Multi-robot arm cooperation control method and system, computer device and storage medium

Abstract

The application belongs to the technical field of robot intelligent control, and discloses a multi-robot arm cooperative control method, a system, computer equipment and a storage medium, which comprises the following steps: acquiring multi-robot arm control requirements; based on the multi-robot arm control requirements, solving a preset multi-robot arm robust cooperative control framework based on Nash game to obtain a multi-robot arm cooperative control scheme; wherein the multi-robot arm robust cooperative control framework based on Nash game is constructed based on a multi-objective optimization scheme combined with Nash game theory; wherein the multi-objective optimization scheme comprises a robot arm joint speed minimization function, a robot arm joint speed infinite norm speed minimization function, a robot arm controllability maximization function and a robot arm repetitive operation generation scheme function. The application can reduce excessive and sudden changes of the robot arm joint speed, improve controllability, eliminate robot arm joint drift and realize multi-robot arm cooperative control optimization.

Description

Technical Field

[0001] This invention belongs to the field of robot intelligent control technology, and relates to a multi-robotic arm collaborative control method, system, computer equipment and storage medium. Background Technology

[0002] The challenge in mission-oriented multi-robotic arm applications lies in the collaborative control of multiple robotic arms, involving a variety of complex tasks, from industrial manufacturing to surgery to nuclear reactors or space exploration. This collaborative nature makes task execution more efficient, but it also brings a series of technical difficulties.

[0003] In practical applications involving multiple robotic arms, these arms may have different motion structures and degrees of freedom. Their coordinated movement requires precise control algorithms, and in many cases, accurate motion models of the robotic arms are unavailable, posing challenges to control and trajectory planning. Furthermore, to ensure safety, it is crucial to prevent collisions between the multiple robotic arms or with obstacles in the workspace during task execution, which involves collision avoidance and task safety. Therefore, sophisticated optimization techniques are needed to effectively allocate resources and optimize multiple objectives. Real-time coordination and adaptability in dynamic and unpredictable environments are essential, requiring the system to be robust to uncertainties and external disturbances.

[0004] However, existing multi-manipulator control methods face significant challenges in coordinating heterogeneous systems. Even when manipulators have different motion structures and degrees of freedom, cooperative control can become complex. Furthermore, in practical applications where precise motion models are lacking, existing methods may encounter problems with control and trajectory planning. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a multi-robotic arm collaborative control method, system, computer equipment, and storage medium.

[0006] To achieve the above objectives, the present invention employs the following technical solution:

[0007] In a first aspect, the present invention provides a multi-robotic arm collaborative control method, comprising:

[0008] Obtain control requirements for multiple robotic arms;

[0009] Based on the control requirements of multiple robotic arms, a pre-defined robust cooperative control framework for multiple robotic arms based on Nash game is solved to obtain a cooperative control scheme for multiple robotic arms.

[0010] Among them, the robust cooperative control framework for multi-manipulators based on Nash game theory is constructed by combining multi-objective optimization schemes with Nash game theory; the multi-objective optimization schemes include the manipulator joint velocity minimization function, the manipulator joint velocity infinite norm velocity minimization function, the manipulator controllability maximization function, and the manipulator repetitive motion generation scheme function.

[0011] Optionally, the function for minimizing the joint velocity of the robotic arm is:

[0012]

[0013] in, Indicates the speed of the robotic arm joints;

[0014] The infinite norm velocity minimization function for the robotic arm joint velocities is:

[0015]

[0016] The function for maximizing the maneuverability of the robotic arm is:

[0017]

[0018] Where J is the Jacobian matrix. q i Let be the angle of the i-th joint of the robotic arm; m be the number of eigenvalues ​​of the Jacobian matrix; I m It is the identity matrix;

[0019] The function for generating the repetitive motion scheme of the robotic arm is:

[0020]

[0021] Where λ>0 is a preset parameter used to adjust the joint displacement response amplitude of the robotic arm; q is the joint angle of the robotic arm; and q0 is the initial desired joint angle of the robotic arm.

