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Model Predictive Control For Mobile Manipulators Based On Neural Dynamics(Extended version)

Tao Su, Shiqi Zheng

TL;DR

The paper addresses trajectory tracking for mobile manipulators subjected to disturbances from base motion. It combines a position-and-orientation model predictive tracking control (POMPTC) with a finite-time convergent neural dynamics (FTCND) solver and an NFTSM controller to achieve synchronous end-effector pose tracking under dynamic disturbances. The POMPTC is cast as a convex optimization over velocity increments with a multi-term objective and joint constraints, while FTCND provides finite-time convergence via a Li-function-based activation and a slack-variable reformulation, with a theoretical convergence bound $t_f \le \frac{2|h_{max}(0)|^{1-\\kappa}}{\\mu(1-\\kappa)}$. NFTSM compensates base-induced disturbances at the dynamic level and guarantees finite-time convergence without singularities. Simulations and experiments demonstrate fast convergence, high accuracy (end-effector errors around $0.01$ m and $0.01$ rad) and strong robustness to base motion.

Abstract

This article focuses on the trajectory tracking problem of mobile manipulators (MMs). Firstly, we construct a position and orientation model predictive tracking control (POMPTC) scheme for mobile manipulators. The proposed POMPTC scheme can simultaneously minimize the tracking error, joint velocity, and joint acceleration. Moreover, it can achieve synchronous control for the position and orientation of the end-effector. Secondly, a finite-time convergent neural dynamics (FTCND) model is constructed to find the optimal solution of the POMPTC scheme. Then, based on the proposed POMPTC scheme, a non-singular fast terminal sliding model (NFTSM) control method is presented, which considers the disturbances caused by the base motion on the manipulator at the dynamic level. It can achieve finite-time tracking performance and improve the anti-disturbances ability. Finally, simulation and experiments show that the proposed control method has the advantages of strong robustness, fast convergence, and high control accuracy.

Model Predictive Control For Mobile Manipulators Based On Neural Dynamics(Extended version)

TL;DR

The paper addresses trajectory tracking for mobile manipulators subjected to disturbances from base motion. It combines a position-and-orientation model predictive tracking control (POMPTC) with a finite-time convergent neural dynamics (FTCND) solver and an NFTSM controller to achieve synchronous end-effector pose tracking under dynamic disturbances. The POMPTC is cast as a convex optimization over velocity increments with a multi-term objective and joint constraints, while FTCND provides finite-time convergence via a Li-function-based activation and a slack-variable reformulation, with a theoretical convergence bound . NFTSM compensates base-induced disturbances at the dynamic level and guarantees finite-time convergence without singularities. Simulations and experiments demonstrate fast convergence, high accuracy (end-effector errors around m and rad) and strong robustness to base motion.

Abstract

This article focuses on the trajectory tracking problem of mobile manipulators (MMs). Firstly, we construct a position and orientation model predictive tracking control (POMPTC) scheme for mobile manipulators. The proposed POMPTC scheme can simultaneously minimize the tracking error, joint velocity, and joint acceleration. Moreover, it can achieve synchronous control for the position and orientation of the end-effector. Secondly, a finite-time convergent neural dynamics (FTCND) model is constructed to find the optimal solution of the POMPTC scheme. Then, based on the proposed POMPTC scheme, a non-singular fast terminal sliding model (NFTSM) control method is presented, which considers the disturbances caused by the base motion on the manipulator at the dynamic level. It can achieve finite-time tracking performance and improve the anti-disturbances ability. Finally, simulation and experiments show that the proposed control method has the advantages of strong robustness, fast convergence, and high control accuracy.
Paper Structure (15 sections, 3 theorems, 44 equations, 8 figures, 2 tables)

This paper contains 15 sections, 3 theorems, 44 equations, 8 figures, 2 tables.

Table of Contents

  1. Introduction
  2. MODELING AND PROBLEM FORMULATION
  3. Kinematic Modeling
  4. Dynamic Modeling
  5. MOTION CONTROL DESIGN
  6. POMPTC Design
  7. FTCND Model Construction
  8. NFTSM CONTROLLER DESIGN
  9. SIMULATIONS AND EXPERIMENTS
  10. Simulations
  11. Experiments
  12. CONCLUSION
  13. FINITE-TIME STABILITY ANALYSIS
  14. STABILITY ANALYSIS
  15. JOINT CONSTRAINTS

Key Result

Theorem 1

Under the designed NFTSM surface given by eq25, in order to ensure that the system error state $\widetilde{q}_1$ converges to zero, the following control law needs to be designed:

Figures (8)

  • Figure 1: Kinematics analysis of MMs
  • Figure 2: MMs Simulation Model
  • Figure 3: The simulation results show that the NFTSM algorithm combined with POMPTC strategy tracks the circular trajectory. (a) Three-dimensional desired trajectory and actual trajectory. (b) Two-dimensional actual trajectory and desired trajectory. (c) Position error of the end-effector. (d) Joint angle of the manipulator. (e) Joint velocity of the manipulator. (f) Joint torque. (g) Actual and desired rotation vector. (h) The errors of the rotation vector.
  • Figure 4: End position and rotation error of redundant manipulator under different motion control algorithms.
  • Figure 5: End position error of redundant manipulator under different control algorithms
  • ...and 3 more figures

Theorems & Definitions (4)

  • Theorem 1
  • Remark 1
  • Theorem 2
  • Theorem 3