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CN-121989262-A - Real-time track tracking control method and system suitable for redundant or non-redundant mechanical arm

CN121989262ACN 121989262 ACN121989262 ACN 121989262ACN-121989262-A

Abstract

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

Inventors

  • YANG MIN
  • LAN YOUSHENG
  • ZHANG HUI
  • WANG YAONAN

Assignees

  • 湖南大学

Dates

Publication Date
20260508
Application Date
20260409

Claims (10)

  1. 1. The real-time track tracking control method suitable for the redundant or non-redundant mechanical arm is characterized by comprising the following steps of: s1, initializing a system, namely setting control parameters, giving an initial joint angle of the mechanical arm, and calculating an initial pose vector of the tail end of the mechanical arm as a starting point of track tracking; S2, generating an expected track, namely calculating continuous three-dimensional space expected track points generated from the initial pose at the tail end of the mechanical arm based on a preset closed curve function; S3, calculating an initial control law, namely calculating a pose jacobian matrix and a pseudo inverse matrix of the tail end of the mechanical arm based on the initial joint angle, calculating an initial joint speed instruction according to the error of the expected pose and the current actual pose at the second moment, and further calculating the joint angle of the mechanical arm in the second control period based on the initial joint speed instruction; S4, recursively and adaptively updating, namely measuring the current actual pose in each subsequent control period, calculating the actual pose increment of the adjacent period, updating the pseudo-inverse matrix on line by using a recursion formula based on the pose increment and a control instruction of the previous period, calculating a joint speed instruction of the current period according to the updated pseudo-inverse matrix, the error of the expected pose and the current actual pose at the next moment and the control instruction of the previous period, and updating the joint angle of the next control period based on the joint speed instruction of the current period; s5, executing S4 in a circulating mode until the tracking of the whole track is completed.
  2. 2. The method of claim 1, wherein the control parameters in S1 include a total track time T, a control period The initial pose vector consists of end position coordinates and end pose angles.
  3. 3. The method of claim 2, wherein the closed curve function preset in S2 is a lissajous-like closed curve, and the desired trajectory of the end effector in the desired pose is generated by the following formula: ; Wherein, the , , Respectively is The desired position coordinates of the moment in time, As a parameter of the dimensions of the track, For the period of the track it is possible, For the current time period of time, , , Is the offset of the track center; The desired pose of the desired poses is an initial pose.
  4. 4. The method of claim 3, wherein calculating the complete pose jacobian of the end of the manipulator and its pseudo-inverse based on the initial joint angles in S3 comprises: Based on the initial joint angles, respectively calculating position jacobian matrices And pose jacobian matrix And splicing the position jacobian matrix and the posture jacobian matrix up and down to obtain a complete posture jacobian matrix: ; Based on complete pose jacobian matrix The pseudo-inverse matrix is calculated, and the method specifically comprises the following steps: 。
  5. 5. the method of claim 4, wherein the initial joint velocity command is calculated in S3 based on the error between the desired pose at the second time and the current actual pose The method specifically comprises the following steps: ; Wherein, the As a pseudo-inverse of the complete pose jacobian at the initial time, For the desired pose vector at the second moment, For the actual pose vector at the initial moment, In order for the rate of learning to be high, Is a regularization parameter; Based on initial joint velocity instructions Calculating joint angle of mechanical arm in second control period The method specifically comprises the following steps: ; Wherein, the As the joint angle vector at the initial moment, For the control period.
  6. 6. The method of claim 5, wherein the recurrence formula for online updating of the pseudo-inverse in S4 is: ; ; Wherein, the And Respectively the first Time of day and time of day The pseudo-inverse of the moment in time, Is the first A command for the velocity of the joint at the moment, Is the first And (3) with The actual pose increment between the moments in time, And In order to control the parameters of the device, The update step size is controlled and, Prevent the zero removal of the material, Representing the square of the two norms of the pose increment.
  7. 7. The method of claim 6, wherein the calculation of the first in S4 The formula of the joint velocity command at the moment is: ; Wherein, the For the joint velocity command at the current moment, Is the first The desired pose vector of the moment in time, Is the first The actual pose vector at the moment; joint velocity command based on current time Update the mechanical arm at the first Control of joint angle of cycle The method specifically comprises the following steps: 。
  8. 8. A real-time trajectory tracking control system for redundant or non-redundant robotic arms, comprising: The system initialization module is used for setting control parameters, giving an initial joint angle of the mechanical arm and calculating an initial pose vector of the tail end of the mechanical arm as a starting point of track tracking; The expected track generation module is used for calculating continuous three-dimensional space expected track points generated from the initial pose at the tail end of the mechanical arm based on a preset closed curve function; The initial control law calculation module is used for calculating a pose jacobian matrix and a pseudo inverse matrix of the tail end of the mechanical arm based on the initial joint angle, calculating an initial joint speed instruction according to the error of the expected pose and the current actual pose at the second moment, and further calculating the joint angle of the mechanical arm in the second control period based on the initial joint speed instruction; The recursion self-adaptive updating module is used for measuring the current actual pose in each subsequent control period, calculating the actual pose increment of the adjacent period, updating the pseudo-inverse matrix on line by using a recursion formula based on the pose increment and the control command of the previous period, calculating the joint speed command of the current period according to the updated pseudo-inverse matrix, the error of the expected pose and the current actual pose at the next moment and the control command of the previous period, and updating the joint angle of the next control period based on the joint speed command of the current period; And the track tracking module is used for circularly executing the recursion self-adaptive updating module until the tracking of the whole track is completed.
  9. 9. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor implements the steps of the method of any of claims 1 to 7 when the computer program is executed.
  10. 10. A computer readable storage medium, on which a computer program is stored, characterized in that the computer program, when being executed by a processor, implements the steps of the method of any of claims 1 to 7.

