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Vector-field guided constraint-following control for path following of uncertain mechanical systems

Hui Yin, Xiang Li, Yifan Liu, Weijia Yao

Abstract

This note proposes a general control approach, called vector-field guided constraint-following control, to solve the dynamics control problem of geometric path-following for a class of uncertain mechanical systems. More specifically, it operates at the dynamics level and can handle both fully-actuated and underactuated mechanical systems, heterogeneous (possibly fast) time-varying uncertainties with unknown bounds, and geometric desired paths that may be self-intersecting. Simulations are conducted to demonstrate the effectiveness of the approach.

Vector-field guided constraint-following control for path following of uncertain mechanical systems

Abstract

This note proposes a general control approach, called vector-field guided constraint-following control, to solve the dynamics control problem of geometric path-following for a class of uncertain mechanical systems. More specifically, it operates at the dynamics level and can handle both fully-actuated and underactuated mechanical systems, heterogeneous (possibly fast) time-varying uncertainties with unknown bounds, and geometric desired paths that may be self-intersecting. Simulations are conducted to demonstrate the effectiveness of the approach.
Paper Structure (20 sections, 2 theorems, 82 equations, 10 figures)

This paper contains 20 sections, 2 theorems, 82 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Preliminaries and problem formulation
  3. Uncertain mechanical systems
  4. Constraint-following control
  5. Guiding vector field
  6. GVF in $\mathbb{R}^2$ for non-self-intersecting desired path
  7. General singularity-free GVF
  8. Problem formulation
  9. Problem statement
  10. Motivated solution strategy
  11. Main results
  12. Vector-field guided constraint
  13. Error analysis
  14. Vanishing disturbance
  15. Non-vanishing but bounded disturbance
  16. ...and 5 more sections

Key Result

Theorem 1

Under Assumptions assump2 and assump_tau2, the path-following control nominal drives the trajectory of the nominal mechanical system nominalsystem to converge to the desired path mdpath4sys, i.e., the path-following error satisfies that ${\rm dist}(\zeta(t), \mathcal{P})\to 0$ as $t\to\infty$.

Figures (10)

  • Figure 1: These are three $\tau$
  • Figure 2: These are three $\tau$
  • Figure 3: NVFCFC and IIOS of the nominal PVTOL aircraft system.
  • Figure 4: These are three $\tau$
  • Figure 5: x.
  • ...and 5 more figures

Theorems & Definitions (19)

  • Remark 1
  • Definition 1: constraint-following for dynamical systems
  • Definition 2: constraint-following for mechanical systems
  • Definition 3: CFC for mechanical systems
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5
  • Remark 6
  • Remark 7
  • ...and 9 more