  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.

Robotics