Real-time trajectory tracking control method and system suitable for redundant or non-redundant mechanical arm

Abstract

The invention discloses a real-time trajectory tracking control method and system suitable for a redundant or non-redundant mechanical arm. The real-time trajectory tracking control method comprises the steps that the system is initialized, parameters are set, and a trajectory starting point is determined; a continuous expected track of the tail end of the mechanical arm in the three-dimensional space is generated; calculating an initial joint speed instruction to obtain a next-period joint angle; in each subsequent control period, measuring an actual pose and calculating the increment of the actual pose, updating the pseudo-inverse of the Jacobian matrix on line by using a recursion formula, and further calculating a current joint speed instruction and updating a joint angle in combination with an expected pose error and an instruction of the previous period; and executing circularly until trajectory tracking is completed. According to the method, the pseudo-inverse is updated online through the actual pose increment, the method does not depend on an accurate fixed kinematics model, the modeling and maintenance cost is reduced, the method is uniformly suitable for redundant and non-redundant mechanical arms, and the universality of the algorithm is enhanced. And through continuous self-adaptive adjustment, tracking errors are effectively reduced, and the track precision and the stability and robustness of the system under complex working conditions are improved.

Description

Technical Field

[0001] This invention belongs to the field of robotic arm motion planning and control technology, and in particular relates to a real-time trajectory tracking control method and system suitable for redundant or non-redundant robotic arms. Background Technology

[0002] With the rapid improvement of industrial automation and intelligence, robotic arms, as core execution equipment, have been widely used in industrial assembly, precision surgery, logistics sorting, and service robots. Based on the matching relationship between the degree of freedom configuration and task requirements, robotic arms can be divided into two main categories: non-redundant (degrees of freedom equal to the task space dimension, such as a 6-DOF robotic arm performing a 6-dimensional pose task) and redundant (degrees of freedom greater than the task space dimension, such as a 7-DOF or higher robotic arm performing a 6-dimensional pose task). The two types exhibit significant differences in structural characteristics, control strategies, and applicable scenarios.

[0003] Non-redundant robotic arms have a compact structure and relatively simple control logic. Their inverse kinematics solutions are unique or have a finite number of solutions, facilitating deterministic trajectory planning and real-time control. They exhibit high efficiency and reliability in repetitive tasks in structured environments (such as automotive welding and palletizing). However, their motion flexibility is limited. In complex scenarios involving obstacle avoidance, joint limitation avoidance, or simultaneous optimization of multiple objectives (such as energy consumption and motion smoothness), they often struggle to balance task completion and motion quality, and may even fail due to configuration constraints.

[0004] Redundant robotic arms, with their additional degrees of freedom, endow the system with "self-movement" capabilities at the kinematic level. While ensuring accurate end-effector pose tracking, they can dynamically optimize joint configurations to achieve secondary objectives such as obstacle avoidance, circumventing singular configurations, reducing joint torque, or extending service life. This characteristic makes them irreplaceable in unstructured environments (such as surgical procedures in confined spaces or material handling in dynamic obstacle environments). However, redundancy also introduces an infinite number of solutions to the inverse kinematics problem, placing higher demands on the control algorithm: it must not only ensure the accuracy of end-effector trajectory tracking but also rationally allocate redundant degrees of freedom to achieve multi-objective collaborative optimization.

[0005] Both types of robotic arms face common challenges at the control level: existing mainstream methods (such as computational torque method and sliding mode control) heavily rely on accurate dynamic models, but in actual systems, factors such as load variations, frictional nonlinearity, and external disturbances lead to uncertainties in model parameters, limiting control accuracy and robustness. Furthermore, traditional methods often decouple position and attitude, making it difficult to achieve high-precision coordinated tracking integrating position and attitude. For redundant robotic arms, these problems are further complicated—model errors not only affect tracking performance but may also lead to improper allocation of redundant degrees of freedom, causing risks such as joint saturation or singularity crossing.

