提出模块化控制框架，实现非完整机器人定点停靠的稳定控制。
Nonholonomic Robot Parking by Feedback -- Part I: Modular Strict CLF Designs
- 通过解耦径向坐标，独立设计转向子系统控制律。
- 构建严格控制李雅普诺夫函数，支持全局渐近稳定与角度约束。
- 适用于需精确轨迹跟踪的移动机器人控制场景。
自1995年以来，机器人学界已知在极坐标下，非完整单轮机器人可通过光滑反馈实现全局渐近稳定。本文提出一种模块化设计框架，通过选择前进速度解耦径向坐标，使转向子系统可独立稳定。在此结构内，我们基于无源性、反步法和积分前馈技术，设计多类反馈律，并配套严格控制李雅普诺夫函数（strict CLF），包括施加角度约束的障碍物变体。这些严格CLF提供构造性类KL收敛估计，并可在目标平衡点实现特征值分配。该框架推广并拓展了先前的模块化与非模块化方法，为后续论文中的逆最优与自适应重构奠定基础。
原文摘要 · Abstract (English)
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.
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