Motion planning methods like navigation functions and harmonic potential fields provide (almost) global convergence and are suitable for obstacle avoidance in dynamically changing environments due to their reactive nature. A common assumption in the control design is that the robot operates in a disjoint star world, i.e. all obstacles are strictly starshaped and mutually disjoint. However, in real-life scenarios obstacles may intersect due to expanded obstacle regions corresponding to robot radius or safety margins. To broaden the applicability of aforementioned reactive motion planning methods, we propose a method to reshape a workspace of intersecting obstacles into a disjoint star world. The algorithm is based on two novel concepts presented here, namely admissible kernel and starshaped hull with specified kernel, which are closely related to the notion of starshaped hull. The utilization of the proposed method is illustrated with examples of a robot operating in a 2D workspace using a harmonic potential field approach in combination with the developed algorithm.

翻译：运动规划方法（如导航函数和谐波势场）因具有反应特性，可实现（几乎）全局收敛，并适用于动态变化环境中的避障。这类控制设计的一个常见假设是机器人运行在不相交的星形世界中，即所有障碍物严格呈星形且互不相交。然而，在实际场景中，由于与机器人半径或安全裕度对应的障碍物扩展区域，障碍物可能相互交叉。为拓宽上述反应式运动规划方法的适用性，我们提出了一种将交叉障碍物工作空间重塑为不相交星形世界的方法。该算法基于本文提出的两个新概念——可容许核与指定核的星形凸包，它们与星形凸包的概念密切相关。通过结合所开发算法与谐波势场方法的二维工作空间机器人运行示例，展示了所提方法的实用性。