[0022] Optionally, the robust optimal control framework based on Nash game theory is as follows:

[0023]

[0024] in, and The weight coefficients are the preset optimization criteria. For Laplace matrix, The adjacency matrix is Let be the connection weight between the s-th robotic arm and the j-th robotic arm, when the j-th robotic arm is in the neighbor set V(s) of the s-th robotic arm. otherwise The degree matrix is It is a diagonal matrix whose diagonal elements are composed of n s If the robotic arm is connected to the virtual robotic arm, then n s =1; otherwise, n s =0; It is a diagonal matrix; J o =diag(J1; ​​...; J k ); Let be the joint angular velocity of the k-th robotic arm; 1 s It is the identity matrix; The command is the joint speed command of the robotic arm from the command center; γ>0 is a preset parameter used to adjust the convergence rate; r d This represents the desired trajectory of the robotic arm; Set the following control law:

[0025]

[0026]

[0027] in, Let be the actual trajectory velocity of the s-th robotic arm; β represents the actual trajectory speed of the j-th robotic arm; β > 0 is a preset parameter used to adjust the convergence speed. Let be the trajectory of the s-th robotic arm; Let J be the trajectory of the j-th robotic arm; For matrix Let be the trajectory of the k-th robotic arm; For the end effector to the predetermined reference trajectory r d The constant distance vector of (t); This is the minimum joint speed of the robotic arm. q represents the maximum joint velocity of the robotic arm. + q represents the maximum joint angle of the robotic arm. - This represents the minimum joint angle of the robotic arm.

[0028] Optionally, the solution to the preset Nash game-based robust cooperative control framework for multi-robotic arms includes:

[0029] A robust cooperative control framework for multi-robotic arms based on Nash game is solved using a recurrent neural network controller, resulting in a cooperative control scheme for multi-robotic arms.

[0030] Optionally, the method of using a recurrent neural network controller to solve the Nash game-based robust cooperative control framework for multi-robotic arms includes:

[0031] Based on the robust optimal control framework based on Nash game, the Lagrange equation is established.

[0032]

[0033]

[0034] Where θ1 and θ2 are Lagrange multipliers, μ = vec((JJ T ) -1 );

[0035] According to the KKT conditions, the Lagrange equations It has the following structure:

[0036]

[0037]

[0038]

[0039]

[0040] The result of the conversion is:

[0041]

[0042]

[0043]

[0044]

[0045]

[0046] The above equations can be expressed as equilibrium equations:

[0047] Γ(t)Υ(t)=ζ(t)

[0048]

[0049]

[0050]

[0051] Error function for constructing equilibrium equations

[0052]

[0053] Construct a neural network model integrating a dynamic error model as a recurrent neural network controller, and use the recurrent neural network controller to minimize... To optimize the target, an iterative optimization scheme for multi-robotic arm collaborative control was obtained.

[0054] In a second aspect, the present invention provides a multi-robotic arm collaborative control system, comprising:

[0055] The requirement acquisition module is used to acquire control requirements for multiple robotic arms;

[0056] The collaborative control module is used to solve a preset Nash game-based robust collaborative control framework for multiple robotic arms based on the control requirements of multiple robotic arms, and obtain a collaborative control scheme for multiple robotic arms.

[0057] Among them, the robust cooperative control framework for multi-manipulators based on Nash game theory is constructed by combining multi-objective optimization schemes with Nash game theory; the multi-objective optimization schemes include the manipulator joint velocity minimization function, the manipulator joint velocity infinite norm velocity minimization function, the manipulator controllability maximization function, and the manipulator repetitive motion generation scheme function.

[0058] Optionally, the function for minimizing the joint velocity of the robotic arm is:

[0059]

[0060] in, Indicates the speed of the robotic arm joints;

[0061] The infinite norm velocity minimization function for the robotic arm joint velocities is:

[0062]

[0063] The function for maximizing the maneuverability of the robotic arm is:

[0064]

[0065] Where J is the Jacobian matrix. q i Let be the angle of the i-th joint of the robotic arm; m be the number of eigenvalues ​​of the Jacobian matrix; I m It is the identity matrix;

[0066] The function for generating the repetitive motion scheme of the robotic arm is:

[0067]

[0068] Where λ>0 is a preset parameter used to adjust the joint displacement response amplitude of the robotic arm; q is the joint angle of the robotic arm; and q0 is the initial desired joint angle of the robotic arm.

