Multi-Robot Coordination Induced in an Adversarial Graph-Traversal Game

TL;DR

This paper formulates a game-theoretic approach to multi-robot coordination in hazardous, adversarial environments modeled as a time-varying graph, enabling strategic decision-making to optimize traversal costs.

Contribution

It introduces a stochastic game framework for multi-robot coordination in adversarial graph traversal, providing numerical methods for Nash equilibrium strategies and bounds on the game value.

Findings

Mixing actions improves traversal success.

Coordinated strategies enhance safety and efficiency.

Numerical simulations validate the approach.

Abstract

This paper presents a game theoretic formulation of a graph traversal problem, with applications to robots moving through hazardous environments in the presence of an adversary, as in military and security scenarios. The blue team of robots moves in an environment modeled by a time-varying graph, attempting to reach some goal with minimum cost, while the red team controls how the graph changes to maximize the cost. The problem is formulated as a stochastic game, so that Nash equilibrium strategies can be computed numerically. Bounds are provided for the game value, with a guarantee that it solves the original problem. Numerical simulations demonstrate the results and the effectiveness of this method, particularly showing the benefit of mixing actions for both players, as well as beneficial coordinated behavior, where blue robots split up and/or synchronize to traverse risky edges.