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Further Results on Safety-Critical Stabilization of Force-Controlled Nonholonomic Mobile Robots

Bo Wang, Tianyu Han, Guangwei Wang

TL;DR

This work tackles safety-critical stabilization of force-controlled nonholonomic mobile robots by unifying stability and safety through a $\gamma m$-QP framework. It introduces a global, time-invariant strict Lyapunov function for the full kinematic–dynamic model using a nominal stabilization controller in polar coordinates, and constructs a cascaded zeroing CBF via integrator backstepping for the safety constraints. The resulting control law guarantees forward invariance of the safety set and asymptotic stability of the origin under appropriate parameter choices, with both simulations and real experiments (parking with obstacle avoidance) validating the approach. The framework advances practical safety-critical control for nonholonomic platforms and lays groundwork for extensions to multi-agent safety formation and robustness analyses, including handling input saturation.

Abstract

In this paper, we address the stabilization problem for force-controlled nonholonomic mobile robots under safety-critical constraints. We propose a continuous, time-invariant control law based on the gamma m-quadratic programming (gamma m-QP) framework, which unifies control Lyapunov functions (CLFs) and control barrier functions (CBFs) to enforce both stability and safety in the closed-loop system. For the first time, we construct a global, time-invariant, strict Lyapunov function for the closed-loop nonholonomic mobile robot full-dynamic system with a nominal stabilization controller in polar coordinates; this strict Lyapunov function then serves as the CLF in the QP design. Next, by exploiting the inherent cascaded structure of the vehicle dynamics, we develop a CBF for the mobile robot via an integrator backstepping procedure. Our main results guarantee both asymptotic stability and safety for the closed-loop system. Both the simulation and experimental results are presented to illustrate the effectiveness and performance of our approach.

Further Results on Safety-Critical Stabilization of Force-Controlled Nonholonomic Mobile Robots

TL;DR

This work tackles safety-critical stabilization of force-controlled nonholonomic mobile robots by unifying stability and safety through a -QP framework. It introduces a global, time-invariant strict Lyapunov function for the full kinematic–dynamic model using a nominal stabilization controller in polar coordinates, and constructs a cascaded zeroing CBF via integrator backstepping for the safety constraints. The resulting control law guarantees forward invariance of the safety set and asymptotic stability of the origin under appropriate parameter choices, with both simulations and real experiments (parking with obstacle avoidance) validating the approach. The framework advances practical safety-critical control for nonholonomic platforms and lays groundwork for extensions to multi-agent safety formation and robustness analyses, including handling input saturation.

Abstract

In this paper, we address the stabilization problem for force-controlled nonholonomic mobile robots under safety-critical constraints. We propose a continuous, time-invariant control law based on the gamma m-quadratic programming (gamma m-QP) framework, which unifies control Lyapunov functions (CLFs) and control barrier functions (CBFs) to enforce both stability and safety in the closed-loop system. For the first time, we construct a global, time-invariant, strict Lyapunov function for the closed-loop nonholonomic mobile robot full-dynamic system with a nominal stabilization controller in polar coordinates; this strict Lyapunov function then serves as the CLF in the QP design. Next, by exploiting the inherent cascaded structure of the vehicle dynamics, we develop a CBF for the mobile robot via an integrator backstepping procedure. Our main results guarantee both asymptotic stability and safety for the closed-loop system. Both the simulation and experimental results are presented to illustrate the effectiveness and performance of our approach.
Paper Structure (11 sections, 4 theorems, 40 equations, 5 figures)

This paper contains 11 sections, 4 theorems, 40 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Preliminaries on Safety-Critical Control
  3. Problem Formulation and Main Results
  4. Construction of the global CLF
  5. Construction of the CBF
  6. Safety-Critical Control Design
  7. Simulation and Experimental Results
  8. Simulation Results
  9. Experimental Results
  10. Conclusions
  11. Proof of Proposition \ref{['prop:1']}

Key Result

Proposition 1

Consider the mobile robot system eq:kinematics and eq:dynamics. Then, there exists a constant $\bar{\mu}>0$ such that for all $\mu\in(0,\bar{\mu}]$, the function $V:\mathbb{R}_{>0}\times\mathbb{R}^4\to \mathbb{R}_{\ge 0}$, defined as is a global CLF for eq:kinematics and eq:dynamics that satisfies the small control property, where $\tilde{v}:=v-v^*$, $\tilde{\omega}:=\omega-\omega^*$, $z:={\tilde

Figures (5)

  • Figure 1: Simulation paths of the robot in the XY plane.
  • Figure 2: Simulation trajectories of the robot in polar coordinates.
  • Figure 3: Experimental system framework.
  • Figure 4: Paths of the robot in the XY plane.
  • Figure 5: Trajectories of the robot in polar coordinates.

Theorems & Definitions (13)

  • Definition 1: CBF
  • Proposition 1: Global CLF
  • proof
  • Remark 1
  • Remark 2
  • Remark 3
  • Proposition 2: CBF
  • proof
  • Remark 4
  • Theorem 1
  • ...and 3 more