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A Stabilizing NMPC Strategy for a Class of Nonholonomic Systems with Drift

Huu Thien Nguyen, Fernando A. C. C. Fontes, Ionela Prodan

Abstract

In this paper, we present a stabilizing Nonlinear Model Predictive Control (NMPC) scheme tailored for a class of nonholonomic systems with drift, where the acceleration is laterally restrained. Examples include a mobile robot with drifting wheels on a planar surface or a spacecraft maneuvering in a vacuum. The novelty lies in the formulation of the terminal set, reachable from a significant distance from the equilibrium, and the terminal cost, represented as the integration of the stage cost. The proposed approach establishes essential steps for ensuring stability and feasibility guarantees. Simulation results substantiate the viability and effectiveness of the NMPC scheme.

A Stabilizing NMPC Strategy for a Class of Nonholonomic Systems with Drift

Abstract

In this paper, we present a stabilizing Nonlinear Model Predictive Control (NMPC) scheme tailored for a class of nonholonomic systems with drift, where the acceleration is laterally restrained. Examples include a mobile robot with drifting wheels on a planar surface or a spacecraft maneuvering in a vacuum. The novelty lies in the formulation of the terminal set, reachable from a significant distance from the equilibrium, and the terminal cost, represented as the integration of the stage cost. The proposed approach establishes essential steps for ensuring stability and feasibility guarantees. Simulation results substantiate the viability and effectiveness of the NMPC scheme.
Paper Structure (13 sections, 3 theorems, 47 equations, 9 figures, 1 algorithm)

This paper contains 13 sections, 3 theorems, 47 equations, 9 figures, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. SPACECRAFT MODEL
  3. AUXILIARY CONTROL STRATEGIES
  4. NMPC FRAMEWORK
  5. Explicit expression for the terminal cost
  6. Stability analysis
  7. SIMULATIONS
  8. Initial forward simulation
  9. NMPC simulation
  10. CONCLUSIONS AND FUTURE WORKS
  11. Steps to calculate the terminal cost
  12. Explicit time derivative of the terminal cost
  13. Auxiliary controller analysis when the spacecraft pointing away from the origin

Key Result

Lemma IV.1

The time stamps $t_1$, $t_2$, and $t_3$ in the auxiliary strategy AC_2--AC_3 when starting from $(r,V)=(r_{t_f}, V_{t_f})$ are calculated as follows:

Figures (9)

  • Figure 1: Spacecraft with an arbitrary pitch angle $\theta$ (left) and when its velocity vector $\bm{V}$ and its vertical axis $x^\mathcal{B}$ point to the origin (right).
  • Figure 2: Proposed auxiliary stabilizing controller and states.
  • Figure 3: The spacecraft when it is inside the terminal set $\mathcal{X}_f$ and points to the origin.
  • Figure 4: The auxiliary stabilizing controller AC and states inside the terminal set.
  • Figure 5: Simulation results for the spacecraft with the auxiliary controller, starting at $(x_0,z_0)=(-4,4)$.
  • ...and 4 more figures

Theorems & Definitions (5)

  • Lemma IV.1
  • Remark 1
  • Proposition IV.2
  • Theorem IV.3
  • Remark 2