Game-Theoretic Safe Multi-Agent Motion Planning with Reachability Analysis for Dynamic and Uncertain Environments (Extended Version)

2025-11-15

AI Summary

In dynamic and uncertain environments, ensuring safety, robustness, and scalability simultaneously in multi-agent motion planning remains challenging. To address this, we propose RE-DPG—a decentralized cooperative decision-making framework integrating dynamic potential games with multi-agent forward reachable sets (MA-FRS) under local interactions. We introduce two novel algorithms: neighborhood-dominant iterative best response (ND-iBR) and iterative ε-best response (iε-BR), enabling rapid convergence to an ε-Nash equilibrium with explicit safety constraints. Theoretical analysis guarantees convergence and establishes proactive safety margins. Evaluated in 2D/3D simulations and on real robotic platforms, RE-DPG significantly improves planning efficiency and obstacle-avoidance reliability while scaling to hundreds of agents. It achieves strong robustness against environmental uncertainty and computational scalability through distributed computation.

Technology Category

• Multiagent Systems: Multiagent Planning
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Intelligent Robots: Motion and Path Planning

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Ensuring safe, robust, and scalable motion planning for multi-agent systems in dynamic and uncertain environments is a persistent challenge, driven by complex inter-agent interactions, stochastic disturbances, and model uncertainties. To overcome these challenges, particularly the computational complexity of coupled decision-making and the need for proactive safety guarantees, we propose a Reachability-Enhanced Dynamic Potential Game (RE-DPG) framework, which integrates game-theoretic coordination into reachability analysis. This approach formulates multi-agent coordination as a dynamic potential game, where the Nash equilibrium (NE) defines optimal control strategies across agents. To enable scalability and decentralized execution, we develop a Neighborhood-Dominated iterative Best Response (ND-iBR) scheme, built upon an iterated $varepsilon$-BR (i$varepsilon$-BR) process that guarantees finite-step convergence to an $varepsilon$-NE. This allows agents to compute strategies based on local interactions while ensuring theoretical convergence guarantees. Furthermore, to ensure safety under uncertainty, we integrate a Multi-Agent Forward Reachable Set (MA-FRS) mechanism into the cost function, explicitly modeling uncertainty propagation and enforcing collision avoidance constraints. Through both simulations and real-world experiments in 2D and 3D environments, we validate the effectiveness of RE-DPG across diverse operational scenarios.

Problem

• Ensuring safe multi-agent motion planning in dynamic uncertain environments
• Addressing computational complexity in coupled multi-agent decision-making
• Providing proactive safety guarantees under stochastic disturbances and uncertainties

Innovation

• Integrates game-theoretic coordination with reachability analysis
• Develops scalable decentralized scheme for strategy computation
• Uses multi-agent reachable sets to ensure safety under uncertainty