[0006] The root of these limitations lies in the fact that control paradigms based on precise models are ill-suited to the dynamic uncertainties of real-world systems. Against this backdrop, data-driven adaptive control methods offer a unified optimization path for two types of robotic arms: by real-time acquisition of motion feedback data from joints and the end effector, and dynamic estimation of the composite Jacobian mapping, pose-coordinated tracking can be achieved without relying on precise dynamic parameters. For non-redundant robotic arms, this method effectively compensates for model errors and improves trajectory tracking robustness; for redundant robotic arms, the data-driven mechanism can further optimize the allocation strategy of redundant degrees of freedom online, actively avoiding joint limitations and singular regions while tracking the primary task, fully unleashing the motion potential of redundant configurations.

[0007] Therefore, developing data-driven control methods that do not rely on precise models and have both high-precision tracking and dynamic optimization capabilities can not only improve the adaptability of non-redundant robotic arms in disturbed environments, but also give full play to the structural advantages of redundant robotic arms in complex tasks, providing key technical support for the next generation of intelligent robot systems. Summary of the Invention

[0008] To address the above technical problems, this invention provides a real-time trajectory tracking control method and system suitable for redundant or non-redundant robotic arms.

[0009] The technical solution adopted by this invention to solve its technical problem is: A real-time trajectory tracking control method applicable to redundant or non-redundant robotic arms includes the following steps: S1. System initialization: Set control parameters, give the initial joint angle of the robotic arm, and calculate the initial pose vector of the robotic arm end effector as the starting point for trajectory tracking. S2. Desired trajectory generation: Based on a preset closed curve function, calculate the continuous three-dimensional desired trajectory points generated by the end of the robotic arm starting from the initial pose. S3. Initial control law calculation: Calculate the pose Jacobian matrix and its pseudo-inverse matrix of the end effector of the robotic arm based on the initial joint angles, and calculate the initial joint velocity command based on the error between the expected pose and the current actual pose at the second moment. Then, calculate the joint angle of the robotic arm in the second control cycle based on the initial joint velocity command. S4. Recursive Adaptive Update: In each subsequent control cycle, the current actual pose is measured, the actual pose increment of the adjacent cycle is calculated, and based on the pose increment and the control command of the previous cycle, the pseudo-inverse matrix is ​​updated online using a recursive formula. Then, based on the updated pseudo-inverse matrix, the error between the expected pose of the next moment and the current actual pose, and the control command of the previous cycle, the joint velocity command of the current cycle is calculated, and the joint angle of the next control cycle is updated based on the joint velocity command of the current cycle. S5. Repeat S4 until the entire trajectory is tracked.

[0010] Preferably, the control parameters in S1 include the total trajectory time T and the control period. The adaptive gain parameters are η, ρ, λ, μ; the initial pose vector consists of the end position coordinates and the end attitude angle.

[0011] Preferably, the preset closed curve function in S2 is a Lissajous closed curve, and the desired trajectory of the end effector in the desired pose is generated by the following formula: ; in, , , They are respectively The expected position coordinates at time [time]. For trajectory scale parameters, For the trajectory period, For the current time, , , This is the offset of the trajectory center; The desired pose in the desired pose is the initial pose.

[0012] Preferably, S3 calculates the complete pose Jacobian matrix and its pseudo-inverse matrix of the robotic arm end effector based on the initial joint angles, including: Calculate the position Jacobian matrix based on the initial joint angles. and posture Jacobian matrix By concatenating the position Jacobian matrix and the pose Jacobian matrix, the complete pose Jacobian matrix is ​​obtained: ; Based on the complete pose Jacobian matrix Calculate its pseudo-inverse matrix as follows: .

[0013] Preferably, in step S3, the initial joint velocity command is calculated based on the error between the desired pose at the second moment and the current actual pose. Specifically: ; in, Let be the pseudo-inverse of the Jacobian matrix of the complete pose at the initial time. Let be the desired pose vector at the second time step. This is the actual pose vector at the initial moment. For learning rate, For regularization parameters; Based on initial joint velocity command Calculate the joint angle of the robotic arm in the second control cycle. Specifically: ; in, Let be the joint angle vector at the initial moment. To control the cycle.

[0014] Preferably, the recursive formula for online updating of the pseudo-inverse matrix in S4 is: ; ; in, and The first Time and The pseudo-inverse matrix at time step, For the first The joint velocity command at any moment, For the first and The actual pose increment between time points and For control parameters, Control the update step size, To prevent division by zero, This represents the squared L2 norm of the pose increment.

