired positions of the robots;

[0043] S330: Introduces a comprehensive error that includes an integral term. To eliminate steady-state errors and enhance system robustness, specifically:

[0044] for :

[0045] (12)

[0046] For the last robot, that is ,have:

[0047] (13)

[0048] in, For the first A robot at any moment The overall error, where ρ>0 is the gain constant. and The first The robot and the first A robot at any moment The overall error, and The first robot and the second robot, respectively. A robot at any moment The overall error.

[0049] Preferably, S400 includes:

[0050] S410: Based on the integrated error model, the control objective is designed to make the integrated error dynamically converge to zero. To this end, the error dynamic equation is designed using the neurodynamics method:

[0051] (14)

[0052] in, For the first A robot at any moment The derivative of the overall error, , Parameters for neurodynamic design, For activation functions;

[0053] S420: Employing an activation function Through derivation, a distributed joint velocity control law integrating online learning update values ​​and collaborative errors was obtained:

[0054] for :

[0055] (15)

[0056] For the last robot :

[0057] (16)

[0058] S430: Obtained through integral updates based on joint speed control commands. Joint angle at any moment:

[0059] (17)

[0060] (18)

[0061] in, For the first Joint angular velocity control commands for a robot For the first The pseudo-inverse of the Jacobian matrix updated by the robot is taken as... .

[0062] Preferably, S500 includes:

[0063] The Euler method is used to discretize the online learning algorithm formulas (5) and (6) and the controller formulas (15) and (16), and iterative calculations are performed in each control cycle k. The specific steps are as follows:

[0064] S510: For the first A robot, based on the desired speed at the current moment. Cooperative error Comprehensive error And what you get from online learning and Calculate joint angular velocity control commands :

[0065] for :

[0066] (19)

[0067] for :

[0068] (20)

[0069] For each robot, update the joint angles for the next moment based on the calculated joint angular velocities:

[0070] (twenty one)

[0071] in, and The first The robot and the first The robot in the first Joint angular velocity at each time step and The first The robot in the first The time step and the first Joint angles at each time step and The first The robot and the first The robot in the first The pseudo-inverse of the Jacobian matrix estimate at each time step and The first The robot and the first The robot in the first The expected end effector speed at each time step and The first The robot and the first The robot in the first Estimates of the velocity disturbance term at each time step. , , and The first robot, the second robot, and the third robot, respectively. The robot, the first The robot and the first The robot in the first The coordination error at each time step and The first The robot and the first The robot in the first The combined error at each time step To control the sampling time of the cycle;

[0072] S520: For the first The robot, based on the current actual end effector speed and joint angular velocity Update the estimates of the Jacobian matrix and the disturbance term:

[0073] (twenty two)

[0074] in, For the first The robot in the first The update amount of the Jacobian matrix estimate at each time step For the first The robot in the first The update amount of the velocity disturbance term estimate at each time step;

[0075] The joint angle vector of the robotic arm at the next moment is calculated through the above steps. As the control quantity for the movement of each robotic arm, this forms a discrete implementation of collaborative planning control for a multi-robot system based on online learning.

[0076] Preferably, the multi-robot system consists of multiple redundant robotic arms, and the robots exchange error information through local communication to achieve distributed collaborative control.

[0077] A model-free adaptive cooperative control system for multi-robots based on neurodynamics, comprising:

[0078] The kinematic model building module is used to build a kinematic model for each robot in a multi-robot system, including the Jacobian matrix to be estimated and unknown disturbance terms.

[0079] The online learning algorithm estimation module is used to estimate the Jacobian matrix and disturbance terms in real time and synchronously using an online learning algorithm driven by gradient descent, based on measurable robot end effector velocity and joint velocity.

[0080] The integrated error model design module is used to design an integrated error model that couples individual tracking error and cooperative error. The individual tracking error is the deviation between the actual trajectory and the expected trajectory of a single robot, and the cooperative error is the difference in individual tracking errors between adjacent robots, forming a closed-loop error propagation structure.

[0081] The distributed motion controller design module is used to design a distributed motion controller for each robot based on the comprehensive error model. The controller uses an online learning algorithm to estimate the Jacobian matrix and disturbance terms obtained online in the estimation module, and calculates the joint control speed that can make the comprehensive error converge to zero.

