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.

翻译：自1995年左右起，机器人学文献已表明，在极坐标系下，非完整独轮车模型可通过光滑反馈实现渐近稳定（甚至全局稳定）。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，使得转向子系统可被独立镇定。在此框架内，我们基于无源性、反步法和积分前推法构建了反馈控制律族。每个控制律均配有严格控制李雅普诺夫函数，其中包含可强化角度约束的屏障函数变体。这些严格控制李雅普诺夫函数提供了构造性的KL类收敛估计，并支持在目标平衡点处进行特征值配置。该框架推广并扩展了先前的模块化与非模块化方法，同时为后续论文中的逆最优与自适应重构设计奠定了基础。