Space-Time Graphs of Convex Sets for Multi-Robot Motion Planning
This addresses motion planning for multiple robots in cluttered environments, offering an incremental improvement over existing decomposition approaches.
The paper tackles the Multi-Robot Motion Planning problem by proposing Space-Time Graphs of Convex Sets (ST-GCS), a planner that uses convex sets to cover collision-free space-time, achieving higher success rates and faster runtimes than state-of-the-art methods.
We address the Multi-Robot Motion Planning (MRMP) problem of computing collision-free trajectories for multiple robots in shared continuous environments. While existing frameworks effectively decompose MRMP into single-robot subproblems, spatiotemporal motion planning with dynamic obstacles remains challenging, particularly in cluttered or narrow-corridor settings. We propose Space-Time Graphs of Convex Sets (ST-GCS), a novel planner that systematically covers the collision-free space-time domain with convex sets instead of relying on random sampling. By extending Graphs of Convex Sets (GCS) into the time dimension, ST-GCS formulates time-optimal trajectories in a unified convex optimization that naturally accommodates velocity bounds and flexible arrival times. We also propose Exact Convex Decomposition (ECD) to "reserve" trajectories as spatiotemporal obstacles, maintaining a collision-free space-time graph of convex sets for subsequent planning. Integrated into two prioritized-planning frameworks, ST-GCS consistently achieves higher success rates and better solution quality than state-of-the-art sampling-based planners -- often at orders-of-magnitude faster runtimes -- underscoring its benefits for MRMP in challenging settings.