Convergence and Collision Avoidance in Formation Control: A Survey of the Artificial Potential Functions Approach

Abstract

We consider a robot swarm in an unknown polygon. All robots have only a limited communication range. We then look for a triangulation of the polygon using the robots as vertices such that the number of robots used for the triangulation is minimized. All edges in the triangulation have a length smaller than the communication range. For this Online Minimum Re- lay Triangulation Problem, we present a lower bound of 9/8 on the competitive ratio for any online algo- rithm. Moreover, we give an algorithm that is 21/4-competitive for simple polygons and 6-competitive for general polygons.