Online learning and fuzzy neurodynamics-based mobile manipulator control method and device

Abstract

The application discloses a mobile manipulator control method and device based on online learning and fuzzy neural dynamics, and relates to the technical field of mobile manipulator control. The method comprises the following steps: acquiring an actual pose of an end effector, a desired pose trajectory and joint speed; introducing an excitation signal formed after superimposing random noise, updating a current Jacobian matrix estimation value of the mobile manipulator; inputting each data into a fuzzy neural dynamic solver; the fuzzy neural dynamic solver is configured to take a quadratic form as an optimization objective, take a differential kinematics tracking equation as an equality constraint, and take a non-convex feasible region as an inequality constraint; and finally outputting a control signal of the joint speed obtained by solving the fuzzy neural dynamic solver to drive the mobile manipulator to move. The application solves the technical problems of low control precision of the mobile manipulator under the conditions of parameter uncertainty and non-convex constraints without an accurate prior model, and realizes high-precision model-free pose control.

Description

Technical Field

[0001] This application relates to the field of mobile robotic arm control technology, and in particular to a mobile robotic arm control method and device based on online learning and fuzzy neurodynamics. Background Technology

[0002] A mobile robotic arm is a composite robot system that combines a mobile platform with a robotic arm, possessing both the environmental adaptability of a mobile platform and the operational flexibility of a robotic arm. Mobile robotic arm technology is increasingly being used in fields such as space exploration, resource exploration, industrial assembly, and home services. Mobile robotic arms are gradually becoming key tools for performing repetitive tasks, high-risk operations, and high-precision tasks.

[0003] The pose control of the end effector of a mobile robotic arm is a crucial issue, as its control performance directly affects the accuracy and stability of the system in performing tasks under complex environments. In practical applications, the mobile robotic arm needs to coordinate with the end effector to complete the task of tracking the predetermined pose trajectory while the mobile platform is moving. This places high demands on the system's real-time performance, coordination, and robustness.

[0004] Currently, mobile robotic arm systems may experience structural parameter drift due to mechanical wear, assembly errors, or load changes after long-term operation, making it difficult to achieve high-precision pose control relying solely on accurate kinematic models. Secondly, existing neurodynamic methods for solving pose control optimization problems generally suffer from large hysteresis errors, high computational complexity, and insufficient parameter adaptation capabilities in practical applications. Furthermore, most methods assume a convex set for the feasible region when designing joint velocity constraints to simplify the solution, limiting their applicability and control performance across all operating conditions.

[0005] Existing technologies struggle to achieve high-precision mobile robotic arm control in the absence of accurate models, and they also have shortcomings in hysteresis suppression, computational efficiency, and handling of non-convex constraints. Summary of the Invention

[0006] The purpose of this application is to provide a mobile robotic arm control method and device based on online learning and fuzzy neurodynamics. By updating the estimated value of the Jacobian matrix in real time through an online learning mechanism, and constructing an optimization problem containing a non-convex feasible region and designing a fuzzy neurodynamics solver for solving it, the technical problems of low control accuracy and poor adaptability of mobile robotic arms in scenarios with uncertain parameters, non-convex constraints, and time-varying trajectory tracking are solved without the need for an accurate prior model. This achieves high-precision, highly adaptive model-free pose control.

[0007] To achieve the above objectives, this application provides the following solution:

[0008] In a first aspect, this application provides a mobile robotic arm control method based on online learning and fuzzy neurodynamics, comprising: acquiring the actual pose and desired pose trajectory of the end effector of the mobile robotic arm, and the actual joint velocities of each joint of the mobile robotic arm; updating the current Jacobian matrix estimate of the mobile robotic arm through an online learning mechanism based on the actual motion velocity of the end effector and the excitation signal formed by superimposing random noise on the actual joint velocities of each joint, to obtain an updated Jacobian matrix estimate; inputting the actual pose, the desired pose trajectory, and the updated Jacobian matrix estimate to a fuzzy neurodynamics solver; wherein the fuzzy neurodynamics solver is configured to: minimize the quadratic form of the joint velocity to be solved as the optimization objective, satisfy the differential kinematic tracking equation based on the updated Jacobian matrix estimate as the equality constraint, and ensure that the joint velocity to be solved is within a non-convex feasible region as the inequality constraint, and solve the joint velocity to be solved; outputting the control signal of the joint velocity obtained by the fuzzy neurodynamics solver to drive the mobile robotic arm to move.

[0009] Optionally, updating the current Jacobian matrix estimate of the mobile robotic arm through an online learning mechanism specifically includes:

[0010] Construct an excitation signal with random noise; and the construction equation is: ,in, This is represented as the excitation signal with random noise. This represents the actual joint velocity of each joint. Represented as random noise;

[0011] The current Jacobian matrix estimate of the mobile robotic arm is updated by the Jacobian matrix learning equation to obtain the updated Jacobian matrix estimate; and the learning equation is: ,in, This is represented by the current Jacobian matrix estimate of the mobile robotic arm. Represented as Time derivative, The learning rate parameter is represented as positive. The speed of motion of the end effector is indicated by the superscript. This is represented as a transpose operation.