[0082] The discretization module is used to discretize the continuous-time formulas of the online learning algorithm and the distributed motion controller, forming an iterative update formula that can run on a digital computer. Based on the discretized update formula, joint control commands are calculated and output in each control cycle to drive the robot joints to move, thereby achieving accurate tracking of the desired trajectory and stable formation coordination among multiple robots.

[0083] A computer device includes a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps of a model-free adaptive cooperative control method for multi-robots based on neurodynamics.

[0084] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a model-free adaptive cooperative control method for multi-robots based on neurodynamics.

[0085] The aforementioned model-free adaptive cooperative control method and system for multi-robots based on neurodynamics eliminates the need for establishing precise kinematic models of the robots. It can adapt to changes in model parameters and unknown external disturbances in real time through online learning, exhibiting high robustness. By coupling individual tracking errors with cooperative errors, the system ensures that the multi-robot system maintains a stable relative pose (formation) while accurately tracking its respective desired trajectory. Each robot's decision-making relies only on its own and neighboring robots' information, reducing dependence on the central processing unit and global communication, resulting in good system scalability. Attached Figure Description

[0086] Figure 1 This is a flowchart of a multi-robot model-free adaptive cooperative control method based on neurodynamics in one embodiment of the present invention;

[0087] Figure 2 A three-dimensional model of the robotic arm to realize the present invention;

[0088] Figure 3 A schematic diagram showing the relative positions of the robotic arm queue used in the simulation experiment of this invention;

[0089] Figure 4 A schematic diagram of the robotic arm's motion trajectory for realizing the present invention;

[0090] Figure 5 A schematic diagram illustrating the tracking error between the actual motion trajectory of the robotic arm and the target tracking trajectory, as presented in this invention;

[0091] Figure 6 To achieve the tracking error norm between the actual motion trajectory of the robotic arm and the target tracking trajectory of this invention Schematic diagram;

[0092] Figure 7 A schematic diagram illustrating the comprehensive error norm of the multi-robot system of this invention;

[0093] Figure 8 A schematic diagram of the joint angle of the robotic arm to realize the present invention;

[0094] Figure 9 A schematic diagram of the angular velocity of the robotic arm joints to realize the present invention. Detailed Implementation

[0095] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings.

[0096] In one embodiment, such as Figure 1 As shown, a model-free adaptive cooperative control method for multi-robots based on neurodynamics includes the following steps:

[0097] S100: For each robot in a multi-robot system, given the corresponding desired trajectory, establish a kinematic model containing the Jacobian matrix to be estimated and unknown disturbance terms;

[0098] S200: Based on measurable robot end effector speed and joint speed, it uses a gradient descent-driven online learning algorithm to estimate the Jacobian matrix and disturbance terms in real time and synchronously.

[0099] S300: Design a comprehensive error model that couples individual tracking error and cooperative error; where individual tracking error is the deviation between the actual trajectory and the expected trajectory of a single robot, and cooperative error is the difference in individual tracking error between adjacent robots, forming a closed-loop error propagation structure;

[0100] S400: Based on the comprehensive error model, a distributed motion controller is designed for each robot. This controller uses the Jacobian matrix and disturbance term learned online in S200, combined with the synchronization error, and uses the neurodynamics method to calculate the joint control speed that can make the comprehensive error converge to zero.

[0101] S500: Discretizes the continuous-time formula of the online learning algorithm and the distributed motion controller to form an iterative update formula that can run on a digital computer. Based on the discretized update formula, it calculates and outputs joint control commands in each control cycle to drive the robot joint movement, thereby achieving accurate tracking of the desired trajectory and stable formation coordination among multiple robots.

[0102] This invention proposes a model-free adaptive cooperative control method for multi-robot systems based on neurodynamics. Addressing the need for efficient cooperation in dynamic and uncertain environments, this method achieves model-free robot control by learning disturbances and the Jacobian matrix online, enhancing system adaptability. Furthermore, through cooperative error tracking synchronization, the neurodynamic approach allows errors to converge to an equivalent model within a short time, thus achieving adaptive control of the multi-robot system and enhancing system coordination. This method enables robots to learn and update their kinematic parameters in real-time from current data, achieving rapid adaptation to the environment and task, and achieving accurate trajectory tracking. It allows robots to adapt to environmental changes in real-time without requiring a precise robot dynamics model. By establishing a distributed controller using neurodynamics, the multi-robot system can efficiently complete cooperative tasks, significantly improving system robustness, scalability, and trajectory tracking accuracy, demonstrating broad engineering application prospects.

