{"ID":2882978,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.10203","arxiv_id":"2508.10203","title":"Systematic Constraint Formulation and Collision-Free Trajectory Planning Using Space-Time Graphs of Convex Sets","abstract":"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.","short_abstract":"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)...","url_abs":"https://arxiv.org/abs/2508.10203","url_pdf":"https://arxiv.org/pdf/2508.10203v2","authors":"[\"Matthew D. Osburn\",\"Cameron K. Peterson\",\"John L. Salmon\"]","published":"2025-08-13T21:31:23Z","proceeding":"cs.RO","tasks":"[\"cs.RO\",\"eess.SY\",\"math.OC\"]","methods":"[]","has_code":false}