Space-Time Graphs of Convex Sets for Multi-Robot Motion Planning
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912455363395584 |
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| author | Tang, Jingtao Mao, Zining Yang, Lufan Ma, Hang |
| author_facet | Tang, Jingtao Mao, Zining Yang, Lufan Ma, Hang |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_00583 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Space-Time Graphs of Convex Sets for Multi-Robot Motion Planning Tang, Jingtao Mao, Zining Yang, Lufan Ma, Hang Robotics Artificial Intelligence 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. |
| title | Space-Time Graphs of Convex Sets for Multi-Robot Motion Planning |
| topic | Robotics Artificial Intelligence |
| url | https://arxiv.org/abs/2503.00583 |