[0103] In one embodiment, S100 includes:

[0104] S110: For a single robotic arm, based on the positive kinematics of the robotic arm, the relationship between the joint angles and the end effector position is established as follows:

[0105] (1)

[0106] in, It is the end effector of the robotic arm. The actual location in the dimensional task space. It is a mapping function determined by the mathematical model of the robotic arm, given a desired target trajectory. In order for the robotic arm to track the target's motion trajectory, it is necessary to find a suitable joint angle vector for the robot. ,make sure Able to converge ;

[0107] S120: Differentiate both sides of formula (1) and introduce an unknown disturbance term, namely the velocity disturbance term. ,get:

[0108] (2)

[0109] in, It is the Jacobian matrix of the robotic arm, the value of which is obtained by considering the joint angles of the robotic arm at any given time. Seeking, It is the task space dimension. It's the number of joints. It is the joint angular velocity vector, which is the joint angle. Regarding time The derivative, , They are , Regarding time The derivative of represents the actual end effector speed and the expected end effector speed.

[0110] Specifically, the robot of this invention is a UR5 robotic arm, such as... Figure 2 As shown, the robotic arm consists of six links, connected by joints 1, 2, 3, 4, 5, and 6, and its workspace is three-dimensional.

[0111] It is worth noting that previous model-based methods meant The mathematical expression for the robot is known, meaning an accurate kinematic model of the robot needs to be established, while a model-free approach means that an accurate kinematic model of the robot is not required. The relevant information is as follows. This invention addresses the case where there is no mathematical model or the mathematical model is inaccurate; therefore, the true Jacobian matrix of the robotic arm may be inaccurate or unknown. To predict and calculate an accurate Jacobian matrix, it is necessary to analyze and calculate the motion information of the actuator at the end effector of the robotic arm.

[0112] In one embodiment, S200 includes:

[0113] S210: For the system's... A robotic arm, based on the real-time measurable actual speed of the end effector. and joint angular velocity Define the velocity prediction residual vector :

[0114] (3)

[0115] in, For the first The velocity prediction error vector of the robotic arm For the first Online estimates of the Jacobian matrix for each robotic arm. For the first Online estimates of the speed disturbance term of the robotic arm. The first one obtained by the sensor measurement The actual speed of the end effector of the robotic arm is required to enable the robotic arm to track the target's motion trajectory. and Converging to the true value, i.e. ;

[0116] S220: Define speed prediction error index :

[0117] (4)

[0118] in, For the first Speed ​​prediction error index of a robotic arm The square of the Euclidean norm;

[0119] In order to obtain and The update rate is determined using a gradient descent-based update algorithm, employing the following online learning algorithm:

[0120] (5)

[0121] (6)

[0122] in, The learning rate for the Jacobian matrix estimate. The learning rate for the estimated velocity disturbance term. For the first Update rate of the Jacobian matrix estimate of each robotic arm For the first Update rate of the estimated speed disturbance term of the robotic arm The partial derivative of the velocity prediction error index with respect to the Jacobian matrix estimate is given by... The partial derivative of the speed prediction error index with respect to the estimated value of the speed disturbance term. For the first The joint angle vectors of the robotic arm, For the first The joint angular velocity vectors of the robotic arm, For the first Speed ​​interference error of the robotic arm;

[0123] Further obtain Update value at time and :

[0124] (7)

[0125] (8)

[0126] in, For the first A robotic arm at any time The Jacobian matrix estimate, For the time step, take , For the first A robotic arm at any time Estimates of the speed disturbance term.

[0127] In one embodiment, S300 includes:

[0128] S310: Define the first The individual tracking error of each robot is:

[0129] (9)

[0130] in, For the first Individual tracking error of the robot It is the end effector of the robotic arm. Dimensional task space The actual location at any given time. For the end effector of the robotic arm Dimensional task space The position of the expected trajectory at any given moment;

[0131] S320: This defines a robot by arranging its members in a chain-like queue, forming a circular structure. Compared to the previous robot Cooperative error between them:

[0132] (10)

[0133] The first robot and the... The coordination error between robots is defined as:

[0134] (11)

[0135] in, For the first The coordination error between the current robot and the previous robot For the first Individual tracking error of each robot and The first The actual and desired positions of the robots. For the individual tracking error of the first robot, For the first Individual tracking error of each robot and These are the actual position and the desired position of the first robot, respectively. and The first The actual and desired positions of the robots;

[0136] S330: Introduces a comprehensive error that includes an integral term. To eliminate steady-state errors and enhance system robustness, specifically:

[0137] for :

[0138] (12)

[0139] For the last robot, that is ,have:

[0140] (13)

[0141] in, For the first A robot at any moment The overall error, where ρ>0 is the gain constant. and The first The robot and the first A robot at any moment The overall error, and The first robot and the second robot, respectively. A robot at any moment The overall error.

