Nonholonomic Robot Parking by Feedback -- Part I: Modular Strict CLF Designs

TL;DR

This paper introduces a modular feedback control framework for nonholonomic robot parking, utilizing strict control Lyapunov functions to ensure stability, convergence, and constraint enforcement, advancing prior methods with new design strategies.

Contribution

It presents a novel modular design approach for stabilizing nonholonomic robots using strict CLFs, incorporating barrier functions and enabling eigenvalue assignment.

Findings

Developed families of feedback laws using passivity, backstepping, and integrator forwarding.

Provided constructive convergence estimates and eigenvalue assignment capabilities.

Extended prior approaches with a modular framework for nonholonomic stabilization.

Abstract

It has been known in the robotics literature since about 1995 that, in polar coordinates, the nonholonomic unicycle is asymptotically stabilizable by smooth feedback, even globally. We introduce a modular design framework that selects the forward velocity to decouple the radial coordinate, allowing the steering subsystem to be stabilized independently. Within this structure, we develop families of feedback laws using passivity, backstepping, and integrator forwarding. Each law is accompanied by a strict control Lyapunov function, including barrier variants that enforce angular constraints. These strict CLFs provide constructive class KL convergence estimates and enable eigenvalue assignment at the target equilibrium. The framework generalizes and extends prior modular and nonmodular approaches, while preparing the ground for inverse optimal and adaptive redesigns in the sequel paper.