[0069] Optionally, the robust optimal control framework based on Nash game theory is as follows:

[0070]

[0071] in, and The weight coefficients are the preset optimization criteria. For Laplace matrix, The adjacency matrix is Let be the connection weight between the s-th robotic arm and the j-th robotic arm, when the j-th robotic arm is in the neighbor set V(s) of the s-th robotic arm. otherwise The degree matrix is It is a diagonal matrix whose diagonal elements are composed of n s If the robotic arm is connected to the virtual robotic arm, then n s =1; otherwise, n s =0; It is a diagonal matrix; J o =diag(J1; ​​...; J k ); Let be the joint angular velocity of the k-th robotic arm; 1 s It is the identity matrix; The command is the joint speed command of the robotic arm from the command center; γ>0 is a preset parameter used to adjust the convergence rate; r d This represents the desired trajectory of the robotic arm; Set the following control law:

[0072]

[0073]

[0074] in, Let be the actual trajectory velocity of the s-th robotic arm; β represents the actual trajectory speed of the j-th robotic arm; β > 0 is a preset parameter used to adjust the convergence speed. Let be the trajectory of the s-th robotic arm; Let J be the trajectory of the j-th robotic arm; For matrix Let be the trajectory of the k-th robotic arm; For the end effector to the predetermined reference trajectory r d The constant distance vector of (t); This is the minimum joint speed of the robotic arm. q represents the maximum joint velocity of the robotic arm. + q represents the maximum joint angle of the robotic arm. - This represents the minimum joint angle of the robotic arm.

[0075] In a third aspect, the present invention provides a computer device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described multi-robotic arm cooperative control method.

[0076] In a fourth aspect, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the above-described multi-robotic arm collaborative control method.

[0077] Compared with the prior art, the present invention has the following beneficial effects:

[0078] This invention presents a multi-manipulator cooperative control method that combines minimizing manipulator joint velocities, minimizing manipulator joint velocities in the infinite norm, maximizing manipulator controllability, and generating repetitive motion schemes to form a multi-objective optimization scheme. Furthermore, it incorporates Nash game theory to construct a robust multi-manipulator cooperative control framework, innovatively integrating game theory into multi-manipulator cooperative control with unknown kinematics. Through efficient distributed task allocation and strategic competition, a robust optimization framework is established to achieve Nash equilibrium. Finally, based on the multi-manipulator control requirements, the pre-defined Nash game-based robust multi-manipulator cooperative control framework is solved to obtain a multi-manipulator cooperative control scheme. This scheme integrates hybrid multi-objective optimization and repetitive motion generation schemes, mitigating excessive and sudden changes in manipulator joint velocities, improving manipulation, eliminating manipulator joint drift, and achieving optimized multi-manipulator cooperative control. Attached Figure Description

[0079] Figure 1 This is a flowchart of a multi-robotic arm collaborative control method according to an embodiment of the present invention.

[0080] Figure 2 This is a block diagram of the multi-robotic arm collaborative control system according to an embodiment of the present invention. Detailed Implementation

[0081] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0082] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0083] The present invention will now be described in further detail with reference to the accompanying drawings:

[0084] See Figure 1 In one embodiment of the present invention, a multi-robotic arm collaborative control method is provided, which enables multi-robotic arms to have higher efficiency, safety, adaptability and robustness in complex task execution.

[0085] Specifically, the multi-robotic arm collaborative control method includes the following steps:

[0086] S1: Obtain the control requirements for multiple robotic arms.

[0087] S2: Based on the control requirements of multiple robotic arms, solve the preset multi-robotic arm robust cooperative control framework based on Nash game to obtain the multi-robotic arm cooperative control scheme.

[0088] Among them, the robust cooperative control framework for multi-manipulators based on Nash game theory is constructed by combining multi-objective optimization schemes with Nash game theory; the multi-objective optimization schemes include the manipulator joint velocity minimization function, the manipulator joint velocity infinite norm velocity minimization function, the manipulator controllability maximization function, and the manipulator repetitive motion generation scheme function.

[0089] This invention presents a multi-manipulator cooperative control method that combines minimizing manipulator joint velocities, minimizing manipulator joint velocities in the infinite norm, maximizing manipulator controllability, and generating repetitive motion schemes to form a multi-objective optimization scheme. Furthermore, it incorporates Nash game theory to construct a robust multi-manipulator cooperative control framework, innovatively integrating game theory into multi-manipulator cooperative control with unknown kinematics. Through efficient distributed task allocation and strategic competition, a robust optimization framework is established to achieve Nash equilibrium. Finally, based on the multi-manipulator control requirements, the pre-defined Nash game-based robust multi-manipulator cooperative control framework is solved to obtain a multi-manipulator cooperative control scheme. This scheme integrates hybrid multi-objective optimization and repetitive motion generation schemes, mitigating excessive and sudden changes in manipulator joint velocities, improving manipulation, eliminating manipulator joint drift, and achieving optimized multi-manipulator cooperative control.

