# Systematic Constraint Formulation and Collision-Free Trajectory Planning Using Space-Time Graphs of Convex Sets

arXiv: https://arxiv.org/abs/2508.10203 · HTML: https://mlsanity.com/paper/2508.10203/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Aug 2025.

## Built on by (most cited first, 1 of 1)

- [Search-Based Spatiotemporal and Multi-Robot Motion Planning on Graphs of Space-Time Convex Sets](https://mlsanity.com/paper/2607.00444/) (2026)

## Abstract (arXiv)

In this paper, we create optimal, collision-free, time-dependent trajectories through cluttered dynamic environments. The many spatial and temporal constraints make finding an initial guess for a numerical solver difficult. Graphs of Convex Sets (GCS) and the recently developed Space-Time Graphs of Convex Sets (ST-GCS) enable us to generate minimum distance collision-free trajectories without providing an initial guess to the solver. We also explore the derivation of general GCS-compatible constraints and document an intuitive strategy for adapting general constraints to the framework. We show that ST-GCS produces equivalent trajectories to the standard GCS formulation when the environment is static, as well as globally optimal trajectories in cluttered dynamic environments.