[0012] Optionally, the random noise Independent and identically distributed noise signals with zero mean.

[0013] Optionally, the random noise The range of values ​​is .

[0014] Optionally, the differential kinematic tracking equation is:

[0015] ;

[0016] in, This is represented by the updated Jacobian matrix estimate. Let be the joint velocity to be solved. This is expressed as the predicted motion speed of the end effector. This is represented as the actual pose. This is represented as the desired pose trajectory. It is expressed as the rate of change of the desired pose trajectory. This is represented as a positive feedback gain coefficient.

[0017] Optionally, the non-convex feasible region is defined as follows:

[0018] ;

[0019] in, Let it be represented as the non-convex feasible region. This is represented as a state vector of joint velocities. The state vector of the joint velocity is represented by the first... There are _n_ state components, where R is the set of real numbers. This represents the total number of joints. and Represented as the first Lower and upper limits of the velocity state components of each joint. Represented as the first Discrete boundary values ​​allowed for each joint velocity state component.

[0020] Optionally, the neurodynamic model of the fuzzy neurodynamics solver is:

[0021] ;

[0022] in, Let be the joint velocity to be solved. Let it be represented as the non-convex feasible region. It is represented as defined in the nonconvex feasible region. Projection operator on, This represents the base learning rate parameter. This is represented as a fuzzy output parameter that is dynamically adjusted through a fuzzy logic system. Represented as an auxiliary variable, Represented as the updated Jacobian matrix estimate, with superscript... This is represented as a transpose operation. This is represented as the actual pose. It is represented as the desired pose trajectory.

[0023] Optionally, the auxiliary variable time derivative Updated by the following kinetic equations:

[0024] ;

[0025] in, Represented as auxiliary variable Time derivative, It is represented as a positive scaling parameter. The desired pose trajectory s is represented as d rate of change, Represented as the updated Jacobian matrix estimate, with superscript... This is represented as a transpose operation.

[0026] Optionally, the input to the fuzzy logic system includes the actual pose. With the desired pose trajectory The error norm between them, and the actual speed of the end effector. Rate of change of the desired pose trajectory The error norm between them.

[0027] Secondly, this application provides a mobile robotic arm control device based on online learning and fuzzy neural dynamics, including: a state acquisition module configured to acquire the actual pose and desired pose trajectory of the end effector of the mobile robotic arm, as well as the actual joint velocity of each joint of the mobile robotic arm.

[0028] The Jacobian matrix online update module is configured to update the current Jacobian matrix estimate of the mobile robotic arm based on the actual motion speed of the end effector and the excitation signal formed by superimposing random noise on the actual joint speed of each joint, through an online learning mechanism, to obtain the updated Jacobian matrix estimate.

[0029] A fuzzy neural dynamics solving module is configured to input the actual pose, the desired pose trajectory, and the updated Jacobian matrix estimate into a fuzzy neural dynamics solver; wherein the fuzzy neural dynamics solver is configured to: minimize the quadratic form of the joint velocity to be solved as the optimization objective, satisfy the differential kinematic tracking equation based on the updated Jacobian matrix estimate as the equality constraint, and ensure that the joint velocity to be solved is within a non-convex feasible region as the inequality constraint, and solve the joint velocity to be solved;

[0030] The control command output module is configured to output the control signal of the joint velocity obtained by the fuzzy neurodynamics solver to drive the movement of the mobile robotic arm.

[0031] According to the specific embodiments provided in this application, the following technical effects are disclosed:

[0032] This application provides a method and apparatus for controlling a mobile robotic arm using online learning and fuzzy neurodynamics. By constructing excitation signals and applying gradient descent, the estimated Jacobian matrix of the mobile robotic arm is updated online in real time. Subsequently, the updated estimate and pose information are input into a pre-configured fuzzy neurodynamics solver. This solver directly generates joint velocity control commands by solving an optimization problem with a quadratic joint velocity as the objective, differential kinematic tracking equations as equality constraints, and a non-convex feasible region as inequality constraints. This solves the problem of the heavy reliance on precise, fixed kinematic models in traditional methods and overcomes the limitation of assuming convex sets for joint velocity constraints in existing technologies to simplify calculations. This makes the control model more closely match the actual physical constraints of the actuator. It achieves high-precision tracking of the desired pose trajectory through data-driven online learning without the need for pre-calibrated precise models, improving the system's robustness and environmental adaptability. Furthermore, the generated joint velocity control commands are strictly limited to the non-convex feasible region, ensuring that the control commands can be directly and safely executed by the actual physical actuator, achieving high-precision, highly adaptive model-free pose control. Attached Figure Description

[0033] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0034] Figure 1 This is a flowchart illustrating a mobile robotic arm control method based on online learning and fuzzy neurodynamics, as described in one embodiment of this application.

[0035] Figure 2 This is a schematic diagram of the structure of a fuzzy neurodynamics solver provided in an embodiment of this application;

[0036] Figure 3 This is a schematic diagram of the error norm between the actual pose and the desired pose trajectory, the error norm between the actual motion speed and the desired rate of change, and the membership function of the fuzzy output parameters of a fuzzy logic system in one embodiment of this application.