[0090] In one possible implementation, the function for minimizing the joint velocity of the robotic arm is:

[0091]

[0092] in, This indicates the speed of the robotic arm joints.

[0093] The infinite norm velocity minimization function for the robotic arm joint velocities is:

[0094]

[0095] The function for maximizing the maneuverability of the robotic arm is as follows.

[0096]

[0097] Where J is the Jacobian matrix. q i Let be the angle of the i-th joint of the robotic arm; m be the number of eigenvalues ​​of the Jacobian matrix; I m It is an identity matrix.

[0098] The function for generating the repetitive motion scheme of the robotic arm is:

[0099]

[0100] Where λ>0 is a preset parameter used to adjust the joint displacement response amplitude of the robotic arm; q is the joint angle of the robotic arm; and q0 is the initial desired joint angle of the robotic arm.

[0101] Specifically, the joint speed and acceleration of a robotic arm are typical indicators reflecting its motion characteristics in engineering. On the one hand, due to the power limitations of the actuators, it is desirable for the robotic arm to operate at a slow and stable speed to ensure smooth task execution. On the other hand, in engineering, large accelerations can easily cause position overshoot or oscillations, so reducing the acceleration is a reliable choice.

[0102] To ensure smooth task execution within the limits of drive power, maintaining controllable and stable joint speeds is essential. Minimizing the joint speeds of the robotic arm is achieved using the minimum speed norm optimization criterion, expressed as: At the same time, to prevent position overshoot or oscillation, it is preferable to minimize the infinite norm velocity of the robotic arm joints, which can be described by the optimization criterion as follows:

[0103] The maneuverability of a robotic arm can be determined by a function of the Jacobian matrix, described as follows:

[0104]

[0105] in, For JJ T The i-th largest eigenvalue is ≥0, and J is a Jacobian matrix.

[0106] Therefore, the optimization criterion for maximizing the maneuverability of the robotic arm can be further expressed as:

[0107]

[0108] In one possible implementation, the robust optimal control framework based on Nash game is as follows:

[0109]

[0110] in, and The weight coefficients are the preset optimization criteria. For Laplace matrix, The adjacency matrix is Let be the connection weight between the s-th robotic arm and the j-th robotic arm, when the j-th robotic arm is in the neighbor set V(s) of the s-th robotic arm. otherwise The degree matrix is It is a diagonal matrix whose diagonal elements are composed of n s If the robotic arm is connected to the virtual robotic arm, then n s =1; otherwise, n s =0; It is a diagonal matrix; J o=diag(J1; ​​...; J k ); Let be the joint angular velocity of the k-th robotic arm; 1 s It is the identity matrix; The command is the joint speed command of the robotic arm from the command center; γ>0 is a preset parameter used to adjust the convergence rate; r d This represents the desired trajectory of the robotic arm; Set the following control law:

[0111]

[0112]

[0113] in, Let be the actual trajectory velocity of the s-th robotic arm; β represents the actual trajectory speed of the j-th robotic arm; β > 0 is a preset parameter used to adjust the convergence speed. Let be the trajectory of the s-th robotic arm; Let J be the trajectory of the j-th robotic arm; For matrix Let be the trajectory of the k-th robotic arm; For the end effector to the predetermined reference trajectory r d The constant distance vector of (t); This is the minimum joint speed of the robotic arm. q represents the maximum joint velocity of the robotic arm. + q represents the maximum joint angle of the robotic arm. - This represents the minimum joint angle of the robotic arm.

[0114] Specifically, the cooperative control of a multi-arm system aims to achieve a coordinated goal for a specific task, involving the translation of the trajectories of each arm to facilitate coordination. This process requires converting the trajectories of adjacent arm i into their reference coordinate systems for comparative analysis, as shown below:

[0115]

[0116] In a multi-arm robotic system with limited communication, the robotic arm not connected to the command center is tracked by its adjacent robotic arm k. The trajectory deviation feedback of the i-th robotic arm is defined as:

[0117]

[0118] Further steps can be taken to ensure consistency between robotic arm i and robotic arm k:

[0119]

[0120] Therefore, the trajectory deviation feedback at the velocity level can be expressed as:

