Creating Star Worlds: Reshaping the Robot Workspace for Online Motion Planning

Closed-loop motion planning is suitable for obstacle avoidance in dynamically changing environments due to its reactive nature, and various methods have been presented to provide (almost) global convergence. 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 closed-loop motion planning methods, such as harmonic potential fields, 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 2-D workspace using a harmonic potential field approach in combination with the developed algorithm.