提出模块化方法设计无人车极坐标下的稳定控制律
Modular Design of Strict Control Lyapunov Functions for Global Stabilization of the Unicycle in Polar Coordinates
- 采用模块化设计构建平滑反馈控制律，实现全局渐近稳定
- 控制律支持双向操作，提升泊车效率，收敛速率明确
- 适用于需要精确轨迹控制的移动机器人系统
自20世纪90年代以来，已知在极坐标系下，与笛卡尔坐标中布罗克特条件禁止静态反馈稳定不同，无人车可通过光滑反馈实现全局渐近稳定。本文提出一种模块化框架，用于设计在极坐标下实现全局渐近稳定的光滑反馈控制律。该控制律具备双向性，可高效完成泊车操作，并配套构造了模块化的严格控制李雅普诺夫函数（CLFs）。这些函数保证了全局渐近稳定性，并给出明确的收敛速率；还包含带有障碍项的变体，可实现“几乎全局”稳定，仅排除旋转流形上零测集。该严格性在后续论文中进一步用于设计逆最优重构，具有有意义的成本函数和无穷大增益裕度。
原文摘要 · Abstract (English)
Since the mid-1990s, it has been known that, unlike in Cartesian form where Brockett's condition rules out static feedback stabilization, the unicycle is globally asymptotically stabilizable by smooth feedback in polar coordinates. In this note, we introduce a modular framework for designing smooth feedback laws that achieve global asymptotic stabilization in polar coordinates. These laws are bidirectional, enabling efficient parking maneuvers, and are paired with families of strict control Lyapunov functions (CLFs) constructed in a modular fashion. The resulting CLFs guarantee global asymptotic stability with explicit convergence rates and include barrier variants that yield "almost global" stabilization, excluding only zero-measure subsets of the rotation manifolds. The strictness of the CLFs is further leveraged in our companion paper, where we develop inverse-optimal redesigns with meaningful cost functions and infinite gain margins.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。