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

2025-08-13

AI Summary

Time-optimal, collision-free trajectory planning in complex dynamic environments suffers from sensitivity to initialization and difficulty handling spatiotemporal coupling constraints. Method: This paper proposes a global optimization framework based on Spatio-Temporal Graph-of-Convex-Sets (ST-GCS). It systematically models diverse spatiotemporal constraints—e.g., obstacle avoidance, dynamic obstacles, timing bounds—as convex set constraints, eliminating dependence on initial guesses. By integrating graph neural network–guided structural modeling with efficient convex optimization, the framework enables consistent time-optimal trajectory generation across both static and dynamic scenarios. Results: Experiments demonstrate that the method reliably produces time-optimal, collision-free trajectories without requiring an initial guess. Its planning performance matches standard GCS while offering greater generality. Crucially, it significantly enhances ST-GCS’s capability to model intricate spatiotemporal constraints and improves solver robustness in dynamic environments.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Constraint Optimization
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

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 formulation (ST-GCS) enable us to generate optimal 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. We then show ST-GCS operating in dynamic environments to find minimum distance collision-free trajectories.

Problem

• Generate collision-free trajectories in dynamic environments
• Solve spatial-temporal constraints without initial solver guess
• Adapt general constraints for GCS-compatible frameworks

Innovation

• Space-Time Graphs of Convex Sets (ST-GCS)
• Optimal collision-free trajectory planning
• No initial guess for numerical solver