This paper addresses the challenge of safe navigation for rigid-body mobile robots in dynamic environments. We introduce an analytic approach to compute the distance between a polygon and an ellipse, and employ it to construct a control barrier function (CBF) for safe control synthesis. Existing CBF design methods for mobile robot obstacle avoidance usually assume point or circular robots, preventing their applicability to more realistic robot body geometries. Our work enables CBF designs that capture complex robot and obstacle shapes. We demonstrate the effectiveness of our approach in simulations highlighting real-time obstacle avoidance in constrained and dynamic environments for both mobile robots and multi-joint robot arms.

翻译：本文针对刚体移动机器人在动态环境中的安全导航问题展开研究。我们提出了一种计算多边形与椭圆之间距离的解析方法，并将其用于构建控制障碍函数（CBF）以实现安全控制综合。现有移动机器人避障的CBF设计方法通常假设机器人呈点状或圆形，这限制了其在更真实机器人本体几何构型中的适用性。本工作突破了这一局限，使CBF设计能够捕捉复杂机器人及障碍物形状。我们通过仿真验证了该方法在约束动态环境下对移动机器人与多关节机械臂进行实时避障的有效性。