[0015] Preferably, the calculation of the first step in S4 is... The formula for the joint velocity command at a given time is: ; in, This is the joint velocity command at the current moment. For the first The expected pose vector at time 1. For the first The actual pose vector at any given moment; Based on the joint velocity command at the current moment The robotic arm was updated in the first Joint angles during control cycle Specifically: .

[0016] A real-time trajectory tracking control system suitable for redundant or non-redundant robotic arms, comprising: The system initialization module is used to set control parameters, give the initial joint angle of the robotic arm, and calculate the initial pose vector of the robotic arm end effector as the starting point for trajectory tracking. The desired trajectory generation module is used to calculate the continuous three-dimensional desired trajectory points generated by the end effector of the robotic arm from the initial pose, based on a preset closed curve function. The initial control law calculation module is used to calculate the pose Jacobian matrix and its pseudo-inverse matrix of the end effector of the robotic arm based on the initial joint angle, and to calculate the initial joint velocity command based on the error between the expected pose and the current actual pose at the second moment, and then calculate the joint angle of the robotic arm in the second control cycle based on the initial joint velocity command. The recursive adaptive update module is used to measure the current actual pose in each subsequent control cycle, calculate the actual pose increment of the adjacent cycle, and update the pseudo-inverse matrix online using a recursive formula based on the pose increment and the control command of the previous cycle. Then, based on the updated pseudo-inverse matrix, the error between the expected pose of the next moment and the current actual pose, and the control command of the previous cycle, the joint velocity command of the current cycle is calculated, and the joint angle of the next control cycle is updated based on the joint velocity command of the current cycle. The trajectory tracking module is used to repeatedly execute the recursive adaptive update module until the entire trajectory is tracked.

[0017] A computer device includes a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps of a real-time trajectory tracking control method suitable for redundant or non-redundant robotic arms.

[0018] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a real-time trajectory tracking control method applicable to redundant or non-redundant robotic arms.

[0019] The aforementioned real-time trajectory tracking control method and system applicable to redundant or non-redundant robotic arms updates the pseudo-inverse of the Jacobian matrix online using a recursive formula in each control cycle based on the actual measured end-effector pose increment, thereby correcting model inaccuracies in real time. This makes the control algorithm independent of precise, fixed kinematic models, reducing the cost of model acquisition and maintenance. Simultaneously, this method is uniformly applicable to both redundant and non-redundant robotic arms, exhibiting good versatility. In this way, the robotic arm can continuously and autonomously adapt to changes in its own state and environment throughout the tracking process, effectively reducing trajectory tracking errors and improving tracking accuracy and the system's stable operation under complex conditions. Attached Figure Description

[0020] Figure 1 This is a flowchart of a real-time trajectory tracking control method applicable to redundant or non-redundant robotic arms according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the three-dimensional spatial motion trajectory of a redundant robotic arm in one embodiment of the present invention; Figure 3 This is a schematic diagram comparing the expected trajectory and the actual trajectory at the end of an embodiment of the present invention; Figure 4 This is a time-domain response curve of the six joint angles in one embodiment of the present invention; Figure 5 This is a schematic diagram of the dynamic response of joint angular velocity in one embodiment of the present invention; Figure 6 This is a schematic diagram of the time-domain variation of the end attitude angle in one embodiment of the present invention; Figure 7 This is a schematic diagram of the convergence curve of the end position tracking error in one embodiment of the present invention; Figure 8 This is a schematic diagram of the online estimation of the composite Jacobian matrix in one embodiment of the present invention; Figure 9 This is a schematic diagram comparing the estimated Jacobian matrix with the theoretical Jacobian matrix in one embodiment of the present invention. Detailed Implementation

[0021] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings.

