Coordinated Motion Planning: The Video (Multimedia Exposition)

Abstract

We motivate, visualize and demonstrate recent work for minimizing the total execution time of a coordinated, parallel motion plan for a swarm of N robots in the absence of obstacles. Under relatively mild assumptions on the separability of robots, the algorithm achieves constant stretch: If all robots want to move at most d units from their respective starting positions, then the total duration of the overall schedule (and hence the distance traveled by each robot) is O(d) steps; this implies constant-factor approximation for the optimization problem. Also mentioned is an NP-hardness result for finding an optimal schedule, even in the case in which robot positions are restricted to a regular grid. On the other hand, we show that for densely packed disks that cannot be well separated, a stretch factor Omega(N^{1/4}) is required in the worst case; we establish an achievable stretch factor of O(N^{1/2}) even in this case. We also sketch geometric difficulties of computing optimal trajectories, even for just two unit disks.