[0037] Figure 4This is a schematic diagram of the input and output curves of a fuzzy logic system and the corresponding fuzzy rule table in one embodiment of this application;

[0038] Figure 5 This is a motion diagram illustrating the self-motion task simulation of Experimental Embodiment 1 of this application;

[0039] Figure 6 The speed curves of each joint and the moving platform of the mobile robotic arm in the first experimental embodiment of this application are shown.

[0040] Figure 7 This is a schematic diagram of the continuous movement of the mobile robotic arm in the second experimental embodiment of this application during the execution of a task;

[0041] Figure 8 This is a schematic diagram of the joint angle versus time curve and the joint velocity versus time curve under non-convex constraint range in the second experimental embodiment of this application.

[0042] Figure 9 This is a schematic diagram showing the changes in position Jacobian matrix error and attitude Jacobian matrix error under the circular trajectory task in Experimental Embodiment 2 of this application;

[0043] Figure 10 This is a schematic diagram showing the changes in end effector position error and quaternion attitude error under a circular trajectory task in Experimental Embodiment 2 of this application;

[0044] Figure 11 This is a schematic diagram showing the changes in the error norm, error rate of change norm, and fuzzy output parameters in the fuzzy logic system under the circular trajectory task in Experimental Embodiment 2 of this application.

[0045] Figure 12 This is a simulation diagram of the end effector's orbital motion for a robotic arm performing a welding / cutting task on a conical surface, as described in Experimental Embodiment 3 of this application. Figure 12 Sub-figures 1-9 in the middle show the different states of the robotic arm from top view during the execution of the end effector orbiting motion task;

[0046] Figure 13 This is a schematic diagram of the actual motion trajectory of the end effector at time 0s in subgraph a, time 2s in subgraph b, and time 4s in subgraph c, under the experiment of the mobile robotic arm platform for the circular trajectory tracking task in Experimental Embodiment 4 of this application.

[0047] Figure 14 This is a schematic diagram of the actual motion trajectory of the end effector at 6s in the d subgraph, 8s in the e subgraph, and 10s in the f subgraph under the experiment of the mobile robotic arm platform for the circular trajectory tracking task in Experimental Embodiment 4 of this application.

[0048] Figure 15This is a schematic diagram of the structure of a mobile robotic arm control device based on online learning and fuzzy neurodynamics, according to one embodiment of this application. Detailed Implementation

[0049] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0050] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0051] This invention provides a mobile robotic arm control method based on online learning and fuzzy neurodynamics. This method is applicable to mobile robotic arm systems consisting of an omnidirectional mobile platform and a multi-degree-of-freedom robotic arm. To facilitate understanding of the physical meaning of each variable in the subsequent control method, the kinematic model framework of the mobile robotic arm system is first briefly described. This kinematic model framework includes:

[0052] Robotic arm kinematics: The standard DH parameter method is used to establish the link coordinate system of the robotic arm, and the pose transformation matrix of the end effector relative to the base coordinates of the robotic arm is obtained through chain multiplication. .

[0053] Kinematics of a moving platform: For an omnidirectional moving platform equipped with Mecanum wheels, the kinematics can be determined based on the wheel rotation speed. With platform pose Based on the geometric relationship between them, we establish their forward and inverse kinematic models; among which, Indicates mobile platform in The length of the direction of movement, Indicates mobile platform in The length of the directional movement.

[0054] Overall kinematic integration: By coupling the motion of the mobile platform with the motion of the robotic arm through coordinate transformation, the pose of the end effector of the mobile robotic arm relative to the world coordinate system is obtained. Its describing function is denoted as ,in It is a generalized joint variable that includes the platform pose and the joint angles of the robotic arm.

[0055] It should be emphasized that the precise analytical kinematic model and parameters (such as DH parameters and platform dimensions) mentioned above are only for illustrating the system configuration. The control method proposed in this application does not claim to be precisely known, and the design of the subsequent controller does not depend on this model.

[0056] This invention provides a method for controlling a mobile robotic arm based on online learning and fuzzy neurodynamics, the process of which is as follows: Figure 1 As shown, the specific steps of this method include:

[0057] S11, Obtain the status information of the mobile robotic arm.

[0058] In practical implementation, the acquired state information of the mobile robotic arm includes the actual pose of the end effector of the mobile robotic arm. and desired pose trajectory And the actual joint speeds of each joint of the mobile robotic arm. .

[0059] In practice, the actual pose 's' of the end effector of the mobile robotic arm can be captured by eight motion capture cameras, and the captured data can be visualized and analyzed using programming tools. Specifically, the NOKOV optical motion capture system can be used to capture the actual pose of the end effector. .

[0060] S12 updates the current Jacobian matrix estimate of the mobile robotic arm through an online learning mechanism.

[0061] This step aims to estimate the differential kinematics of a mobile robotic arm online without relying on an accurate prior model. The specific implementation is as follows:

[0062] S121, the actual joint velocity of each joint. Add random noise Construct incentive signals to ensure sufficient motivation during the learning process. The equation is constructed as follows:

[0063] (1);

[0064] In equation (1), random noise Independent and identically distributed noise signals with zero mean, and random noise. The range of values ​​is .