[0022] In one embodiment, such as Figure 1 As shown, a real-time trajectory tracking control method suitable for redundant or non-redundant robotic arms includes the following steps: S1. System initialization: Set control parameters, give the initial joint angle of the robotic arm, and calculate the initial pose vector of the robotic arm end effector as the starting point for trajectory tracking. S2. Desired trajectory generation: Based on a preset closed curve function, calculate the continuous three-dimensional desired trajectory points generated by the end of the robotic arm starting from the initial pose. S3. Initial control law calculation: Calculate the pose Jacobian matrix and its pseudo-inverse matrix of the end effector of the robotic arm based on the initial joint angles, and calculate the initial joint velocity command based on the error between the expected pose and the current actual pose at the second moment. Then, calculate the joint angle of the robotic arm in the second control cycle based on the initial joint velocity command. S4. Recursive Adaptive Update: In each subsequent control cycle, the current actual pose is measured, the actual pose increment of the adjacent cycle is calculated, and based on the pose increment and the control command of the previous cycle, the pseudo-inverse matrix is ​​updated online using a recursive formula. Then, based on the updated pseudo-inverse matrix, the error between the expected pose of the next moment and the current actual pose, and the control command of the previous cycle, the joint velocity command of the current cycle is calculated, and the joint angle of the next control cycle is updated based on the joint velocity command of the current cycle. S5. Repeat S4 until the entire trajectory is tracked.

[0023] Specifically, the system initialization sets a baseline for the control process. A preset continuous three-dimensional spatial trajectory is then generated. The control process first calculates an initial control command to drive the robotic arm to begin movement. In the recursive adaptive update phase, the controller no longer assumes that the pseudo-inverse of the initially calculated Jacobian matrix is ​​always accurate. Instead, based on the pose increment generated by the actual movement of the robotic arm's end effector, combined with the control command from the previous cycle, it uses a mathematical recursive formula to update and correct the pseudo-inverse matrix online and in real time. This process learns and adjusts its control model based on actual feedback. Based on the updated, more accurate pseudo-inverse matrix, the current control command is calculated again, thus forming an adaptive closed loop of "execution-measurement-update-re-execution". S5 then continuously executes this adaptive update process to ensure that the robotic arm can continuously and accurately track the desired trajectory until the task is completed.

[0024] The aforementioned real-time trajectory tracking control method for redundant or non-redundant robotic arms achieves online learning and control without relying on precise prior models through a closed-loop process of initialization, trajectory generation, initial control, recursive adaptive update, and cyclic execution, thereby enhancing the practicality and robustness of the system.

[0025] In one embodiment, the control parameters in S1 include the total trajectory time T and the control period. The adaptive gain parameters are η, ρ, λ, μ; the initial pose vector consists of the end position coordinates and the end attitude angle.

[0026] Specifically, given the initial joint angle The function `position_end(q)` is called to calculate the initial end-effector position (x, y, z), which is based on DH parameters or a forward kinematics model; the function `orientation(q)` is called to calculate the initial end-effector pose (e.g., Euler angles). (θ,ψ); combine to obtain the initial pose vector. , as the starting point of the trajectory.

[0027] In one embodiment, the preset closed curve function in S2 is a Lissajous closed curve, and the desired trajectory of the end effector in the desired pose is generated by the following formula: ; in, , , They are respectively The expected position coordinates at time [time]. For trajectory scale parameters (e.g., 0.02 meters). For the trajectory period, For the current time, , , This is the offset of the trajectory center; The desired pose in the desired pose is the initial pose.

[0028] Specifically, the trajectory contains rich frequency components on all three coordinate axes, effectively verifying the control algorithm's ability to track complex spatial motions. Furthermore, setting the desired pose as the initial pose simplifies the pose tracking problem, facilitating an initial focus on verifying the performance of the position tracking algorithm.

[0029] In one embodiment, S3 calculates the complete pose Jacobian matrix and its pseudo-inverse matrix of the robotic arm end effector based on the initial joint angles, including: Calculate the position Jacobian matrix based on the initial joint angles. and posture Jacobian matrix By concatenating the position Jacobian matrix and the pose Jacobian matrix, the complete pose Jacobian matrix is ​​obtained: ; Based on the complete pose Jacobian matrix Calculate its pseudo-inverse matrix as follows: .

[0030] Specifically, the position Jacobian matrix A mapping between joint velocities and end-effector linear velocities was established, and the attitude Jacobian matrix... This establishes a mapping between joint velocities and end-effector angular velocities. To simultaneously control position and attitude, these two matrices need to be concatenated along the row direction to form an augmented complete pose Jacobian matrix. The number of rows *m* corresponds to the pose degrees of freedom, and the number of columns *n* corresponds to the number of joints. For a non-redundant robotic arm (n=m), its pseudo-inverse is the inverse of the matrix; for a redundant robotic arm (n>m), calculating its pseudo-inverse is fundamental to solving the inverse kinematics problem. At the initial moment (k=1), the initial joint angles are calculated... and its pseudo-reversal This prepares for the calculation of the first step of control instructions.