[0142] In one embodiment, S400 includes:

[0143] S410: Based on the integrated error model, the control objective is designed to make the integrated error dynamically converge to zero. To this end, the error dynamic equation is designed using the neurodynamics method:

[0144] (14)

[0145] in, For the first A robot at any moment The derivative of the overall error, , Parameters for neurodynamic design, For activation functions;

[0146] S420: Employing an activation function Through derivation, a distributed joint velocity control law integrating online learning update values ​​and collaborative errors was obtained:

[0147] for :

[0148] (15)

[0149] For the last robot :

[0150] (16)

[0151] S430: Obtained through integral updates based on joint speed control commands. Joint angle at any moment:

[0152] (17)

[0153] (18)

[0154] in, For the first Joint angular velocity control commands for a robot For the first The pseudo-inverse of the Jacobian matrix updated by the robot is taken as... .

[0155] Specifically, this control law integrates the updated values ​​from online learning with the collaborative error, and uses a neurodynamic approach to build a distributed solver, thereby improving the overall error. It can quickly converge to zero, realizing distributed adaptive control.

[0156] In one embodiment, S500 includes:

[0157] The Euler method is used to discretize the online learning algorithm formulas (5) and (6) and the controller formulas (15) and (16). The following steps are performed in each control cycle k to iteratively calculate the state of control cycle k+1. The specific steps are as follows:

[0158] S510: For the first A robot, based on the desired speed at the current moment. Cooperative error Comprehensive error And what you get from online learning and Calculate joint angular velocity control commands :

[0159] for :

[0160] (19)

[0161] for :

[0162] (20)

[0163] For each robot, update the joint angles for the next moment based on the calculated joint angular velocities:

[0164] (twenty one)

[0165] in, and The first The robot and the first The robot in the first Joint angular velocity at each time step and The first The robot in the first The time step and the first Joint angles at each time step and The first The robot and the first The robot in the first The pseudo-inverse of the Jacobian matrix estimate at each time step and The first The robot and the first The robot in the first The expected end effector speed at each time step and The first The robot and the first The robot in the first Estimates of the velocity disturbance term at each time step. , , and The first robot, the second robot, and the third robot, respectively. The robot, the first The robot and the first The robot in the first The coordination error at each time step and The first The robot and the first The robot in the first The combined error at each time step To control the sampling time of the cycle;

[0166] S520: For the first The robot, based on the current actual end effector speed and joint angular velocity Update the estimates of the Jacobian matrix and the disturbance term:

[0167] (twenty two)

[0168] in, For the first The robot in the first The update amount of the Jacobian matrix estimate at each time step For the first The robot in the first The update amount of the velocity disturbance term estimate at each time step;

[0169] The joint angle vector of the robotic arm at the next moment is calculated through the above steps. As the control quantity for the movement of each robotic arm, this forms a discrete implementation of collaborative planning control for a multi-robot system based on online learning.

[0170] Specifically, each robot within a time interval In this process, the actual position and velocity of the current end effector are measured and calculated by sensors. Based on the expected trajectory, the current integrated error, the cooperative error, and the estimated value obtained through online learning, the joint angular velocity is calculated according to the discrete control law. The joint angle vector of the robot arm at the next moment is calculated through the discretization processing formula as the control quantity for the motion of each robot arm. Using the measured actual velocity and the calculated joint angular velocity, the Jacobian matrix and disturbance update value at the next moment are updated according to the discretized online learning algorithm for the calculation of the next control cycle. Through the above iterative process, a model-free adaptive cooperative control model for multi-robots based on neurodynamics is obtained.

[0171] In one embodiment, the multi-robot system consists of multiple redundant robotic arms, which exchange error information through local communication to achieve distributed collaborative control.

[0172] The relevant settings used in the computer simulation are as follows:

[0173] A ring structure is formed using six UR5 robotic arms. The relative positions of the six robotic arms used in the simulation experiment are as follows: Figure 3 As shown.

