Temporal logics and formal synthesis for robot planning and control

2026-06-19

AI Summary

This work proposes a unified planning and control framework that integrates formal specifications with efficient synthesis to ensure reliable robot operation in complex, dynamic environments. By precisely encoding spatiotemporal and logical constraints using Linear Temporal Logic (LTL) and Signal Temporal Logic (STL), the approach synergistically combines multiple paradigms—including graph search, reactive synthesis via game-theoretic methods, sampling-based motion planning, trajectory optimization, and control barrier functions—to simultaneously guarantee correctness of behavior and computational tractability. The framework establishes a coherent theoretical foundation and practical synthesis pipeline for high-assurance autonomous systems, explicitly elucidating the fundamental trade-offs among modeling fidelity, scalability, and verification strength.

Abstract

As robots move from controlled environments into real-world settings, it becomes increasingly crucial to ensure that they perform as expected. A key step toward that goal is a rigorous specification of the desired robot behavior, capturing intricate temporal, spatial, and logical requirements. Complementing this, plan and control synthesis methods are needed to fulfill these specifications with provable guarantees. This manuscript presents temporal logics - particularly linear and signal temporal logic - as expressive specification languages for robot behavior over time. We then discuss principles of formal synthesis, from discrete graph- and game-based approaches to sampling-based motion planning, trajectory optimization, and control-certificate-based synthesis. Finally, we outline challenges in deploying formal synthesis in real-world robotics, emphasizing the interplay between modeling fidelity, computational tractability, and the types of rigorous guarantees that can be achieved.

Problem

• temporal logics
• formal synthesis
• robot planning
• correctness guarantees
• real-world deployment

Innovation

• temporal logic
• formal synthesis
• robot planning
• control certificates
• signal temporal logic