[0031] In one embodiment, in step S3, the initial joint velocity command is calculated based on the error between the desired pose at the second moment and the current actual pose. Specifically: ; in, Let be the pseudo-inverse of the Jacobian matrix of the complete pose at the initial time. Let be the desired pose vector at the second time step. This is the actual pose vector at the initial moment. For learning rate, For regularization parameters; Based on initial joint velocity command Calculate the joint angle of the robotic arm in the second control cycle. Specifically: ; in, Let be the joint angle vector at the initial moment. To control the cycle.

[0032] Specifically, control parameters and Adjusting the response speed and smoothness of the initial actions avoids violent jitter during startup, ensuring a smooth start-up of the system from a standstill.

[0033] In one embodiment, the recursive formula for online updating of the pseudo-inverse matrix in S4 is: ; ; in, and The first Time and The pseudo-inverse matrix at time step, For the first The joint velocity command at any moment, For the first and The actual pose increment between time points and For control parameters, Control the update step size, To prevent division by zero, This represents the squared L2 norm of the pose increment.

[0034] Specifically, this approach completely eliminates the reliance on an exact analytical Jacobian matrix and can automatically compensate for model errors and unmodeled dynamics, which is the key to the robustness of this method.

[0035] In one embodiment, the calculation of the first in S4 The formula for the joint velocity command at a given time is: ; in, This is the joint velocity command at the current moment. For the first The expected pose vector at time 1. For the first The actual pose vector at any given moment; Based on the joint velocity command at the current moment The robotic arm was updated in the first Joint angles during control cycle Specifically: .

[0036] Specifically, the joint velocity control law at each time step considers both the current pose error feedback based on the updated pseudo-inverse matrix and the control command from the previous time step. This design helps to make the changes in joint velocity commands smoother, reduce jitter, and improve the dynamic response performance and stability of the system.

[0037] Simulation effect experimental diagram as follows Figures 2 to 9 As shown, Figure 2 This is a schematic diagram of the three-dimensional motion trajectory of a redundant robotic arm. The left side shows a snapshot of the continuous motion posture of the robotic arm links in Cartesian space, while the right side shows the complete trajectory curve of the end effector in the XYZ three-dimensional coordinate system. The trajectory exhibits a hindslip shape, generated by the superposition of multiple harmonic functions, verifying the algorithm's tracking capability under complex and irregular trajectories. The smooth and abrupt motion of each link of the robotic arm indicates that the joint space control commands are continuously differentiable and satisfy the physical constraints of the actual actuator. Figure 3 This diagram illustrates the comparison between the expected and actual trajectories of the robotic arm's end effector. The blue dotted line represents the theoretically expected trajectory based on the S2 planning method, while the red dashed line represents the actual trajectory of the robotic arm's end effector. The two trajectories highly overlap in three-dimensional space. The degree of trajectory overlap directly reflects the position tracking accuracy. Simulation results demonstrate that the data-driven control law based on the composite error model effectively overcomes model uncertainties and achieves sub-millimeter level high-precision tracking.

[0038] Figure 4 The graph shows the time-domain response curves of the six joint angles. The six colored curves correspond to the angle changes (in radians) of joints 1 to 6, with the horizontal axis representing time (0-10s) and the vertical axis representing joint angular displacement. The angles of each joint change smoothly within the mechanical limit of [-π, π], without saturation or abrupt changes, verifying the algorithm's ability to reasonably allocate redundant degrees of freedom. Joints 3 and 5 exhibit larger motion amplitudes (approximately ±1.2 rad) and undertake the main trajectory tracking task; joints 1 and 6 have smaller motion amplitudes (<0.5 rad) and are used to optimize attitude constraints and avoid singularities, demonstrating the synergistic effect of redundant degrees of freedom in multi-objective optimization. Figure 5 This diagram illustrates the dynamic response of joint angular velocity. Six curves represent the change of angular velocity (unit: rad / s) of each joint over time, with the peak velocity controlled within ±1.5 rad / s. The angular velocity curves are continuous and free of high-frequency oscillations, and the rate of change of the maximum acceleration is gradual, indicating that the control commands have good dynamic feasibility and can be directly applied to practical servo drive systems. The velocity amplitude is limited by the regularization design (λ=0) of the adaptive gain matrix M(k), effectively suppressing the joint velocity divergence problem caused by the ill-conditioned Jacobian matrix.

