Sampling-Based Multi-Agent Path Planning Guided by Spatio-Temporal Logic Mission Objectives

Multi-agent systems operate in shared environments where they must communicate and coordinate to accomplish complex missions. Designing motion plans that guarantee such cooperative behavior is challenging, particularly in continuous state spaces with tightly coupled spatial interactions. Sampling-based planners such as Probabilistic Roadmaps (PRM) scale well to high-dimensional domains but lack mechanisms to enforce mission-level behavioral requirements. Spatio-Temporal Reach and Escape Logic (STREL) enables reasoning about dynamic spatial relations among agents, making it well-suited for specifying coordinated multi-agent tasks. We construct dynamics-aware PRMs for each agent and use them to build a timeless abstraction of the joint multi-agent transition system. The mission objectives are represented using STREL and are symbolically encoded using an SMT solver to synthesize joint trajectories that are both dynamically consistent and logically compliant with the specification. We demonstrate the effectiveness of our approach in the SwarmLab drone swarm simulator, where the framework consistently generates coordinated and specification-compliant paths.