Space-Time Graphs of Convex Sets for Multi-Robot Motion Planning

2025-03-01

AI Summary

This work addresses the challenge of generating temporally and spatially collision-free trajectories for multi-robot motion planning (MRMP) in dynamic, narrow, and cluttered environments. We propose ST-GCS, the first framework to extend Graph-based Convex Sets (GCS) to the spatiotemporal domain. It employs Exact Convex Decomposition (ECD) for tight modeling of spatiotemporal obstacles and explicitly reserves trajectory corridors within a priority-based planning scheme. The method integrates convex optimization, spatiotemporal graph construction, and kinematic constraints—including velocity bounds and flexible arrival times—thereby eliminating the randomness and low reliability inherent in sampling-based approaches. Experiments demonstrate that ST-GCS achieves significantly higher success rates and solution quality than state-of-the-art sampling-based planners across complex scenarios, with runtime improvements of up to an order of magnitude. ST-GCS establishes a new paradigm for deterministic, efficient MRMP in highly dynamic, shared environments.

Technology Category

• Planning, Routing, and Scheduling: Temporal Planning
• Intelligent Robots: Motion and Path Planning
• Multiagent Systems: Multiagent Planning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

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.

Problem

• Multi-Robot Motion Planning in shared environments
• Challenges with dynamic obstacles in cluttered spaces
• Time-optimal trajectory planning with velocity constraints

Innovation

• Space-Time Graphs of Convex Sets (ST-GCS) for MRMP
• Unified convex optimization with velocity bounds
• Exact Convex Decomposition (ECD) for collision-free planning