This paper introduces Space-Time Graphs of Convex Sets (ST-GCSs) for motion planning in environments where collision-free regions are transient and geometrically constrained. Time-optimal planning is formulated as graph search over path-indexed states, with continuous trajectory optimization used to evaluate partial paths. The solver combines best-first search, admissible heuristics, and dominance checks. An Exact Convex Decomposition (ECD) method reserves trajectory occupancy in space-time, supporting dynamic obstacles and multi-robot interactions. Integrated with prioritized and windowed coordination, the approach reportedly solves instances with up to 100 robots within a few minutes while maintaining high solution quality.
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