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 transform a workspace of intersecting obstacles to 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：动态规划方法,如导航功能和共振潜力领域,提供了(近乎)全球趋同,适合在动态变化环境中由于其反应性质而避免障碍。控制设计的一个共同假设是,机器人在离散的恒星世界中运行,即所有障碍都是纯星形和相互脱节。然而,在现实生活中,由于与机器人半径或安全边缘相对应的障碍区域扩大,障碍可能相互交织。为了扩大上述反应性动作规划方法的适用性,我们提议了一种方法,将一个交叉障碍的工作空间转换到一个脱节的恒星世界中。算法基于这里提出的两个新概念,即可允许的内核和星形外壳,与恒星形外壳的概念密切相关。拟议方法的利用情况以机器人在2D工作空间使用与开发的算法相结合的调和潜在场法进行操作的例子为例证。