Capturing a convex object with three discs

Abstract— This paper addresses the problem of capturing an arbitrary convex object P in the plane with three congruent disc-shaped robots. Given two stationary robots in contact with P , we characterize the set of positions of a third robot, the so-called capture region, that prevent P from escaping to infinity via continuous rigid motion. We show that the computation of the capture region reduces to a visibility problem. We present two algorithms for solving this problem and computing the capture region when P is a polygon and the robots are points (zero-radius discs). The first algorithm is exact and has polynomial time complexity. The second one uses simple hidden-surface removal techniques from computer graphics to output an arbitrarily accurate approximation of the capture region; it has been implemented and examples are presented.

• Type: Conference
• Year: 2003
• Where: ICRA
• Authors: Jeff Erickson, Shripad Thite, Fred Rothganger, Jean Ponce
• Keywords: Capture Region, Congruent Disc-shaped Robots, ICRA 2003, Robotics, So-called Capture Region