Fast and Near-Optimal Collision-Free Robot Scheduling On Paths

Abstract

In this paper, we address the problem of scheduling a set of robots to complete tasks in a laboratory environment, modelled as a graph, while avoiding collisions. We analyze the dynamic programming algorithm (PA) introduced in arXiv:2402.12019 and present three baselines for comparison: an integer programming approach (IP) that always yields an optimal solution, a greedy algorithm (GA), and a simple randomized algorithm (RA). We show that for a path graph, PA, GA, and RA find solutions several orders of magnitude faster than IP (the optimal baseline), with PA returning optimal results in the vast majority of cases. Our scaled experiments comparing non-optimal algorithms show that the average schedule timespan produced by PA is less than half that of RA and GA. This outperformance is consistent across varying path lengths, task durations and distributions, number and allocations of tasks and robots, and task-to-robot ratios. This work serves two purposes. First, we present three algorithms for scheduling on line graphs, including a novel integer programming formulation for finding optimal solutions. Second, we demonstrate that PA produces near-optimal schedules that outperform all non-optimal baselines while maintaining a comparable runtime. Code is available at https://github.com/sea26-robots/code.