STL-GCS: A Planner-Controller Framework for Signal Temporal Logic via Graphs of Time-varying Convex Sets

2026-07-21

AI Summary

This work addresses the robust satisfaction of Signal Temporal Logic (STL) specifications under tracking errors and model mismatch by proposing a unified planning-and-control framework. The approach uniquely translates STL specifications into time-varying convex sets in configuration space and embeds them within a Graph of Convex Sets (GCS) framework for trajectory planning. Continuous-time constraint satisfaction is achieved through B-spline parameterization, while a feedback controller is designed to prioritize specification compliance during execution. By employing a shared convex-set representation across both planning and control layers, the method enhances system consistency and robustness. Simulations and real-world experiments on a space robot demonstrate that the proposed framework generates smooth, collision-free trajectories that robustly satisfy STL specifications even in the presence of disturbances.

Abstract

We present a unified trajectory planning and control framework for the satisfaction of Signal Temporal Logic (STL) specifications defined over convex predicates. At the planning layer, STL tasks are encoded as time-varying convex sets in configuration space, specifically designed so that forward invariance of the system with respect to these sets implies satisfaction of the specification with a prescribed robustness margin. This representation is then lifted to the joint time--configuration space and combined with the Graphs of Convex Sets (GCS) framework, yielding a shortest-path formulation of the planning problem over convex spatio-temporal sets. Trajectories are parameterized by B-splines, which enable continuous-time enforcement of STL satisfaction, collision avoidance, and smoothness constraints. At the control layer, the same time-varying sets used for planning are exploited to design a feedback controller that tracks the planned trajectory while prioritizing satisfaction of the STL specification during execution in the presence of tracking errors and model mismatch. We validate the proposed approach in simulation and in real-world experiments on space robotic platforms.

Problem

• Signal Temporal Logic
• Trajectory Planning
• Convex Sets
• Robustness
• Robot Control

Innovation

• Signal Temporal Logic
• Graphs of Convex Sets
• Time-varying Convex Sets
• B-spline Trajectory
• Robust Feedback Control