[0065] S122. Based on the gradient descent principle, an online learning equation for the Jacobian matrix is ​​designed, and the current Jacobian matrix estimate of the mobile robotic arm is updated.

[0066] Specifically, based on the gradient descent principle, the process of designing the online learning equation for the Jacobian matrix is ​​as follows: First, define the error function for the Jacobian matrix estimation as... And satisfy Then, by applying gradient descent to the error function, the online learning equation for the Jacobian matrix can be derived as follows:

[0067] (2);

[0068] in, This is expressed as the current Jacobian matrix estimate. This represents the theoretically estimated motion speed of the end effector. This represents the actual speed of the end effector. Represented as Time derivative, The superscript indicates a positive learning rate parameter. This is represented as a transpose operation.

[0069] Therefore, after step S12, the controller can, within each control cycle, determine the actual speed of the end effector based on the real-time acquired data. With excitation signal containing random noise The updated Jacobian matrix estimate is obtained by updating the online learning equation of the Jacobian matrix according to the above equation (2). .

[0070] S13, input the actual pose, the desired pose trajectory and the updated Jacobian matrix estimate into a fuzzy neurodynamics solver, which solves for the joint velocities to be solved.

[0071] This step aims to construct the pose tracking task as a constrained optimization problem and solve it in real time using a fuzzy neurodynamics solver.

[0072] The pose tracking task described above is constructed as a constrained optimization problem, which is structured as follows:

[0073] 1. The objective function is designed to minimize the joint velocity to be solved. The form is a quadratic form. Where, the joint velocity to be solved is... The quadratic form is:

[0074] (3);

[0075] In equation (3), The weighting matrix determines the state variables during the minimization process. The weighting of each component during the optimization process is used to characterize the relative importance of different joint velocity components. The objective function is constructed using a quadratic form, which is essentially equivalent to minimizing the weighted joint velocity norm, thus ensuring the uniqueness of the solution to the optimization problem.

[0076] 2. Based on the updated Jacobian matrix estimate obtained in step S12 Construct the differential kinematic tracking equation.

[0077] Specifically, the updated Jacobian matrix estimate This can be understood as being composed of positional components. With attitude components The differential kinematic tracking equations essentially integrate the following two relationships:

[0078] (4), (5);

[0079] In equations (4) and (5), Indicates the current time. Expressed as joint velocity, Expressed as the desired linear velocity, It is represented as the desired rotation vector.

[0080] By introducing a pose error feedback term, the final differential kinematic tracking equation is:

[0081] (6);

[0082] In equation (6), This represents the predicted motion speed of the end effector. Represented as the desired pose trajectory rate of change, This is represented as a positive feedback gain coefficient.

[0083] 3. The joint velocities to be solved The constraint is set as a non-convex feasible region. ,Right now Among them, the non-convex feasible region The definition of is:

[0084] (7);

[0085] In equation (7), This is represented as a state vector of joint velocities. The state vector of the joint velocity is represented by the first... There are _n_ state components, where R is the set of real numbers. This represents the total number of joints. It is represented as a non-negative threshold parameter, used to define the boundary of the non-saturation interval of joint velocity near zero. and Represented as the first Lower and upper limits of the velocity state components of each joint. This represents the maximum permissible saturation value of the joint velocity, used to define the upper and lower boundaries of the joint velocity. Represented as the first Discrete boundary values ​​allowed for each joint velocity state component. The total number of joints can be 10.

[0086] To solve the above three optimization problems, the following design is proposed: Figure 2 The fuzzy neurodynamics solver shown is designed based on the gradient descent principle and gradually introduces compensation and adaptive mechanisms. Figure 2 middle, Represented as actual pose, Represented as the desired pose trajectory, This is represented as a summation operation. Represented as the learning rate parameter, This is represented as a fuzzy output parameter that is dynamically adjusted through a fuzzy logic system. This is represented as a multiplication operation. It is represented as defined in a non-convex feasible region Projection operator on, Represented as joint data, Represented as an excitation signal, Represented as excitation signal transpose, Represented as random noise, Represented as the desired pose trajectory rate of change, This is expressed as the time derivative of the Jacobian matrix estimate. The time derivative of the Jacobian matrix estimate is expressed as... transpose, This is represented as the transpose of the matrix within the parentheses. Represented as an auxiliary variable, Represented as auxiliary variable Time derivative, This is expressed as an estimate of the Jacobian matrix. Represented as the Jacobian matrix estimate The derivative with respect to time, Represented as scaling parameters, This represents the actual speed of the end effector. The learning rate parameter for online learning is represented as a negative Jacobian matrix. This is represented as an integration operation.

[0087] Figure 2 The solver's input consists of real-time status signals of the mobile robotic arm and preset fixed parameters, which are divided into two categories: pose and velocity signals and preset fixed parameters; the pose and velocity signals include the actual pose of the end effector. Desired pose trajectory Rate of change of desired pose trajectory Joint data This type of signal is collected by the state acquisition module and directly input to the solver, serving as the core input source for the solver; preset fixed parameters include the learning rate parameter. Learning rate parameter for negative Jacobian matrices in online learning Scaling parameters .