[0121]

[0122] In a distributed network, each terminal node is both a sender and a receiver. Operators in the network adhere to established communication protocols to ensure reliable information exchange. Due to limitations in power, bandwidth, and communication range, operators with non-overlapping communication areas cannot establish direct connections for data transmission. Therefore, each robotic arm can only infer or estimate the state of other robotic arms based on information received from neighboring arms, employing an information acquisition method similar to game theory. In this context, each operator relies on local information exchange to define its private decision domain, which operates independently but influences other decision domains. The methods used to guide the robotic arm to effectively complete tasks are considered strategies. Each robotic arm carefully adjusts its strategy to improve performance and facilitate the execution of specific subtasks required by the robotic arm.

[0123] In game theory, the strategies of all manipulators in a system constitute a strategy profile. Within this profile, no manipulator can arbitrarily change their strategy to maximize their own profit, thus forming a Nash equilibrium among k manipulators. The control law is an effective action plan that drives the robotic arm's operation, comprehensively considering the performance gain and information acquisition rules during task execution. Each robotic arm can be imagined as a participant seeking to maximize profit within the default rules; they are rational and will not act in a way that harms their own interests. Each robotic arm's final strategy can be seen as the optimal response to the strategies of other robotic arms. In fact, game theory has proven that, under such limited information exchange, the information obtained by the robotic arms through estimation will eventually converge, which is the most advantageous choice for them. Within the framework of game theory, a control law was developed for the i-th robotic arm, solving the cooperation challenge among k robotic arms. The specific control law can be expressed as:

[0124]

[0125]

[0126] Due to the nonlinear mapping and unique distributed information transmission method in the above equation, direct solution is challenging and impractical. Therefore, the error function in the above equation is initially expressed and defined as:

[0127]

[0128] By utilizing parallel processing in neurodynamic methods, the constructed error function is forced to drive the error value to zero, ensuring that the generated solution converges to the theoretical solution, and causing the error function to further evolve into:

[0129]

[0130] Then, the open-loop system is converted into a closed-loop system, which significantly improves the operating efficiency by reducing the velocity level error in the design equations. This allows the above equation to be transformed into:

[0131]

[0132] The physical constraints of multiple robotic arms are represented as velocity levels, as described below:

[0133]

[0134] Finally, a robust cooperative control framework for multi-robot arms based on Nash game theory is proposed, which uses redefined multi-objective optimization schemes, constraints, and bias feedback:

[0135]

[0136] In one possible implementation, solving the preset Nash game-based robust cooperative control framework for multiple robotic arms includes: using a recurrent neural network controller to solve the Nash game-based robust cooperative control framework for multiple robotic arms to obtain a cooperative control scheme for multiple robotic arms.

[0137] Specifically, a computationally efficient recurrent neural network controller is introduced, enabling the Nash game-based robust cooperative control framework for multi-robotic arms to coordinate and respond more promptly, thus enhancing performance in real-time execution. The recurrent neural network controller can employ a power-law modified recurrent neural network model.

[0138] In one possible implementation, the method of using a recurrent neural network controller to solve a Nash game-based robust cooperative control framework for multi-robotic arms includes:

[0139] Based on the robust optimal control framework based on Nash game, the Lagrange equation is established.

[0140]

[0141] Where θ1 and θ2 are Lagrange multipliers, μ = vec((JJ T ) -1 ).

[0142] According to the KKT conditions, the Lagrange equations It has the following structure:

[0143]

[0144]

[0145]

[0146]

[0147] The result of the conversion is:

[0148]

[0149]

[0150]

[0151]

[0152]

[0153] The above equations can be expressed as equilibrium equations:

[0154] Γ(t)Υ(t)=ζ(t)

[0155]

[0156]

[0157]

[0158] Error function for constructing equilibrium equations

[0159]

[0160] Construct a neural network model integrating a dynamic error model as a recurrent neural network controller, and use the recurrent neural network controller to minimize... To optimize the target, an iterative optimization scheme for multi-robotic arm collaborative control was obtained.

