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CN-116175585-B - UDE control method for multi-joint mechanical arm with input saturation and output constraint

CN116175585BCN 116175585 BCN116175585 BCN 116175585BCN-116175585-B

Abstract

The invention discloses a multi-joint mechanical arm UDE control method with input saturation and output constraint, which comprises the specific steps of (1) establishing a multi-joint mechanical arm dynamics model with input saturation and time-varying output constraint in joint space, (2) converting the dynamics model obtained in the step (1) by using a jacobian matrix of the mechanical arm to obtain the multi-joint mechanical arm dynamics model in task space, and (3) designing a nonlinear state constraint function to ensure that the time-varying output constraint is not violated. (4) Designing a UDE for approximating an unknown item of mechanical arm dynamics, (5) defining a tracking error signal, and (6) designing a stable track tracking controller based on the UDE aiming at a mechanical arm system under a task space by combining a back-stepping method. The invention can realize accurate track tracking of the mechanical arm under the conditions of modeling error, input saturation and time-varying output constraint, and ensure the satisfaction of the input saturation and time-varying output constraint.

Inventors

  • WU YUXIANG
  • Wan Fuxi

Assignees

  • 华南理工大学

Dates

Publication Date
20260508
Application Date
20230315

Claims (8)

  1. 1. The method for controlling the UDE of the multi-joint mechanical arm with input saturation and output constraint is characterized by comprising the following specific steps: (1) Establishing a multi-joint mechanical arm dynamics model with input saturation and time-varying output constraint in joint space; (2) Converting the dynamics model obtained in the step (1) by using a jacobian matrix of the mechanical arm to obtain a multi-joint mechanical arm dynamics model in a task space; (3) Establishing a nonlinear state constraint function to ensure that the time-varying output constraint is not violated; Nonlinear state constraint function vector And Expressed as: Wherein, the And (3) with Respectively represent And (3) with In the item i of (c), Indicating that a positive constant needs to be set, Representation of In the item i of (c), Representing a desired motion profile of the end effector of the robotic arm, Representation of In the item i of (c), Representing the position of the robotic arm end effector; (4) Establishing an uncertainty item and interference estimator UDE for approximating a mechanical arm dynamics unknown item; Laplacian function matrix of uncertainty term and interference estimator UDE Expressed as: Wherein, the Representation of The i-th element on the diagonal line, Representing the complex frequency of the signal, Indicating a time constant to be set; (5) Defining a tracking error signal; (6) And combining a back-stepping method, and establishing a stable UDE-based track tracking controller aiming at the mechanical arm system in the task space.
  2. 2. The method of claim 1, wherein in step (1), the multi-joint mechanical arm dynamics model under the input saturation and time-varying output constraint is a mechanical arm dynamics model with strong nonlinear coupling, expressed as: Wherein, the Respectively representing angular displacement, angular velocity and angular acceleration; representing an inertia matrix of the device, Representing a matrix of the centripetal forces, The vector of the universal gravitation is expressed, Representing the input torque vector of the vehicle, Representation of In the item i of (c), Representing the input torque saturation function vector, Representation of In the item i of (c), Representing disturbance terms from humans and the outside; representing the number of joints of a rigid mechanical arm with time-varying output constraints, Representing the dimensions of the robot arm task space, Respectively an inertia matrix, a centripetal force matrix and an unknown part of universal gravitation, Respectively an inertia matrix, a centripetal force matrix and a known part of the gravitational force.
  3. 3. The method for controlling a UDE of a multi-joint mechanical arm with input saturation and output constraint of claim 2, wherein an input moment saturation function vector is established Any one of them The expression is as follows: Wherein, the Is a standard sign function, known as positive number Is that Is defined in the specification.
  4. 4. A method according to claim 2 having input saturation a method for controlling a UDE of an articulated mechanical arm constrained by output, characterized in that in the step (2), a jacobian matrix is used Is combined with Converting the dynamics model obtained in the step (1) to obtain a multi-joint mechanical arm dynamics model in a task space, wherein the multi-joint mechanical arm dynamics model is expressed as follows: Wherein, the Respectively representing the position, the speed and the acceleration of the end effector of the mechanical arm; represents angular velocity; , , Unknown item ; A derivative matrix representing the jacobian matrix, Representing the pseudo-inverse of the jacobian matrix.
  5. 5. The method of controlling a multi-joint manipulator UDE with input saturation and output constraints of claim 1, wherein the time-varying output constraints of the manipulator are expressed as: Wherein, the And (3) with Respectively outputs to the mechanical arm Lower bound and upper bound of (2).
  6. 6. The method for controlling the UDE of the multi-joint mechanical arm with input saturation and output constraint according to claim 1, wherein the nonlinear state constraint function satisfies the property of satisfying an initial value of time-varying output constraint for any If and only if Upper bound for approximating time-varying output constraints Or lower bound of In the time-course of which the first and second contact surfaces, Will approach infinity, i.e. as long as Bounded, it can be ensured that the time-varying output constraint is not violated.
  7. 7. A method according to claim 1 having input saturation a method for controlling a UDE of an articulated mechanical arm constrained by output, characterized in that the uncertainty item and interference estimator UDE is a filter for a frequency of Is used for the input signal of the (a), , In imaginary units, the amplitude gain is: theoretically, the smaller the time constant, the closer the amplitude gain is to 1, i.e., the higher the accuracy of approximation.
  8. 8. The method for controlling the UDE of the multi-joint mechanical arm with input saturation and output constraint of claim 1, wherein the time constant is The selection mode of (2) is as follows: at a time constant In the range of the value of (1), firstly, a time constant is set For the value near the upper limit of the value range, verifying whether the control precision of the system meets the requirement, if so, stopping the selection, if not, continuing to reduce Is adaptively set.

