Safety-Critical Stabilization of Force-Controlled Nonholonomic Mobile Robots

TL;DR

This paper introduces a safety-critical control approach for force-controlled nonholonomic mobile robots, combining Lyapunov and barrier functions to ensure stability and safety in a continuous, implementable manner.

Contribution

It develops a novel control law using CLFs and CBFs for cascaded systems, addressing nonholonomicity and safety in a unified, practical framework.

Findings

Guarantees safety and stability of the robot system.

Employs quadratic programming to integrate stability and safety.

Ensures the control law is time-invariant and continuous.

Abstract

We present a safety-critical controller for the problem of stabilization for force-controlled nonholonomic mobile robots. The proposed control law is based on the constructions of control Lyapunov functions (CLFs) and control barrier functions (CBFs) for cascaded systems. To address nonholonomicity, we design the nominal controller that guarantees global asymptotic stability and local exponential stability for the closed-loop system in polar coordinates and construct a strict Lyapunov function valid on any compact sets. Furthermore, we present a procedure for constructing CBFs for cascaded systems, utilizing the CBF of the kinematic model through integrator backstepping. Quadratic programming is employed to combine CLFs and CBFs to integrate both stability and safety in the closed loop. The proposed control law is time-invariant, continuous along trajectories, and easy to implement. Our main results guarantee both safety and local asymptotic stability for the closed-loop system.