[0161] Specifically, a Lagrangian function is established to further process the optimal solution of the robust optimal control framework based on Nash game:

[0162]

[0163] Meanwhile, for ease of representation, the following definition is provided:

[0164]

[0165] According to the Karush-Kuhn-Tucker (KKT) conditions, which are widely used in optimization problems, especially in nonlinear programming, they are a set of necessary and sufficient conditions used to determine whether a solution to an optimization problem is optimal. Therefore, the Lagrange equation above has the following structure:

[0166]

[0167]

[0168]

[0169]

[0170] Furthermore, the optimal strategy set for the robotic arm, i.e., the equilibrium point of the Nash equilibrium, can be obtained. Therefore, the nonlinear equations ultimately satisfy the following relationship:

[0171]

[0172]

[0173]

[0174]

[0175]

[0176] For ease of description, the above equations are expressed as equilibrium equations:

[0177] Γ(t)Υ(t)=ζ(t)

[0178] The solution to the above equation reveals the optimal strategy for the robotic arm, encapsulating the equilibrium point within a Nash equilibrium. Therefore, the error function of this equilibrium equation is defined as:

[0179]

[0180] By minimizing To zero, guide the Nash game-based multi-manipulator robust collaborative control framework to Nash equilibrium, optimizing the response of each manipulator.

[0181] The introduced neural network model integrates a dynamic error model. Through the derived evolution, the error function tends to zero, resulting in: in, Controlling the convergence speed, activation function array It contains a monotonically increasing group of odd functions.

[0182] This invention presents a multi-manipulator cooperative control method that innovatively integrates game theory into the cooperative control of multi-manipulators with unknown kinematics. It establishes a robust optimization framework through efficient distributed task allocation and strategic competition to achieve Nash equilibrium. The optimal cooperative scheme integrates hybrid multi-objective optimization and repetitive motion generation schemes to mitigate excessive and abrupt changes in joint velocities, improve operability, eliminate joint drift, and decouple errors between joint space and Cartesian space. Furthermore, a recurrent neural network controller is proposed to ensure rapid response with optimal strategy.

[0183] The following are embodiments of the apparatus of the present invention, which can be used to execute embodiments of the method of the present invention. For details not disclosed in the apparatus embodiments, please refer to the embodiments of the method of the present invention.

[0184] See Figure 2 In another embodiment of the present invention, a multi-robotic arm collaborative control system is provided, which can be used to implement the above-mentioned multi-robotic arm collaborative control method. Specifically, the multi-robotic arm collaborative control system includes a demand acquisition module and a collaborative control module.

[0185] The module includes a requirement acquisition module for acquiring the control requirements of multiple robotic arms; and a collaborative control module for solving a pre-defined Nash game-based robust collaborative control framework for multiple robotic arms based on these requirements, thereby obtaining a collaborative control scheme for multiple robotic arms. The Nash game-based robust collaborative control framework is constructed based on a multi-objective optimization scheme combined with Nash game theory. The multi-objective optimization scheme includes a function for minimizing the joint velocity of the robotic arms, a function for minimizing the infinite norm velocity of the joint velocity of the robotic arms, a function for maximizing the maneuverability of the robotic arms, and a function for generating repetitive motion schemes of the robotic arms.

[0186] In one possible implementation, the function for minimizing the joint velocity of the robotic arm is:

[0187]

[0188] in, This indicates the speed of the robotic arm joints.

[0189] The infinite norm velocity minimization function for the robotic arm joint velocities is:

[0190]

[0191] The function for maximizing the maneuverability of the robotic arm is:

[0192]

[0193] Where J is the Jacobian matrix. q iLet be the angle of the i-th joint of the robotic arm; m be the number of eigenvalues ​​of the Jacobian matrix; I m It is an identity matrix.

[0194] The function for generating the repetitive motion scheme of the robotic arm is:

[0195]

[0196] Where λ>0 is a preset parameter used to adjust the joint displacement response amplitude of the robotic arm; q is the joint angle of the robotic arm; and q0 is the initial desired joint angle of the robotic arm.

[0197] In one possible implementation, the robust optimal control framework based on Nash game is as follows:

[0198]

[0199] in, and The weight coefficients are the preset optimization criteria. For Laplace matrix, The adjacency matrix is Let be the connection weight between the s-th robotic arm and the j-th robotic arm, when the j-th robotic arm is in the neighbor set V(s) of the s-th robotic arm. otherwise The degree matrix is It is a diagonal matrix whose diagonal elements are composed of n s If the robotic arm is connected to the virtual robotic arm, then n s =1; otherwise, n s =0; It is a diagonal matrix; J o =diag(J1; ​​...; J k ); Let be the joint angular velocity of the k-th robotic arm; 1 s It is the identity matrix; The command is the joint speed command of the robotic arm from the command center; γ>0 is a preset parameter used to adjust the convergence rate; r d This represents the desired trajectory of the robotic arm; Set the following control law:

