CN-121973219-A - Mechanical arm track tracking control method integrating model prediction and synovial membrane control

Abstract

The invention provides a mechanical arm track tracking control method integrating model prediction and slide film control, which comprises the steps of constructing a discrete slide film controller, designing a discrete slide film surface based on track tracking errors, calculating a slide film control law, constructing a dynamics prediction model based on an echo state network, carrying out online learning and updating by taking historical state data of a mechanical arm and the slide film control law as inputs so as to predict a state track of the mechanical arm in a future time domain, constructing a model prediction controller embedded with the slide film control, introducing a prediction state and the slide film control law into an optimization objective function of the model prediction controller, converting an optimization problem into a quadratic programming problem under the model prediction controller, solving the quadratic programming problem, obtaining a smooth optimization control quantity meeting physical constraint, and acting the control quantity on a mechanical arm system. The invention effectively solves the problem of high-frequency buffeting of the sliding film control, and simultaneously ensures the high-precision track tracking of the mechanical arm under strong nonlinear interference.

Inventors

• WANG JUNSONG
• REN ZHONGXING

Assignees

• 深圳技术大学

Dates

Publication Date

20260505

Application Date

20260206

Claims (10)

1. 1. A mechanical arm track tracking control method integrating model prediction and synovial membrane control is characterized by comprising the following steps: Step S1, constructing a discrete synovial membrane controller, designing a discrete synovial membrane surface based on a track tracking error, and calculating a synovial membrane control law as a reference control input of a system; S2, constructing a dynamics prediction model based on an echo state network, and carrying out online learning and updating through sparse connection and dynamic memory characteristics of the echo state network by using historical state data and a synovial control law of the mechanical arm as inputs so as to predict a state track of the mechanical arm in a future time domain; step S3, constructing a model predictive controller embedded with the synovial membrane control, and introducing the predictive state obtained in the step S2 and the synovial membrane control law obtained in the step S1 into an optimization objective function of the model predictive controller; and S4, under a model predictive controller, considering joint angle and speed constraint of the mechanical arm, converting the optimization problem into a quadratic programming problem for solving, obtaining smooth optimization control quantity meeting physical constraint through rolling optimization, and applying the control quantity to the mechanical arm system.
2. 2. The method of claim 1, wherein in step S1, the slip film surface is discretized Is defined as the following formula: Wherein, the For a desired tip speed of the robotic arm at time k, In the form of a jacobian matrix, As the angle vector of the joint, In order to achieve the angular velocity of the joint, For the end position error of the mechanical arm at time k, Is a positive constant for adjusting the error convergence rate.
3. 3. The method of claim 2, wherein synovial control law The calculation formula is as follows: Wherein, the A pseudo-inverse matrix obtained for the damped least squares method, In order for the gain to be a function of, Is a saturation function.
4. 4. A method according to claim 3, characterized in that in step S2 the input vector of the echo state network Including the joint angle at the current moment And the synovial control law obtained in the step S1 I.e. ; Network pool state for echo state networks The recursive update formula of (2) is: Wherein, the For the moment of time Network pool state, parameters For determining the short-term memory capacity of the system, the leakage rate is used for determining the short-term memory capacity of the system; In order to input the weight matrix, Connecting weight matrix for the interior of the reserve pool for the state of the reserve pool at the previous moment Weighted, tanh is a hyperbolic tangent function as an activation function of reservoir conditions.
5. 5. The method according to claim 4, wherein: the output predictions of the echo state network are updated according to the following formula: Wherein, the At time for echo state network The predicted end position of the robot arm, And (3) for outputting a weight matrix, carrying out online real-time updating on the matrix by a recursive least square method so as to adapt to the time-varying nonlinear characteristic of the mechanical arm.
6. 6. The method according to claim 5, wherein in step S3, the model predicts an optimized objective function of the controller The structure is as follows: Wherein, the To predict the time domain, for defining the length of the future time range considered by the model predictive control, The predicted end-of-arm position for the echo state network, At the moment for the mechanical arm Is used to determine the desired trajectory of the object, The control input is predicted for the model to be optimized, For the slip film reference control amount, And A tracking error weight matrix and a control input bias weight matrix, respectively.
7. 7. The method of claim 6, wherein the optimization objective function is constrained by the following physical constraints: joint angle constraint: Wherein, the Is the minimum allowed by the joint angle of the mechanical arm, Is the maximum value allowed by the joint angle of the mechanical arm, The joint angle of the mechanical arm at time k+i.
8. 8. The method of claim 6, wherein the optimization objective function is constrained by the following physical constraints: Joint velocity constraint: Wherein, the Is the minimum allowable speed of the mechanical arm joint, Is the maximum value allowed by the joint speed of the mechanical arm, The joint speed of the mechanical arm at time k+i.
9. 9. The method according to claim 6, wherein: in step S4, the optimization problem is converted into a standard quadratic programming problem to be solved, where the optimization problem uses a minimized objective function as an optimization direction, and the expression of the objective function is: Wherein, the hessian matrix T is a matrix related to system dynamics and prediction time domain, linear term vector , A robot arm end position vector predicted for the echo state network, In order for the desired trajectory vector to be present, Referencing a control quantity vector for the synovial membrane, and simultaneously, uniformly expressing the constraint condition as a linear inequality constraint The constraint covers the joint angle constraint And joint velocity constraints 。
10. 10. The method according to any of claims 1 to 9, characterized in that for state recursion in a model predictive controller, an on-line jacobian matrix estimation strategy based on an echo state network is employed, comprising the steps and features of: by applying a small perturbation to the predicted joint angle using a trained echo state network Based on the input-output variation relationship, calculating an approximate jacobian matrix : Wherein F is% ) Representing a dynamics prediction model function based on the echo state network; Based on the calculated approximate jacobian matrix, a linearization prediction model is constructed in a prediction time domain, and the expression is as follows: Wherein, the For the future The predicted output sequence of steps is then used, For the control input sequence to be optimized, As an initial trajectory for the current state, Is a coefficient matrix consisting of a series of jacobian matrices.

