Workshop — Topological Complexity and Motion Planning

Teaching a robot to move about on an empty football field is easy. There is exactly one line joining the robot's starting and finishing points, and the robot can be instructed to move from start to finish along this line. This instruction scheme is robust in the sense that nearby starting and finishing points give rise to similar instructions. If the robot is attached to a circular track, teaching it to move is harder. The instructions ``move along the shortest arc'' lead to confusion if the starting and finishing points are precisely opposite one another, as the robot doesn't know whether to move in the clockwise or counterclockwise direction. Choosing one of these two, say, the instructions ``move clockwise'', yields confusion when the starting and finishing points are the same. From these instructions, the robot does not know if it should simply stay at the start/finish point, or move in a less efficient manner, looping around the circle once or twice or\ldots