Description

Real-time track tracking control method and system suitable for redundant or non-redundant mechanical arm Technical Field The invention belongs to the technical field of mechanical arm motion planning and control, and particularly relates to a real-time track tracking control method and system suitable for redundant or non-redundant mechanical arms. Background With the rapid promotion of industrial automation and intelligence level, the mechanical arm as a core execution device is widely applied to the fields of industrial assembly, precision surgery, logistics sorting, service robots and the like. According to the matching relation between the degree of freedom configuration and the task requirement, the mechanical arm can be divided into two major categories, namely non-redundant (the degree of freedom is equal to the task space dimension, for example, the 6-dimensional pose task is executed by the 6-degree of freedom mechanical arm) and redundant (the degree of freedom is larger than the task space dimension, for example, the 6-dimensional pose task is executed by the 7-degree of freedom and above mechanical arm), and the two major categories show significant differences in structural characteristics, control strategies and application scenes. The non-redundant mechanical arm has compact structure and relatively simple control logic, and the inverse kinematics solution has uniqueness or limited multiple solutions, so that deterministic track planning and real-time control are conveniently realized, and the high efficiency and the high reliability are shown in repeated operations (such as automobile welding and stacking and carrying) in a structured environment. However, the flexibility of movement is limited, and in complex scenes facing obstacle avoidance, joint limit avoidance or needing to simultaneously optimize multiple targets (such as energy consumption and movement smoothness), task completion and movement quality are often difficult to achieve, and even task failure is caused due to configuration constraint. The redundant mechanical arm gives the system a 'self-movement' capability in the kinematic layer by virtue of the extra degree of freedom, and can dynamically optimize the joint configuration to realize secondary targets such as obstacle avoidance, singular configuration avoidance, joint moment reduction or service life prolongation while ensuring the accurate tracking of the terminal pose. This property makes it an irreplaceable advantage in unstructured environments (e.g. narrow space surgical procedures, logistics grasping in dynamic obstacle environments). The redundancy also introduces the problem of infinite solution of inverse kinematics solution, and has higher requirements on a control algorithm, namely, not only the tracking precision of the tail end track is ensured, but also the redundancy freedom degree is reasonably distributed to realize multi-objective collaborative optimization. The two types of mechanical arms face common challenges in the control level, the existing main stream method (such as a calculation moment method and sliding mode control) highly depends on an accurate dynamic model, and the uncertainty of model parameters is caused by factors such as load change, friction nonlinearity, external disturbance and the like in an actual system, so that the control precision and the robustness are restricted. In addition, the traditional method often decouples the position and the gesture, and high-precision coordination tracking of pose integration is difficult to realize. For redundant mechanical arms, the above problems are further complicated—model errors not only affect tracking performance, but also may cause misdistribution of redundant degrees of freedom, and cause risks such as joint saturation or singular point crossing. The root of the above limitations is that the control paradigm based on an accurate model is difficult to accommodate for the dynamic uncertainty of the actual system. Under the background, the data-driven self-adaptive control method provides a unified optimization path for two types of mechanical arms, namely, the position and pose collaborative tracking can be realized without depending on accurate dynamic parameters by collecting motion feedback data of joints and tail ends in real time and dynamically estimating a composite jacobian mapping relation. For the redundant mechanical arm, the data driving mechanism can optimize the distribution strategy of the redundant degree of freedom on line, actively avoid joint limit and singular areas while tracking a main task, and fully release the motion potential of a redundant configuration. Therefore, the development does not depend on an accurate model, and has the data driving control method with high-precision tracking and dynamic optimizing capabilities, so that the adaptability of the non-redundant mechanical arm in a disturbance environment can be improved, the structural advantage of the re