[0200]

[0201]

[0202] in, Let be the actual trajectory velocity of the s-th robotic arm; β represents the actual trajectory speed of the j-th robotic arm; β > 0 is a preset parameter used to adjust the convergence speed. Let be the trajectory of the s-th robotic arm; Let J be the trajectory of the j-th robotic arm; For matrix Let be the trajectory of the k-th robotic arm; For the end effector to the predetermined reference trajectory r d The constant distance vector of (t); This is the minimum joint speed of the robotic arm. q represents the maximum joint velocity of the robotic arm. + q represents the maximum joint angle of the robotic arm. - This represents the minimum joint angle of the robotic arm.

[0203] All relevant content of each step involved in the aforementioned embodiments of the multi-robotic arm collaborative control method can be referenced from the functional description of the corresponding functional module of the multi-robotic arm collaborative control system in the embodiments of the present invention, and will not be repeated here.

[0204] The module division in this embodiment of the invention is illustrative and represents only one logical functional division. In actual implementation, other division methods may be used. Furthermore, the functional modules in the various embodiments of the invention can be integrated into a single processor, exist as separate physical entities, or be integrated into a single module. The integrated modules described above can be implemented in hardware or as software functional modules.

[0205] In another embodiment of the present invention, a computer device is provided, comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions from the computer storage medium to achieve a corresponding method flow or corresponding function. The processor described in this embodiment of the present invention can be used for the operation of a multi-robotic arm collaborative control method.

[0206] In another embodiment of the present invention, a storage medium is provided, specifically a computer-readable storage medium (Memory), which is a memory device in a computer device used to store programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the computer device and extended storage media supported by the computer device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, the storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be high-speed RAM or non-volatile memory, such as at least one disk storage device. The processor can load and execute one or more instructions stored in the computer-readable storage medium to implement the corresponding steps of the multi-robotic arm cooperative control method in the above embodiments.

[0207] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0208] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0209] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0210] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0211] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A multi-robotic arm collaborative control method, characterized in that, include: Obtain control requirements for multiple robotic arms; Based on the control requirements of multiple robotic arms, a pre-defined robust cooperative control framework for multiple robotic arms based on Nash game is solved to obtain a cooperative control scheme for multiple robotic arms. Among them, the robust cooperative control framework for multi-manipulators based on Nash game theory is constructed by combining multi-objective optimization schemes with Nash game theory; the multi-objective optimization schemes include the manipulator joint velocity minimization function, the manipulator joint velocity infinite norm velocity minimization function, the manipulator controllability maximization function, and the manipulator repetitive motion generation scheme function. The function for minimizing the arm joint velocity is: in, Indicates the speed of the robotic arm joints; The infinite norm velocity minimization function for the robotic arm joint velocities is: The function for maximizing the maneuverability of the robotic arm is: in, For Jacobian matrices, , , ; For the first robotic arm i Each joint angle; The number of eigenvalues ​​of the Jacobian matrix; It is the identity matrix; The function for generating the repetitive motion scheme of the robotic arm is: Wherein, λ>0 is a preset parameter used to adjust the joint displacement response amplitude of the robotic arm; For the joint angle of the robotic arm; The initial desired joint angles of the robotic arm; The robust optimal control framework based on Nash game theory is as follows: in, , , and The weight coefficients are the preset optimization criteria. For Laplace matrix, The adjacency matrix is , For the first s robotic arm and the j The connection weights between robotic arms, when the first... j The robotic arm in the first s Neighbor set of robotic arm China Times, =1, otherwise =0; The degree matrix is ; It is a diagonal matrix, whose diagonal elements are formed by... If the robotic arm is connected to the virtual robotic arm, then n s =1; otherwise, n s =0; It is a diagonal matrix; =diag(J1;...;J k ); , For the first k The joint angular velocity of a robotic arm; It is the identity matrix; The speed command for the robotic arm joints comes from the command center; γ>0 is a preset parameter used to adjust the convergence rate. This represents the desired trajectory of the robotic arm; Set the control law as follows: in, For the first s The actual trajectory speed of the robotic arm; For the first j The actual trajectory speed of the robotic arm; These are preset parameters used to adjust the convergence speed; For the first s The trajectory of a robotic arm; For the first j The trajectory of a robotic arm; For matrix , For the first k The trajectory of a robotic arm; For the end effector to the predetermined reference trajectory r d The constant distance vector of (t); , , , , This is the minimum joint speed of the robotic arm. This represents the maximum joint speed of the robotic arm. This represents the maximum joint angle of the robotic arm. This represents the minimum joint angle of the robotic arm.