[0088] Figure 2 The overall function of the solver is as follows: taking the pose and velocity signals of the mobile robotic arm and preset fixed parameters as input, it dynamically corrects the Jacobian matrix through online learning, and then combines the dynamic adjustment of the fuzzy logic system and the projection on the non-convex feasible region to solve for the optimal joint velocity control command that meets the physical limits. It realizes the whole process of real-time updating of the Jacobian matrix based on online learning and optimization of joint velocity under non-convex constraints, and finally outputs the joint velocity control signal that meets the physical constraints of the mobile robotic arm and adapts to the pose tracking requirements.

[0089] The detailed derivation of the fuzzy neurodynamics solver is as follows:

[0090] First, define the pose tracking error function. for:

[0091] (8);

[0092] Then, to Applying gradient descent, assuming the Jacobian matrix is... The initial joint velocities are obtained as follows:

[0093] (9);

[0094] in, .

[0095] Then, to ensure that the joint velocities satisfy the physical constraints, they are projected onto a non-convex feasible region. Then the joint velocity is:

[0096] (10);

[0097] in, It is represented as defined in a non-convex feasible region The projection operator on the projection function is constructed as follows:

[0098] (11);

[0099] In equation (11), The internal threshold is near zero.

[0100] Then, to suppress the hysteresis error in time-varying trajectory tracking, a compensation term is introduced. Then the joint velocity is:

[0101] (12);

[0102] Then, multiply both sides by the same amount. get:

[0103] (13);

[0104] Then, in a stable state, under certain conditions ,get:

[0105] (14);

[0106] Then, applying the least squares solution, we get: ,in , To represent the pseudo-inverse operation, an auxiliary variable is introduced to replace the direct calculation of the pseudo-inverse. And auxiliary variables time derivative The following dynamic equations are solved recursively. :

[0107] (15) (16);

[0108] in, Represented as auxiliary variable Time derivative, It is represented as a positive scaling parameter.

[0109] Therefore, the above compensation mechanism is combined with fuzzy adaptive adjustment, and the Jacobian matrix used in the derivation is used to represent it. Replace with the Jacobian matrix estimate obtained from the actual update in step S12 within the current control cycle. The velocity variable to be solved is explicitly defined as the joint velocity. This yields the final model of the fuzzy neurodynamics solver:

[0110] (17);

[0111] In equation (17), It is represented as a fuzzy output parameter that is dynamically adjusted through a fuzzy logic system.

[0112] Furthermore, the fuzzy output parameters of the fuzzy logic system are dynamically adjusted. This is used to improve the adaptive capability of the control system. The two inputs of this fuzzy logic system are: the error norm between the actual pose and the desired pose trajectory. ,and And the error norm between the actual velocity and the expected rate of change. ,and The output of a fuzzy logic system is a fuzzy output parameter. The error norm between the actual pose and the desired pose trajectory of the fuzzy logic system. Error norm between actual velocity and expected rate of change and fuzzy output parameters Membership functions are shown in Figure 3 , Figure 3 middle , , , All are fuzzy linguistic variables. The input and output curves of the fuzzy logic system and the corresponding fuzzy rule tables are shown in [the table]. Figure 4 , Figure 4 The surface plot on the left shows the distribution of membership functions corresponding to the input variables, and the rule table on the right shows the inference rules for fuzzy control. , , , These are all fuzzy linguistic variables, for example, when , When, output .

[0113] In practical implementation, the fuzzy logic system performs inference based on fuzzy rules and uses the centroid method to convert the fuzzy output values ​​obtained from the fuzzy inference into specific numerical values, outputting fuzzy output parameters that are adjusted in real time. , .

[0114] S14 outputs the control signal of the joint velocity obtained by the fuzzy neurodynamics solver to drive the movement of the mobile robotic arm.

[0115] In practice, the joint velocities obtained in real time from the fuzzy neurodynamics solver in step S13 are used. The control signals are output to the joint actuators of the mobile robotic arm. The mobile platform and the joints of the robotic arm move in coordination according to these commands, thereby controlling the actual pose of the end effector. Able to stably and accurately track the desired pose trajectory .

[0116] By implementing steps S11 to S14 above, and constructing excitation signals and executing online learning equations, the online real-time estimation and updating of the differential kinematics of the mobile robotic arm is achieved. This eliminates the need for any pre-calibrated or offline-established precise kinematic models and allows the arm to autonomously adapt to system parameter drift and uncertainties caused by mechanical wear, assembly errors, or load changes. This solves the performance degradation problem of traditional model-dependent control methods under model mismatch conditions. Furthermore, by defining joint velocity constraints as non-convex feasible regions and constructing corresponding projection operators, the optimization problem can more realistically characterize the non-convex physical limitations of joint velocities in actual mechanical systems, such as saturation and dead zones. This overcomes the limitations of existing methods that simplify constraints to convex sets, which leads to control... This addresses the limitation of control instructions exceeding the capabilities of the actual execution mechanism. By introducing auxiliary variables and their update laws, a recursive solution form that eliminates the need to calculate matrix pseudo-inverses is constructed, effectively replacing the complex pseudo-inverse calculations in traditional neurodynamic methods and improving the algorithm's real-time performance. Furthermore, by dynamically adjusting key parameters through a fuzzy logic system, online adaptive optimization of control parameters is achieved. This enables the system to intelligently adjust its convergence rate based on real-time pose and velocity errors, overcoming the inherent contradiction between convergence speed and stability margin in fixed-parameter controllers when tracking trajectories with different dynamic characteristics. This effectively suppresses tracking lag errors and comprehensively enhances the system's adaptive capability, response speed, and steady-state accuracy in complex trajectory tracking tasks.

