用几何映射让机器人在复杂环境里安全避障，还能保证不卡死。
Reactive Robot Navigation Using Quasi-conformal Mappings and Control Barrier Functions
- 把障碍物转成球形表示，用保角映射高效构建虚拟空间
- 结合屏障函数确保运动全程无碰撞且不陷入死锁
- 适用于机械臂和移动机器人，实测效果稳定可靠
本文提出一种适用于复杂环境中安全实时导航的机器人控制算法。该方法将机器人工作空间映射到一个称为'球世界'的虚拟表示中，其中所有障碍物区域均表示为闭球。基于外感知传感器获取的多面体障碍物表示，利用拟共形映射与莫比乌斯变换，高效构建球形障碍物模型。球世界的几何结构支持通过控制屏障函数实现可证明安全的导航，确保机器人运动既无碰撞风险，也无死锁问题。所提导航算法通过多种机器人系统（包括机械臂和移动机器人）的大量仿真与实验进行了验证与分析，展现出优异性能。
原文摘要 · Abstract (English)
This paper presents a robot control algorithm suitable for safe reactive navigation tasks in cluttered environments. The proposed approach consists of transforming the robot workspace into the \emph{ball world}, an artificial representation where all obstacle regions are closed balls. Starting from a polyhedral representation of obstacles in the environment, obtained using exteroceptive sensor readings, a computationally efficient mapping to ball-shaped obstacles is constructed using quasi-conformal mappings and Möbius transformations. The geometry of the ball world is amenable to provably safe navigation tasks achieved via control barrier functions employed to ensure collision-free robot motions with guarantees both on safety and on the absence of deadlocks. The performance of the proposed navigation algorithm is showcased and analyzed via extensive simulations and experiments performed using different types of robotic systems, including manipulators and mobile robots.
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