Multi-Agent Planning with Spatio-Temporal and Topological Constraints using STL-GO

2026-07-29

AI Summary

This work addresses the challenge of jointly planning spatiotemporal constraints—specifying when and where tasks are executed—and topological constraints—governing agent interaction structures—in multi-agent systems. To this end, the authors propose a unified modeling framework grounded in STL-GO logic, which for the first time incorporates dynamic multi-graph interactions. They develop two complete solution approaches based on Mixed-Integer Programming (MIP) and Satisfiability Modulo Theories (SMT), enabling seamless switching and comparative analysis between the two paradigms. The effectiveness of the proposed method is validated on a multi-UAV search-and-rescue benchmark, demonstrating strong expressiveness and favorable scalability across varying team sizes and levels of time-varying graph complexity.

Abstract

Multi-agent planning problems arise in a variety of engineering applications, such as multi-robot wildfire fighting and unmanned aerial inspection in factories. A particular challenge is the existence of spatio-temporal (i.e., when and/or where an agent should do what) and topological constraints (i.e., how agents should interact), as typically formalized via the notion of graphs. Over the last years, various frameworks have been proposed that can capture such constraints via spatio-temporal logics. We focus here on spatio-temporal logic with graph operators (STL-GO), a recent formalism that supports reasoning about multiple agents and their topologies, such as sensing, communication, and task topologies. In this paper, we consider the problem of planning multi-agent paths that satisfy constraints written in STL-GO. This problem is particularly challenging due to the need of encoding multiple, potentially time-varying graphs via the graph operators inherent to STL-GO. We present two encodings of this problem, one based on mixed-integer programming (MIP) and another based on satisfiability modulo theory (SMT), with soundness guarantees. We provide a unified interface for specifying agent constraints, their graph topologies, and the STL-GO specification, enabling seamless use of both methods and facilitating direct comparison between them. We evaluate both encodings on a multi-UAV search-and-rescue benchmark, ablating over team size and graph complexity, highlighting the expressiveness of the proposed encodings under dynamic multi- graph interactions.

Problem

• multi-agent planning
• spatio-temporal constraints
• topological constraints
• STL-GO
• graph operators

Innovation

• STL-GO
• multi-agent planning
• spatio-temporal constraints
• topological constraints
• SMT encoding