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

arXiv: https://arxiv.org/abs/2607.28679 · HTML: https://mlsanity.com/paper/2607.28679/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 31 references that are in the map.
- First posted on arXiv 29 Jul 2026.

## Builds on (most cited first, 14 of 14)

- [Multi-agent Motion Planning from Signal Temporal Logic Specifications](https://mlsanity.com/paper/2201.05247/) (2022)
- [Monitoring Mobile and Spatially Distributed Cyber-Physical Systems](https://mlsanity.com/paper/1904.08847/) (2019)
- [Robust Multi-Agent Coordination from CaTL+ Specifications](https://mlsanity.com/paper/2210.01732/) (2022)
- [Census Signal Temporal Logic Inference for Multi-Agent Group Behavior Analysis](https://mlsanity.com/paper/1610.05612/) (2016)
- [Predictive Monitoring with Logic-Calibrated Uncertainty for Cyber-Physical Systems](https://mlsanity.com/paper/2011.00384/) (2020)
- [Hyperproperties for Robotics: Planning via HyperLTL](https://mlsanity.com/paper/1911.11870/) (2019)
- [Prescribed Performance Control for Signal Temporal Logic Specifications](https://mlsanity.com/paper/1703.07094/) (2017)
- [SwarmLab: a Matlab Drone Swarm Simulator](https://mlsanity.com/paper/2005.02769/) (2020)
- [Multi-agent Path Finding for Timed Tasks using Evolutionary Games](https://mlsanity.com/paper/2411.10558/) (2024)
- [Neural Network-based Control for Multi-Agent Systems from Spatio-Temporal Specifications](https://mlsanity.com/paper/2104.02737/) (2021)
- [A Logic for Monitoring Dynamic Networks of Spatially-distributed Cyber-Physical Systems](https://mlsanity.com/paper/2105.11400/) (2021)
- [Logics and Algorithms for Hyperproperties](https://mlsanity.com/paper/2501.08063/) (2025)
- [HypRL: Reinforcement Learning of Control Policies for Hyperproperties](https://mlsanity.com/paper/2504.04675/) (2025)
- [STL-GO: Spatio-Temporal Logic with Graph Operators for Distributed Systems with Multiple Network Topologies](https://mlsanity.com/paper/2507.15147/) (2025)

## Abstract (arXiv)

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.