[0117] To verify the effectiveness of the methods proposed in the embodiments of this application, digital simulation experiments and physical platform experiments were conducted respectively.

[0118] Experimental Example 1: Simulation of a self-movement task with non-convex boundary constraints.

[0119] This embodiment aims to verify the effectiveness of the method in handling velocity constraints of non-convex joints. The parameter settings are as follows:

[0120] , , ;

[0121] ;

[0122] , , ;

[0123] , ;

[0124] The range is .

[0125] In this task, the desired pose trajectory is... It is set to a fixed value. Its positional components are: The attitude components (represented by quaternions) are:

[0126] .

[0127] The task requires the robotic arm to perform self-motion while maintaining its end-effector pose, and the execution time is set to 6 seconds. The motion simulation diagram for the self-motion task in Experiment Example 1 is shown below. Figure 5 As shown.

[0128] Experimental results are as follows Figure 6 As shown, Figure 6 middle These represent the angular velocities of the six joints of the robotic arm, with different line styles corresponding to different joints; These represent the motion velocity components of the mobile platform, distinguished by different line styles. In the initial phase of the task, the joint velocity is effectively limited by constraint 1; approximately 0.07 seconds later, constraint 2 is activated to further limit the velocity amplitude. Since both 1 rad / s and 5 rad / s belong to non-convex feasible regions... However, their average value of 3 rad / s does not belong to this category. This result intuitively verifies the non-convexity of the constraints processed in this application and the projection operator. The effectiveness indicates that joint movement is strictly restricted within a pre-defined non-convex physical boundary, and the movement process is smooth.

[0129] Experimental Example 2: Simulation of a circular trajectory tracking task.

[0130] This embodiment aims to verify the overall performance of the method when simultaneously performing position and attitude tracking. The task requires the end effector to track a spatial circular trajectory with a radius of 0.25 meters, i.e., the desired pose trajectory. The positional component is a circular path. The attitude components are set to change continuously over time, specifically defined by the following quaternion operations: The quaternion used to represent the attitude is... and Hamiltonian product, and The task time was set to 10 seconds, and other parameters were the same as those in the self-movement task settings of Experiment Example 1.

[0131] Simulation results are as follows Figures 7 to 11 As shown. Figure 7 This demonstrates the continuous movement of a mobile robotic arm during task execution, with the end effector's posture constantly changing. Figure 8 middle , , , , , These represent the variables that represent the angles of each joint of the robotic arm. These represent the angular velocities of each joint of the robotic arm. , , , These represent the pose variables for each round on the mobile platform. , , , This represents the velocity components of each wheel of the mobile platform. Figure 8 The curves of joint angle variation with time and the variation of joint velocity with time under non-convex constraint range are presented. The results show that the joint motion of the moving robot arm is smooth and continuous throughout the task, which verifies the effectiveness of the non-convex constraint design. Figure 9 This is a schematic diagram illustrating the changes in position Jacobian matrix error and attitude Jacobian matrix error under a circular trajectory task. Figure 9 This indicates that the Jacobian matrix estimation error converges rapidly to within 0.02 seconds. The magnitude demonstrates that the Jacobian matrix learning process has high efficiency and accuracy. Figure 10 This diagram illustrates the changes in end-effector position error and quaternion attitude error under a circular trajectory task. Figure 10 middle This represents the position tracking error in the x-direction. This represents the position tracking error in the y-direction. This represents the position tracking error in the z-direction. This is expressed as attitude angle tracking error. This represents the linear velocity tracking error in the x-direction. This represents the linear velocity tracking error in the y-direction. Represents the linear velocity tracking error in the z-direction, from Figure 10 It can be seen that during the entire circular trajectory tracking process, the position error and quaternion attitude error of the end effector remained stable at a constant level. The magnitude of the data proves that the model in this application has high control accuracy. Figure 11 The diagram illustrates the changes in the error norm, error rate of change norm, and fuzzy output parameters over time in a fuzzy logic system. for , for ,and Represented as the error norm, Let Δσ be the error rate of change norm, and Δσ be the fuzzy output parameter. Therefore, from Figure 11 As can be seen from this, the fuzzy output parameters can be adaptively adjusted according to the error norm and the error rate of change norm, thereby quickly suppressing the deviation, demonstrating the system's good adaptability and robustness.

[0132] Experimental Example 3: Attitude Control Simulation Based on CoppeliaSim Platform.

