Capturing a convex object with three discs

J. Erickson, S. Thite, F. Rothganger, J. Ponce
2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422)  
This paper addresses the problem of capturing an arbitrary convex object P in the plane with three congruent discshaped robots. Given two stationary robots in contact with P, we characterize the set of positions of a third robot that prevent P from escaping to infinity and show that the computation of this so-called capture region reduces to the resolution of a visibility problem. We present two algorithms for solving this problem and computing the capture region when P is a polygon and the
more » ... polygon and the robots are points (zero-radius discs). The first algorithm is exact and has polynomial-time complexity. The second one uses simple hiddensurface removal techniques from computer graphics to output an arbitrarily accurate approximation of the capture region; it has been implemented and examples are presented. 0-7803-7736-2/03/$17.00 ©2003 IEEE
doi:10.1109/robot.2003.1241927 dblp:conf/icra/EricksonTRP03 fatcat:r4mdnppu7rfuxgm4o7sevijdje