Description

UDE control method for multi-joint mechanical arm with input saturation and output constraint Technical Field The invention relates to the field of automation, in particular to a UDE control method for an articulated mechanical arm with input saturation and output constraint. Background The rapid development of science and technology provides assistance for further application and popularization of mechanical arms, and the multi-joint mechanical arm is the most widely applied automatic mechanical equipment and has wide application in the fields of industrial manufacture, military, medical treatment, entertainment, space exploration and the like. In practical applications, there are various constraints on the robotic arm control system, such as input saturation, limited task space, limited speed, etc. Once these constraints are violated, it may lead to degradation in the performance of the robotic system, even damage to the system and threat to the safety of the personnel associated with the robotic system. With further development of technology, the concept of human-computer interaction is proposed, and more robots will work at the side of human beings in the future, so that the design controller for the mechanical arm system with specified constraint has important theoretical significance and practical application value. However, in most of the current researches, the stability and control accuracy of the robot system are mainly studied, and the design of the controller considering input saturation and time-varying output constraint is insufficient. By adopting the existing recursive design method, most of research results only solve the problem of mechanical arm control with constant output constraint, and the upper and lower bounds of limited output are generally set to be loose, so that the algorithm conservation is increased, and meanwhile, the algorithm practicability is limited. The multi-joint mechanical arm is used as a time-varying, coupled multi-input and multi-output complex nonlinear system, motion control and complexity thereof are realized, and parameters of the mechanical arm are often unknown or have larger errors in parameter measurement in the actual control design process, so that a controller design tool aiming at an unknown parameter model is needed. The UDE approximates an unknown kinetic model of the mechanical arm system and external interference through a filter, so that the purpose of accurate control can be achieved under the condition that unknown parameters exist in the system. A control algorithm based on UDE is provided (Y.Dong and B.Ren,"UDE-Based variable impedance control of uncertain robot systems,"IEEETrans.Syst.ManCybernet.Syst.49(12),2487–2498(2019)). for a variable impedance control algorithm under the condition of model uncertainty of a multi-joint mechanical arm system, the algorithm is helpful for the mechanical arm to complete given interaction tasks under an unknown environment, the overall performance of the robot environment system is improved, and when the uncertainty item of the UDE approximation system is used, only bandwidth information of the system is needed to be known. However, the above algorithm achieves better control, but does not take into account input saturation and output constraint issues. Based on neural network theory, considering input dead zone, an adaptive neural network algorithm for an uncertain multi-joint mechanical arm is proposed (Q.Zhou,S.Zhao,H.Li,R.Lu and C.Wu,"Adaptive neural network tracking control for robotic manipulators with deadzone,"IEEE Trans.Neural Netw.Learn.Syst.30(12),3611–3620(2019))., and the algorithm ensures the stability of the mechanical arm system and obtains better control performance by designing an adaptive neural network controller. In the algorithm, the neural network is used for approximating the uncertain term of the mechanical arm, and the approximation effect is good, but as the joint number of the mechanical arm increases, the calculation amount of the neural network is huge, and the requirement on hardware is high. Compared with a neural network, the UDE used by the method is simpler in design, easy to realize, fewer in parameters required to be designed and less in calculated amount. Along with the increase of man-machine cooperation scenes, constraint control is important to ensure the safety of operators. In order to solve the input saturation and output constraint problems, a great deal of research has been conducted. Aiming at the mechanical arm with input constraint, a mechanical arm model prediction control method based on a neural network is provided (E.Kang,H.Qiao,J.Gao and W.Yang,"Neural network-based model predictive tracking control of an uncertain robotic manipulator with input constraints,"ISA Trans.109(3),89–101(2021)), and a non-quadratic cost function is introduced to solve the input constraint. Based on the neural network theory, a mechanical arm fixed time control method is propose