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

TL;DR

This paper introduces a novel approach using Space-Time Graphs of Convex Sets (ST-GCS) to generate optimal, collision-free trajectories in dynamic environments without initial guesses, improving planning efficiency and robustness.

Contribution

The paper develops the ST-GCS framework for trajectory planning, enabling collision avoidance in dynamic environments and deriving general GCS-compatible constraints.

Findings

ST-GCS produces trajectories equivalent to standard GCS in static environments.

ST-GCS finds globally optimal trajectories in cluttered dynamic environments.

The method eliminates the need for initial guess in numerical solvers.

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.