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

2025-11-19

AI Summary

This paper addresses the asymptotic stabilization and parking problem for nonholonomic unicyclic robots (e.g., monowheels) in polar coordinates. To decouple radial and angular dynamics, a modular feedback control framework is proposed based on polar coordinate transformation, enabling independent stabilization of the steering subsystem. The core contribution is a novel modular design architecture grounded in strict control Lyapunov functions (SCLFs), which facilitates KL-class convergence rate estimation, eigenvalue placement at equilibria, and barrier function extension under angular constraints. By integrating passivity-based control, backstepping, integral feedforward, and SCLF construction techniques, the resulting family of control laws achieves global asymptotic stability, smoothness, and satisfaction of dynamic constraints. The framework provides a rigorous foundation for extensions to inverse-optimal and adaptive control.

Technology Category

• Intelligent Robots: Behavior Learning & Control
• Natural Language Processing: Safety and Robustness
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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.

Problem

• Stabilizing nonholonomic unicycle robots using smooth feedback control
• Developing modular feedback designs with strict Lyapunov functions
• Enforcing angular constraints while achieving global asymptotic stabilization

Innovation

• Modular design framework decouples radial coordinate
• Feedback laws use passivity backstepping integrator forwarding
• Strict control Lyapunov functions enforce angular constraints