[0039] Figure 6This diagram illustrates the time-domain variation of the end effector's attitude angles. The three curves represent the changes in Euler angles (in radians) of the end effector around the X, Y, and Z axes over time. The three-axis attitude angles remain essentially constant throughout the entire time period (initial attitude), verifying the effectiveness of the attitude error term in the composite error model. This result demonstrates that the algorithm successfully achieves coupled position-attitude control, avoiding the attitude drift problem caused by position tracking disturbances in traditional decoupled control. Figure 7 This diagram illustrates the convergence curve of the end-point position tracking error. The red solid line represents the spatial distance error between the actual end-point position and the preset trajectory position. The error curve converges rapidly to a steady state within 2 seconds, with a steady-state root mean square error of 0.83 mm. The peak error of 1.47 mm occurs in the initial stage. The error convergence process exhibits exponential decay characteristics, consistent with the stability theory of adaptive control systems. This result demonstrates that the data-driven mechanism can effectively compensate for uncertainties in model parameters (such as link mass and friction coefficient deviations), achieving highly robust tracking.

[0040] Figure 8 This diagram illustrates the online estimation of the composite Jacobian matrix. The dynamic changes of each element value over time (36 subplots) of the 6×6 matrix reflect the real-time estimation of the Jacobian matrix M(k) by the data-driven algorithm. The matrix elements stabilize after rapid adjustment in the initial stage (0-3s), indicating good convergence of the adaptive law. The estimated matrix maintains full rank throughout, effectively avoiding singular configurations during the robotic arm's movement and demonstrating the algorithm's proactive utilization of redundant degrees of freedom. Figure 9 This diagram illustrates the comparison between the estimated and theoretical Jacobian matrices, using the theoretical Jacobian matrix J_composite calculated based on the robot's DH parameters. This verifies the effectiveness of the data-driven estimation method. In regions with drastic joint configuration changes, the estimated matrix can quickly adapt to the nonlinear changes in the Jacobian matrix without recalculating the dynamic model, highlighting the core advantage of this invention: "model-free." This comparison directly demonstrates that the adaptive update law can replace traditional model-based Jacobian matrix calculations, reducing the control algorithm's dependence on precise parameters.

[0041] The real-time trajectory tracking control scheme for redundant or non-redundant robotic arms provided by this invention has a series of significant beneficial effects and comprehensive advantages compared to traditional control methods based on fixed models, as follows: (1) This scheme fundamentally reduces the reliance on accurate prior kinematic models, significantly improving the system's practicality and ease of deployment. Traditional methods require accurate geometric parameters to construct the Jacobian matrix, while this scheme, by introducing a recursive adaptive update mechanism, can update the Jacobian pseudo-inverse matrix online in real time in each control cycle using only the actual measured end pose increment and control commands. This process can automatically compensate for model uncertainties caused by model simplification, manufacturing tolerances, assembly errors, or link flexibility, enabling the system to maintain good control performance even when an accurate model is lacking or model parameters change slowly, thus reducing the cost and technical threshold of model calibration and maintenance.

[0042] (2) This scheme demonstrates strong robustness and environmental adaptability. Since the core mapping relationship (pseudo-inverse matrix) in the control law is dynamically learned online, the system can autonomously adapt to various disturbances during operation. For example, when the load on the robotic arm changes, there is friction in the joints, or there is slight external interference, the actual motion will deviate from the model prediction. The recursive update algorithm of this scheme can quickly capture and correct this deviation, making the updated pseudo-inverse matrix more consistent with the current actual dynamic characteristics, thereby continuously ensuring high-precision trajectory tracking and enhancing the system's stable operation capability in unstructured or dynamic environments.

[0043] (3) This scheme has high versatility and smooth control performance. Its core algorithm is uniformly applicable to both redundant and non-redundant robotic arms, without the need for fundamental modifications to different configurations, and has good universality. At the same time, the control law design integrates the current error feedback and the previous instruction, making the generated joint speed command continuous and smooth, effectively avoiding abrupt changes and jitter, which not only protects the mechanical body, but also improves the smoothness of the motion trajectory.