[0133] To more intuitively verify the effectiveness of the attitude control, a robotic arm end effector's circular motion task for welding / cutting conical surfaces was set up in the CoppeliaSim simulation environment. While moving along a circular trajectory, the end effector needs to maintain a constant attitude angle relative to the conical surface. For example... Figure 12 As shown, Figure 12 Sub-figures 1-9 in the middle section respectively illustrate the different top-down views of the robotic arm during the end-effector orbiting motion task, and Figure 12 Sub-image number 1 shows the starting point of the robotic arm's end effector's path around the conical workpiece. Figure 12 Subgraphs 2-9 in the diagram illustrate the progressive positions of the end effector along the circular path. The path is continuous and without breaks, verifying the smoothness of trajectory tracking. Simulation results show that even with unknown system structural parameters, the method described in this application can still accurately control the end effector's attitude, verifying its applicability in complex attitude synchronization tracking tasks.

[0134] Example 4: Experiment on a mobile robotic arm platform for a circular trajectory tracking task.

[0135] This embodiment verifies the feasibility of the method on a real hardware platform. The experimental platform consists of a mobile robotic arm, a NOKOV optical motion capture system (measurement accuracy ±0.2mm), and a host computer. The software is based on the ROS Melodic framework and implemented in C++. The experimental task and parameters are consistent with the simulation settings of the circular trajectory tracking task in Experimental Embodiment Two.

[0136] Experimental results are as follows Figure 13 and Figure 14 As shown, Figure 13 and Figure 14 In the figure, (a), (b), (c), (d), (e), and (f) represent the states of the moving robotic arm at times 0s, 2s, 4s, 6s, 8s, and 10s, respectively, during the circular trajectory tracking task; and Figure 13 and Figure 14 The top row shows the real-time trajectory of the end effector of the mobile robotic arm captured by motion capture software; the middle row shows the trajectory of the end effector in a spatial coordinate system; and the bottom row shows the state diagram of the mobile robotic arm during its actual movement. Thus, the actual motion trajectory of the end effector captured by the motion capture system closely matches the expected circular trajectory, fully verifying the feasibility and effectiveness of the proposed method in real physical systems. In practical applications, such as welding and spraying, where the end effector needs to be aligned with the target surface during movement, this application demonstrates excellent application potential.

[0137] In one exemplary embodiment, such as Figure 15 As shown, a mobile robotic arm control device based on online learning and fuzzy neurodynamics is provided, comprising:

[0138] The state acquisition module 101 is configured to acquire the actual pose and desired pose trajectory of the end effector of the mobile robotic arm, as well as the actual joint velocity of each joint of the mobile robotic arm.

[0139] The Jacobian matrix online update module 102 is configured to update the current Jacobian matrix estimate of the mobile robotic arm through an online learning mechanism based on the actual motion speed of the end effector and the excitation signal formed by superimposing random noise on the actual joint speed of each joint, so as to obtain the updated Jacobian matrix estimate.

[0140] The fuzzy neural dynamics solving module 103 is configured to input the actual pose, the desired pose trajectory, and the updated Jacobian matrix estimate into a fuzzy neural dynamics solver; wherein, the fuzzy neural dynamics solver is configured to: minimize the quadratic form of the joint velocity to be solved as the optimization objective, satisfy the differential kinematic tracking equation based on the updated Jacobian matrix estimate as the equality constraint, and ensure that the joint velocity to be solved is within a non-convex feasible region as the inequality constraint, and solve the joint velocity to be solved;

[0141] The control command output module 104 is configured to output the control signal of the joint velocity obtained by the fuzzy neurodynamics solver to drive the movement of the mobile robotic arm.

[0142] In one exemplary embodiment, a computer device is also provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0143] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0144] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0145] Those skilled in the art will understand that all or part of the processes in 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. When executed, the computer program can include the processes of the embodiments of the above methods. Furthermore, any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory.

[0146] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0147] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for controlling a mobile robotic arm based on online learning and fuzzy neural dynamics, executed by a controller, characterized in that, The method includes: The actual pose and desired pose trajectory of the end effector of the mobile robotic arm, as well as the actual joint velocity of each joint of the mobile robotic arm, are obtained. Based on the actual motion speed of the end effector and the excitation signal formed by superimposing random noise on the actual joint speeds of each joint, the current Jacobian matrix estimate of the mobile robotic arm is updated through an online learning mechanism to obtain the updated Jacobian matrix estimate. The actual pose, the desired pose trajectory, and the updated Jacobian matrix estimate are input into a fuzzy neurodynamics solver. The fuzzy neurodynamics solver is configured to: minimize the quadratic form of the joint velocities to be solved as the optimization objective; satisfy the differential kinematic tracking equations based on the updated Jacobian matrix estimate as equality constraints; and ensure that the joint velocities to be solved are within a non-convex feasible region as inequality constraints; the neurodynamic model of the fuzzy neurodynamics solver is: ； In the formula, Let be the joint velocity to be solved. Let it be represented as the non-convex feasible region. It is represented as defined in the nonconvex feasible region. Projection operator on, This represents the base learning rate parameter. This is represented as a fuzzy output parameter that is dynamically adjusted through a fuzzy logic system. Represented as an auxiliary variable, Represented as the updated Jacobian matrix estimate, with superscript... This is represented as a transpose operation. This is represented as the actual pose. This is represented as the desired pose trajectory; The auxiliary variable time derivative Updated by the following kinetic equations: ； In the formula, Represented as auxiliary variable Time derivative, It is represented as a positive scaling parameter. Represented as the desired pose trajectory rate of change, Represented as the updated Jacobian matrix estimate, with superscript... This is represented as a transpose operation; The control signal of the joint velocity obtained by the fuzzy neurodynamics solver is output to drive the movement of the mobile robotic arm.