[0174] The target trajectory of the robotic arm is defined as a heart-shaped trajectory, and its expression is:

[0175] ;

[0176] Pick ,in Task execution time in seconds, sampling interval is Milliseconds, the initial joint angles of the robotic arm from joint 1 to joint 6 are set to... The online update parameters are set as follows: ; ; .

[0177] Experimental results show that the end effectors of the six robotic arms successfully drew the planar figure, as shown below. Figure 4 As shown, the position of the robotic arm's end effector was accurately controlled. Figure 5 and Figure 6 Each robotic arm was demonstrated in , and Direction tracking error , and and tracking error norm , and The diagram shows the changes, with steady-state errors in all three directions. The accuracy is on the order of meters, with high precision; a schematic diagram of the comprehensive error norm of a multi-robot system is shown below. Figure 7 As shown, the combined error of the multi-robot system is small in magnitude and eventually converges. A schematic diagram illustrating the changes in the joint angles and angular velocities of the robotic arm is shown below. Figure 8 and 9 As shown, the angle and angular velocity changes smoothly during the movement of each robotic arm, the system operates smoothly, and it has excellent trajectory accuracy and dynamic performance.

[0178] Compared with the prior art, the present invention has the following beneficial effects:

[0179] Compared to existing robot control methods, this invention effectively overcomes the shortcomings of existing methods in establishing accurate models under unknown disturbances and complex environments by establishing a model-free control method. It solves the problem of model failure caused by traditional control systems under complex environments and dynamic disturbances. This invention has high robustness compared to existing technologies.

[0180] Compared to existing centralized multi-robot systems, this invention effectively achieves rapid communication between multiple robots by establishing a distributed system.

[0181] Compared to existing error tracking models, this invention solves the problem of existing mathematical models requiring high speed, parallelism, and robustness to uncertainty by employing a neurodynamics approach, significantly improving the response speed and robustness of multi-robot systems.

[0182] A model-free adaptive cooperative control system for multi-robots based on neurodynamics, comprising:

[0183] The kinematic model building module is used to build a kinematic model for each robot in a multi-robot system, including the Jacobian matrix to be estimated and unknown disturbance terms.

[0184] The online learning algorithm estimation module is used to estimate the Jacobian matrix and disturbance terms in real time and synchronously using an online learning algorithm driven by gradient descent, based on measurable robot end effector velocity and joint velocity.

[0185] The integrated error model design module is used to design an integrated error model that couples individual tracking error and cooperative error. The individual tracking error is the deviation between the actual trajectory and the expected trajectory of a single robot, and the cooperative error is the difference in individual tracking errors between adjacent robots, forming a closed-loop error propagation structure.

[0186] The distributed motion controller design module is used to design a distributed motion controller for each robot based on the comprehensive error model. The controller uses an online learning algorithm to estimate the Jacobian matrix and disturbance terms obtained online in the estimation module, and calculates the joint control speed that can make the comprehensive error converge to zero.

[0187] The discretization module is used to discretize the continuous-time formulas of the online learning algorithm and the distributed motion controller, forming an iterative update formula that can run on a digital computer. Based on the discretized update formula, joint control commands are calculated and output in each control cycle to drive the robot joints to move, thereby achieving accurate tracking of the desired trajectory and stable formation coordination among multiple robots.

[0188] Specific limitations regarding a model-free adaptive cooperative control system for multi-robots based on neurodynamics can be found in the limitations described above for a model-free adaptive cooperative control method for multi-robots based on neurodynamics, and will not be repeated here. Each module in the aforementioned model-free adaptive cooperative control system for multi-robots based on neurodynamics can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0189] A computer device includes a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps of a model-free adaptive cooperative control method for multi-robots based on neurodynamics.

[0190] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a model-free adaptive cooperative control method for multi-robots based on neurodynamics.

[0191] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the methods described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0192] The foregoing has provided a detailed description of a model-free adaptive cooperative control method and system for multi-robots based on neurodynamics, as provided by this invention. Specific examples have been used to illustrate the principles and implementation methods of this invention, and the descriptions of the embodiments are merely for the purpose of helping to understand the core ideas of this invention. It should be noted that those skilled in the art can make various improvements and modifications to this invention without departing from its principles, and these improvements and modifications also fall within the protection scope of the claims of this invention.