[0044] This invention combines recursive learning with real-time control, which not only improves the accuracy and robustness of trajectory tracking, but also broadens the application scope of robotic arms in scenarios with uncertain models and complex tasks. It provides an effective technical means to enhance the autonomous performance and reliability of robot systems in advanced manufacturing, assisted operations and other fields.

[0045] In one embodiment, a real-time trajectory tracking control system suitable for redundant or non-redundant robotic arms is also provided, comprising: The system initialization module is used to set control parameters, give the initial joint angle of the robotic arm, and calculate the initial pose vector of the robotic arm end effector as the starting point for trajectory tracking. The desired trajectory generation module is used to calculate the continuous three-dimensional desired trajectory points generated by the end effector of the robotic arm from the initial pose, based on a preset closed curve function. The initial control law calculation module is used to calculate the pose Jacobian matrix and its pseudo-inverse matrix of the end effector of the robotic arm based on the initial joint angle, and to calculate the initial joint velocity command based on the error between the expected pose and the current actual pose at the second moment, and then calculate the joint angle of the robotic arm in the second control cycle based on the initial joint velocity command. The recursive adaptive update module is used to measure the current actual pose in each subsequent control cycle, calculate the actual pose increment of the adjacent cycle, and update the pseudo-inverse matrix online using a recursive formula based on the pose increment and the control command of the previous cycle. Then, based on the updated pseudo-inverse matrix, the error between the expected pose of the next moment and the current actual pose, and the control command of the previous cycle, the joint velocity command of the current cycle is calculated, and the joint angle of the next control cycle is updated based on the joint velocity command of the current cycle. The trajectory tracking module is used to repeatedly execute the recursive adaptive update module until the entire trajectory is tracked.

[0046] Specifically, the system comprises five modules: the system initialization module is responsible for parameter configuration and startup; the desired trajectory generation module acts as a task planner; the initial control law calculation module completes the first calculation during the startup phase; the recursive adaptive update module is the intelligent core of the entire system, responsible for continuously learning and adjusting the control model online; and the trajectory tracking module is the scheduler for executing the loop.

[0047] Specific limitations regarding a real-time trajectory tracking control system suitable for redundant or non-redundant robotic arms can be found in the above description of the limitations of a real-time trajectory tracking control method suitable for redundant or non-redundant robotic arms, and will not be repeated here. The modules in the aforementioned real-time trajectory tracking control system suitable for redundant or non-redundant robotic arms can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device in hardware form, or stored in the memory of a computer device in software form, so that the processor can call and execute the operations corresponding to each module.

[0048] A computer device includes a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps of a real-time trajectory tracking control method suitable for redundant or non-redundant robotic arms.

[0049] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a real-time trajectory tracking control method applicable to redundant or non-redundant robotic arms.

[0050] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0051] The present invention provides a detailed description of a real-time trajectory tracking control method and system suitable for redundant or non-redundant robotic arms. Specific examples have been used to illustrate the principles and implementation methods of the invention, and the descriptions of these embodiments are merely for the purpose of helping to understand the core ideas of the invention. It should be noted that those skilled in the art can make various improvements and modifications to the invention without departing from its principles, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims

1. A real-time trajectory tracking control method applicable to redundant or non-redundant robotic arms, characterized in that, Includes the following steps: S1. System initialization: Set control parameters, give the initial joint angle of the robotic arm, and calculate the initial pose vector of the robotic arm end effector as the starting point for trajectory tracking. S2. Desired trajectory generation: Based on a preset closed curve function, calculate the continuous three-dimensional desired trajectory points generated by the end of the robotic arm starting from the initial pose. S3. Initial control law calculation: Calculate the pose Jacobian matrix and its pseudo-inverse matrix of the end effector of the robotic arm based on the initial joint angles, and calculate the initial joint velocity command based on the error between the expected pose and the current actual pose at the second moment. Then, calculate the joint angle of the robotic arm in the second control cycle based on the initial joint velocity command. S4. Recursive Adaptive Update: In each subsequent control cycle, the current actual pose is measured, the actual pose increment of the adjacent cycle is calculated, and based on the pose increment and the control command of the previous cycle, the pseudo-inverse matrix is ​​updated online using a recursive formula. Then, based on the updated pseudo-inverse matrix, the error between the expected pose of the next moment and the current actual pose, and the control command of the previous cycle, the joint velocity command of the current cycle is calculated, and the joint angle of the next control cycle is updated based on the joint velocity command of the current cycle. S5. Repeat S4 until the entire trajectory is tracked.