Description

Mechanical arm track tracking control method integrating model prediction and synovial membrane control Technical Field The invention relates to the technical field of robot control, in particular to a mechanical arm track tracking control method integrating model prediction and synovial membrane control, aiming at improving track tracking precision and robustness of a mechanical arm in a complex dynamic environment and meeting capacity of physical constraint on joints. Background With the rapid development of industrial automation, precision manufacturing and intelligent robot technology, the mechanical arm is widely applied to high-end fields such as aerospace operation, precision assembly, medical operation and man-machine cooperation. In these high-precision application scenarios, the robotic arm system is required to have high-precision trajectory tracking capabilities in the millimeter level and even sub-millimeter level, but must also remain extremely robust against external disturbances, load variations, and unmodeled dynamics. However, the mechanical arm is essentially a multiple-input multiple-output system with strong nonlinearity, strong coupling, time-varying characteristics, and often faces extremely complex dynamics challenges in its practical operation. At present, the Control method for tracking the track of the mechanical arm mainly comprises traditional methods such as inverse kinematics Control (INVERSE KINEMATIC Control, IKC), model predictive Control (Model Predictive Control, MPC), synovial membrane Control (Sliding Mode Control, SMC) and the like, but the methods have obvious limitations in practical application: 1. Inverse kinematics control, which is capable of resolving joint angles based on a geometric model, generally operates in an open loop manner ignoring dynamic characteristics such as inertia, coriolis force, friction force, etc., and once the system is subject to external dynamic disturbance or has parameter uncertainty, the accumulated error increases rapidly due to lack of real-time dynamic feedback compensation. 2. Model predictive control, namely, although the physical constraint of a multivariable system can be explicitly processed and rolling optimization is carried out, the performance of the model predictive control is highly dependent on the precision of a predictive model, and when a strong nonlinear mechanical arm system is processed, linear processing such as traditional Taylor expansion and the like can cause exponential amplification of a long-time domain prediction error, and the model predictive control is difficult to adapt to complex geometric structures or unknown environmental disturbance. 3. While the synovial membrane control has excellent robustness to invariance of perturbation and disturbance, the inherent discontinuous switching gain of the synovial membrane control can cause high-frequency buffeting, so that not only is track smoothness reduced, but also mechanical abrasion of an actuator can be aggravated, and even unsteady system caused by excitation of unmodeled high-frequency dynamics is caused. In order to achieve both robustness and tracking accuracy, attempts have been made in the prior art to use a composite control strategy that combines MPC with SMC, such as a neural network-based MPC or a method that combines SMC as a disturbance observer with MPC. However, these existing complex control methods still have core technical pain points. First, most compounding methods employ a "decoupled" or "series" architecture, i.e., directly superimposing the SMC compensation terms on an MPC optimization control law basis, which structural mismatch results in the total control input ultimately applied to the robotic arm often exceeding the MPC set constraint boundaries, causing actuator saturation or system failure. Secondly, the method of replacing the symbol function with a saturated function or a continuous approximation law for alleviating buffeting often comes at the expense of limited time convergence characteristics and noise immunity of the SMC, and the contradiction between buffeting inhibition and robustness maintenance cannot be fundamentally solved. In addition, the existing data driving control method mostly adopts an offline training mode, and when the mechanical arm grabs different weight loads to cause working condition change, the model cannot be updated in real time, and prediction distortion is easy to occur. Therefore, it is needed to develop a novel mechanical arm track tracking control method capable of embedding the robustness depth of the synovial membrane control into the optimization framework of the model predictive control and combining the online learning capability to adapt to the time-varying nonlinear characteristic, so as to solve the problems of buffeting inhibition, full constraint satisfaction and insufficient dynamic modeling precision. Disclosure of Invention The invention aims to solve the core technical problems