We design a motion planning algorithm to coordinate the movements of two robots along a figure eight track, in such a way that no collisions occur. We use a topological approach to robot motion planning that relates instabilities in motion planning algorithms to topological features of configuration spaces. The topological complexity of a configuration space is an invariant that measures the complexity of motion planning algorithms. We show that the topological complexity of our problem is 3 and construct an explicit algorithm with three continuous instructions.
Paper
References (9)
05If they are in different circles, move them away from the center until at least one of them reaches a pole position
06Move back from the final Z -position to the final position reversing the movement done in the first step
07In the following case scenarios, we describe the movements in the physical space as well as in the configuration spacethe pump journal of undergraduate research
08Execute algorithm 7.1 for the initial Z -position and final Z -position
09Repeat steps 1 and 2 with the final position. Let us call initial Z -position and final Z -position the output of this step