Claims

1. A model-free adaptive cooperative control method for multi-robots based on neurodynamics, characterized in that, Includes the following steps: S100: For each robot in a multi-robot system, given the corresponding desired trajectory, establish a kinematic model containing the Jacobian matrix to be estimated and unknown disturbance terms; S200: Based on measurable robot end effector speed and joint speed, it uses a gradient descent-driven online learning algorithm to estimate the Jacobian matrix and disturbance terms in real time and synchronously. S300: Design a comprehensive error model that couples individual tracking error and cooperative error; where individual tracking error is the deviation between the actual trajectory and the expected trajectory of a single robot, and cooperative error is the difference in individual tracking error between adjacent robots, forming a closed-loop error propagation structure; S400: Based on the comprehensive error model, a distributed motion controller is designed for each robot. This controller uses the Jacobian matrix and disturbance term learned online in S200, combined with the synchronization error, and uses the neurodynamics method to calculate the joint control speed that can make the comprehensive error converge to zero. S500: Discretizes the continuous-time formula of the online learning algorithm and the distributed motion controller to form an iterative update formula that can run on a digital computer. Based on the discretized update formula, it calculates and outputs joint control commands in each control cycle to drive the robot joint movement, thereby achieving accurate tracking of the desired trajectory and stable formation coordination among multiple robots.

2. The method according to claim 1, characterized in that, S100 includes: S110: For a single robotic arm, based on the positive kinematics of the robotic arm, the relationship between the joint angles and the end effector position is established as follows: (1) in, It is the end effector of the robotic arm. The actual location in the 3D task space. It is a mapping function determined by the mathematical model of the robotic arm, given a desired target trajectory. In order for the robotic arm to track the target's motion trajectory, it is necessary to find a suitable joint angle vector for the robot. ,make sure Able to converge ; S120: Differentiate both sides of formula (1) and introduce an unknown disturbance term, namely the velocity disturbance term. ,get: (2) in, It is the Jacobian matrix of the robotic arm, the value of which is obtained by considering the joint angles of the robotic arm at any given time. Seeking, It is the task space dimension. It's the number of joints. It is the joint angular velocity vector, which is the joint angle. Regarding time The derivative, , They are , Regarding time The derivative of represents the actual end effector speed and the expected end effector speed.

3. The method according to claim 2, characterized in that, S200 includes: S210: For the system's... A robotic arm, based on the real-time measurable actual speed of the end effector. and joint angular velocity Define the velocity prediction residual vector : (3) in, For the first The velocity prediction error vector of the robotic arm For the first Online estimates of the Jacobian matrix for each robotic arm. For the first Online estimates of the speed disturbance term of the robotic arm. The first one obtained by the sensor measurement The actual speed of the end effector of the robotic arm is required to enable the robotic arm to track the target's motion trajectory. and Converging to the true value, i.e. ; S220: Define speed prediction error index : （4） in, For the first Speed ​​prediction error index of a robotic arm The square of the Euclidean norm; In order to obtain and The update rate is determined using a gradient descent-based update algorithm, employing the following online learning algorithm: （5） （6） in, The learning rate for the Jacobian matrix estimate. The learning rate for the estimated velocity disturbance term. For the first Update rate of the Jacobian matrix estimate of each robotic arm For the first Update rate of the estimated speed disturbance term of the robotic arm The partial derivative of the velocity prediction error index with respect to the Jacobian matrix estimate is given by... The partial derivative of the speed prediction error index with respect to the estimated value of the speed disturbance term. For the first The joint angle vectors of the robotic arm, For the first The joint angular velocity vectors of the robotic arm, For the first Speed ​​interference error of the robotic arm; Further obtain Update value at time and : （7） (8) in, For the first A robotic arm at any time The Jacobian matrix estimate, For the time step, take , For the first A robotic arm at any time Estimates of the speed disturbance term.

4. The method according to claim 3, characterized in that, The S300 includes: S310: Define the first The individual tracking error of each robot is: (9) in, For the first Individual tracking error of the robot It is the end effector of the robotic arm. Dimensional task space The actual location at any given time. For the end effector of the robotic arm Dimensional task space The position of the expected trajectory at any given moment; S320: This defines a robot by arranging its members in a chain-like queue, forming a circular structure. Compared to the previous robot Cooperative error between them: (10) The first robot and the first The coordination error between robots is defined as: (11) in, For the first The coordination error between the current robot and the previous robot For the first Individual tracking error of each robot and The first The actual and desired positions of the robots. For the individual tracking error of the first robot, For the first Individual tracking error of each robot and These are the actual position and the desired position of the first robot, respectively. and The first The actual and desired positions of the robots; S330: Introduce a comprehensive error that includes an integral term. To eliminate steady-state errors and enhance system robustness, specifically: for : (12) For the last robot, that is ,have: (13) in, For the first A robot at any moment The overall error, where ρ>0 is the gain constant. and The first The robot and the first A robot at any moment The overall error, and The first robot and the second robot, respectively. A robot at any moment The overall error.

