用极坐标设计新控制算法，让汽车自动停得像人一样自然。
Global Exponential Stabilization of the Kinematic Bicycle Model of a Car in Polar Coordinates
- 将车辆模型转到极坐标系，避开传统方法的理论限制。
- 提出光滑反馈控制律，实现全局指数稳定与真实泊车轨迹。
- 适合自动驾驶泊车系统研发，尤其关注轨迹自然性的人类行为模拟。
在停车速度下，运动学自行车模型是类车车辆的主流模型。然而，尽管应用广泛，该系统的稳定反馈控制律仍很稀缺，现有设计往往无法复现真实的泊车动作。这一局限源于笛卡尔坐标系下的布罗克特条件，导致平滑静态反馈无法实现稳定。本文通过将系统转换至极坐标，并引入额外的归一化距离坐标以编码类人泊车几何特征，使动力学呈现严格反馈形式，从而采用非传统反步法设计。利用该结构，我们开发出在变换坐标系下实现全局指数稳定的光滑反馈律，进而仅通过反馈生成与人类司机操作相似的泊车轨迹。
原文摘要 · Abstract (English)
At parking speeds, the kinematic bicycle is the prevailing model for car-like vehicles. Yet, despite its wide use, stabilizing feedback laws for this system are scarce in the literature, and existing designs often do not reproduce realistic parking maneuvers. This limitation is inherent to the Cartesian coordinates, where Brockett's condition rules out smooth static feedback stabilization. We bypass this obstruction by transforming the system into polar coordinates together with additional range-normalized coordinates that encode the geometry of human-like parking maneuvers. In the transformed coordinates, the dynamics take a strict-feedback form, enabling a nonconventional backstepping design. We exploit the particular structure to develop smooth feedback laws that achieve global exponential stabilization in the transformed coordinates which in turn generates parking trajectories resembling the one performed by human drivers through feedback alone.
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