2. The online learning and fuzzy neurodynamics-based mobile robotic arm control method according to claim 1, characterized in that, The step of updating the current Jacobian matrix estimate of the mobile robotic arm through an online learning mechanism specifically includes: Construct an excitation signal with random noise; and the construction equation is: ,in, This is represented as the excitation signal with random noise. This represents the actual joint velocity of each joint. Represented as random noise; The current Jacobian matrix estimate of the mobile robotic arm is updated by the Jacobian matrix learning equation to obtain the updated Jacobian matrix estimate; and the learning equation is: ,in, This is represented by the current Jacobian matrix estimate of the mobile robotic arm. Represented as Time derivative, The learning rate parameter is represented as positive. The speed of motion of the end effector is indicated by the superscript. This is represented as a transpose operation.

3. The online learning and fuzzy neurodynamics-based mobile robotic arm control method according to claim 2, characterized in that, The random noise Independent and identically distributed noise signals with zero mean.

4. The online learning and fuzzy neurodynamics-based mobile robotic arm control method according to claim 3, characterized in that, The random noise The range of values ​​is .

5. The online learning and fuzzy neurodynamics-based mobile robotic arm control method according to claim 1, characterized in that, The differential kinematic tracking equation is as follows: ； in, This is represented by the updated Jacobian matrix estimate. Let be the joint velocity to be solved. This is expressed as the predicted motion speed of the end effector. This is represented as the actual pose. This is represented as the desired pose trajectory. It is expressed as the rate of change of the desired pose trajectory. This is represented as a positive feedback gain coefficient.

6. The online learning and fuzzy neurodynamics-based mobile robotic arm control method according to claim 1, characterized in that, The definition of the non-convex feasible region is: ； in, Let it be represented as the non-convex feasible region. This is represented as a state vector of joint velocities. The state vector of the joint velocity is represented by the first... There are _n_ state components, where R is the set of real numbers. This represents the total number of joints. and Represented as the first Lower and upper limits of the velocity state components of each joint. Represented as the first Discrete boundary values ​​allowed for each joint velocity state component.

7. The online learning and fuzzy neurodynamics-based mobile robotic arm control method according to claim 1, characterized in that, The input to the fuzzy logic system includes the actual pose. With the desired pose trajectory The error norm between them, and the actual speed of the end effector. Rate of change of the desired pose trajectory The error norm between them.

8. A mobile robotic arm control device based on online learning and fuzzy neurodynamics, characterized in that, include: The state acquisition module is configured to acquire the actual pose and desired pose trajectory of the end effector of the mobile robotic arm, as well as the actual joint velocity of each joint of the mobile robotic arm. The Jacobian matrix online update module is configured to update the current Jacobian matrix estimate of the mobile robotic arm based on the actual motion speed of the end effector and the excitation signal formed by superimposing random noise on the actual joint speed of each joint, through an online learning mechanism, to obtain the updated Jacobian matrix estimate. A fuzzy neurodynamics solving module is configured to input the actual pose, the desired pose trajectory, and the updated Jacobian matrix estimate into a fuzzy neurodynamics solver; wherein, the fuzzy neurodynamics solver is configured to: minimize the quadratic form of the joint velocity to be solved as the optimization objective, satisfy the differential kinematic tracking equation based on the updated Jacobian matrix estimate as the equality constraint, and ensure that the joint velocity to be solved is within a non-convex feasible region as the inequality constraint, and solve the joint velocity to be solved; the neurodynamic model of the fuzzy neurodynamics solver is: ； In the formula, Let be the joint velocity to be solved. Let it be represented as the non-convex feasible region. It is represented as defined in the nonconvex feasible region. Projection operator on, This represents the base learning rate parameter. This is represented as a fuzzy output parameter that is dynamically adjusted through a fuzzy logic system. Represented as an auxiliary variable, Represented as the updated Jacobian matrix estimate, with superscript... This is represented as a transpose operation. This is represented as the actual pose. This is represented as the desired pose trajectory; The auxiliary variable time derivative Updated by the following kinetic equations: ； In the formula, Represented as auxiliary variable Time derivative, It is represented as a positive scaling parameter. Represented as the desired pose trajectory rate of change, Represented as the updated Jacobian matrix estimate, with superscript... This is represented as a transpose operation; The control command output module is configured to output the control signal of the joint velocity obtained by the fuzzy neurodynamics solver to drive the movement of the mobile robotic arm.

Images