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振势能场提供（几乎）全局收敛并适用于动态变化环境中的障碍物避免，这是由于其反应性质。在控制设计中的一个常见假设是机器人在不相交的星际世界中运行，即所有障碍物都是严格的星型并且互不相交。但在现实场景中，由于机器人半径或安全间隙的扩展障碍区域会相交。为了拓宽前述反应性运动规划方法的适用范围，我们提出了一种方法，将相交的障碍物工作空间重塑为不相交的星际世界。该算法基于两个新颖概念，即可接受的核和带有指定核的星形船体，它们与星形船体概念密切相关。该提出的方法的利用以2D工作空间中的机器人为例，使用谐振势能场方法结合所开发的算法进行说明。