In a companion paper, we present a modular framework for unicycle stabilization in polar coordinates that provides smooth steering laws through backstepping. Surprisingly, the same problem also allows the application of integrator forwarding. In this work, we leverage this feature and construct new smooth steering laws together with control Lyapunov functions (CLFs), expanding the set of CLFs available for inverse optimal control design. In the case of constant forward velocity (Dubins car), backstepping produces finite-time (deadbeat) parking, and we show that integrator forwarding yields the very same class of solutions. This reveals a fundamental connection between backstepping and forwarding in addressing both the unicycle and, the Dubins car parking problems.

翻译：在配套论文中，我们提出了一种极坐标下单轮车镇定问题的模块化框架，该框架通过反步法提供了平滑的转向律。令人惊讶的是，同一问题也允许应用积分器前馈方法。在本工作中，我们利用这一特性，构建了新的平滑转向律以及控制李雅普诺夫函数（CLFs），从而扩展了可用于逆最优控制设计的CLFs集合。在恒定前向速度（Dubins车）的情况下，反步法产生有限时间（无差拍）泊车，而我们证明积分器前馈方法可产生完全相同的解类。这揭示了在解决单轮车及Dubins车泊车问题时，反步法与积分器前馈方法之间存在的基本联系。