5. The method according to claim 4, characterized in that, The S400 includes: S410: Based on the integrated error model, the control objective is designed to make the integrated error dynamically converge to zero. To this end, the error dynamic equation is designed using the neurodynamics method: (14) in, For the first A robot at any moment The derivative of the overall error, , Parameters for neurodynamic design, For activation functions; S420: Employing an activation function Through derivation, a distributed joint velocity control law integrating online learning update values ​​and collaborative errors was obtained: for : (15) For the last robot : (16) S430: Obtained through integral updates based on joint speed control commands. Joint angle at any moment: （17） （18） in, For the first Joint angular velocity control commands for a robot For the first The pseudo-inverse of the Jacobian matrix updated by the robot is taken as... .

6. The method according to claim 5, characterized in that, The S500 includes: The Euler method is used to discretize the online learning algorithm formulas (5) and (6) and the controller formulas (15) and (16), and iterative calculations are performed in each control cycle k. The specific steps are as follows: S510: For the first A robot, based on the desired speed at the current moment. Cooperative error Comprehensive error And what you get from online learning and Calculate joint angular velocity control commands : for : （19） for : （20） For each robot, update the joint angles for the next moment based on the calculated joint angular velocities: （21） in, and The first The robot and the first The robot in the first Joint angular velocity at each time step and The first The robot in the first The time step and the first Joint angles at each time step and The first The robot and the first The robot in the first The pseudo-inverse of the Jacobian matrix estimate at each time step and The first The robot and the first The robot in the first The expected end effector speed at each time step and The first The robot and the first The robot in the first Estimates of the velocity disturbance term at each time step. , , and The first robot, the second robot, and the third robot, respectively. The robot, the first The robot and the first The robot in the first The coordination error at each time step and The first The robot and the first The robot in the first The combined error at each time step To control the sampling time of the cycle; S520: For the first The robot, based on the current actual end effector speed and joint angular velocity Update the estimates of the Jacobian matrix and the disturbance term: （22） in, For the first The robot in the first The update amount of the Jacobian matrix estimate at each time step For the first The robot in the first The update amount of the velocity disturbance term estimate at each time step; The joint angle vector of the robotic arm at the next moment is calculated through the above steps. As the control quantity for the movement of each robotic arm, this forms a discrete implementation of collaborative planning control for a multi-robot system based on online learning.

7. The method according to claim 6, characterized in that, The multi-robot system consists of multiple redundant robotic arms. The robots exchange error information through local communication to achieve distributed collaborative control.

8. A model-free adaptive cooperative control system for multi-robots based on neurodynamics, characterized in that, include: The kinematic model building module is used to build a kinematic model for each robot in a multi-robot system, including the Jacobian matrix to be estimated and unknown disturbance terms. The online learning algorithm estimation module is used to estimate the Jacobian matrix and disturbance terms in real time and synchronously using an online learning algorithm driven by gradient descent, based on measurable robot end effector velocity and joint velocity. The integrated error model design module is used to design an integrated error model that couples individual tracking error and cooperative error. The individual tracking error is the deviation between the actual trajectory and the expected trajectory of a single robot, and the cooperative error is the difference in individual tracking errors between adjacent robots, forming a closed-loop error propagation structure. The distributed motion controller design module is used to design a distributed motion controller for each robot based on the comprehensive error model. The controller uses an online learning algorithm to estimate the Jacobian matrix and disturbance terms obtained online in the estimation module, and calculates the joint control speed that can make the comprehensive error converge to zero. The discretization module is used to discretize the continuous-time formulas of the online learning algorithm and the distributed motion controller, forming an iterative update formula that can run on a digital computer. Based on the discretized update formula, joint control commands are calculated and output in each control cycle to drive the robot joints to move, thereby achieving accurate tracking of the desired trajectory and stable formation coordination among multiple robots.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 8.

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