2. The multi-robotic arm cooperative control method according to claim 1, characterized in that, The proposed solution for the pre-defined Nash game-based robust cooperative control framework for multi-robotic arms includes: A robust cooperative control framework for multi-robotic arms based on Nash game is solved using a recurrent neural network controller, resulting in a cooperative control scheme for multi-robotic arms.

3. The multi-robotic arm cooperative control method according to claim 2, characterized in that, The method of using a recurrent neural network controller to solve the Nash game-based robust cooperative control framework for multi-robotic arms includes: Based on the robust optimal control framework based on Nash game, the Lagrange equation is established. : in, 1 and 2 is a Lagrange multiplier. ; According to the KKT conditions, the Lagrange equations It has the following structure: The result of the conversion is: The above equations can be expressed as equilibrium equations: Error function for constructing equilibrium equations : Construct a neural network model integrating a dynamic error model as a recurrent neural network controller, and use the recurrent neural network controller to minimize... To optimize the target, an iterative optimization scheme for multi-robotic arm collaborative control was obtained.

4. A multi-robotic arm collaborative control system, characterized in that, include: The requirement acquisition module is used to acquire control requirements for multiple robotic arms; The collaborative control module is used to solve a preset Nash game-based robust collaborative control framework for multiple robotic arms based on the control requirements of multiple robotic arms, and obtain a collaborative control scheme for multiple robotic arms. Among them, the robust cooperative control framework for multi-manipulators based on Nash game theory is constructed by combining multi-objective optimization schemes with Nash game theory; the multi-objective optimization schemes include the manipulator joint velocity minimization function, the manipulator joint velocity infinite norm velocity minimization function, the manipulator controllability maximization function, and the manipulator repetitive motion generation scheme function. The function for minimizing the joint velocity of the robotic arm is: in, Indicates the speed of the robotic arm joints; The infinite norm velocity minimization function for the robotic arm joint velocities is: The function for maximizing the maneuverability of the robotic arm is: in, For Jacobian matrices, , , ; For the first robotic arm i Each joint angle; The number of eigenvalues ​​of the Jacobian matrix; It is the identity matrix; The function for generating the repetitive motion scheme of the robotic arm is: Wherein, λ>0 is a preset parameter used to adjust the joint displacement response amplitude of the robotic arm; For the joint angle of the robotic arm; Let be the initial desired joint angle of the robotic arm.

5. The multi-robotic arm collaborative control system according to claim 4, characterized in that, The robust optimal control framework based on Nash game theory is as follows: in, , , and The weight coefficients are the preset optimization criteria. For Laplace matrix, The adjacency matrix is , For the first s robotic arm and the j The connection weights between robotic arms, when the first... j The robotic arm in the first s Neighbor set of robotic arm China Times, =1, otherwise =0; The degree matrix is ; It is a diagonal matrix, whose diagonal elements are formed by... If the robotic arm is connected to the virtual robotic arm, then n s =1; otherwise, n s =0; It is a diagonal matrix; =diag(J1;...;J k ); , For the first k The joint angular velocity of a robotic arm; It is the identity matrix; The speed command for the robotic arm joints comes from the command center; γ>0 is a preset parameter used to adjust the convergence rate. This represents the desired trajectory of the robotic arm; Set the control law as follows: in, For the first s The actual trajectory speed of the robotic arm; For the first j The actual trajectory speed of the robotic arm; These are preset parameters used to adjust the convergence speed; For the first s The trajectory of a robotic arm; For the first j The trajectory of a robotic arm; For matrix , For the first k The trajectory of a robotic arm; For the end effector to the predetermined reference trajectory r d The constant distance vector of (t); , , , , This is the minimum joint speed of the robotic arm. This represents the maximum joint speed of the robotic arm. This represents the maximum joint angle of the robotic arm. This represents the minimum joint angle of the robotic arm.

6. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the multi-robotic arm collaborative control method as described in any one of claims 1 to 3.

7. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the multi-robotic arm collaborative control method as described in any one of claims 1 to 3.

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