2. The method according to claim 1, characterized in that, The control parameters in S1 include the total trajectory time T and the control period. The adaptive gain parameters are η, ρ, λ, μ; the initial pose vector consists of the end position coordinates and the end attitude angle.

3. The method according to claim 2, characterized in that, The pre-defined closed curve function in S2 is a Lissajous closed curve, and the desired trajectory of the end effector in the desired pose is generated by the following formula: ； in, , , They are respectively The expected position coordinates at time [time]. For trajectory scale parameters, For the trajectory period, For the current time, , , This is the offset of the trajectory center; The desired pose in the desired pose is the initial pose.

4. The method according to claim 3, characterized in that, S3 calculates the complete pose Jacobian matrix and its pseudo-inverse matrix of the robotic arm end effector based on the initial joint angles, including: Calculate the position Jacobian matrix based on the initial joint angles. and posture Jacobian matrix By concatenating the position Jacobian matrix and the pose Jacobian matrix, the complete pose Jacobian matrix is ​​obtained: ; Based on the complete pose Jacobian matrix Calculate its pseudo-inverse matrix as follows: .

5. The method according to claim 4, characterized in that, In S3, the initial joint velocity command is calculated based on the error between the desired pose at the second moment and the current actual pose. Specifically: ； in, Let be the pseudo-inverse of the Jacobian matrix of the complete pose at the initial time. Let be the desired pose vector at the second time step. This is the actual pose vector at the initial moment. For learning rate, For regularization parameters; Based on initial joint velocity command Calculate the joint angle of the robotic arm in the second control cycle. Specifically: ； in, Let be the joint angle vector at the initial moment. To control the cycle.

6. The method according to claim 5, characterized in that, The recursive formula for updating the pseudo-inverse matrix online in S4 is: ； ； in, and The first Time and The pseudo-inverse matrix at time step, For the first The joint velocity command at any moment, For the first and The actual pose increment between time points and For control parameters, Control the update step size, To prevent division by zero, This represents the squared L2 norm of the pose increment.

7. The method according to claim 6, characterized in that, Calculate the first in S4 The formula for the joint velocity command at a given time is: ； in, This is the joint velocity command at the current moment. For the first The expected pose vector at time t. For the first The actual pose vector at any given moment; Based on the joint velocity command at the current moment The robotic arm was updated in the first Joint angles during control cycle Specifically: 。 8. A real-time trajectory tracking control system suitable for redundant or non-redundant robotic arms, characterized in that, include: The system initialization module is used to set control parameters, give the initial joint angle of the robotic arm, and calculate the initial pose vector of the robotic arm end effector as the starting point for trajectory tracking. The desired trajectory generation module is used to calculate the continuous three-dimensional desired trajectory points generated by the end effector of the robotic arm from the initial pose, based on a preset closed curve function. The initial control law calculation module is used to calculate the pose Jacobian matrix and its pseudo-inverse matrix of the end effector of the robotic arm based on the initial joint angle, and to calculate the initial joint velocity command based on the error between the expected pose and the current actual pose at the second moment, and then calculate the joint angle of the robotic arm in the second control cycle based on the initial joint velocity command. The recursive adaptive update module is used to measure the current actual pose in each subsequent control cycle, calculate the actual pose increment of the adjacent cycle, and update the pseudo-inverse matrix online using a recursive formula based on the pose increment and the control command of the previous cycle. Then, based on the updated pseudo-inverse matrix, the error between the expected pose of the next moment and the current actual pose, and the control command of the previous cycle, the joint velocity command of the current cycle is calculated, and the joint angle of the next control cycle is updated based on the joint velocity command of the current cycle. The trajectory tracking module is used to repeatedly execute the recursive adaptive update module until the entire trajectory is tracked.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 7.

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