Stochastic Strategies for Robotic Surveillance as Stackelberg Games

TL;DR

This paper models a stochastic robotic surveillance problem as a Stackelberg game, deriving optimal strategies for different graph structures to maximize intruder capture probability.

Contribution

It introduces a game-theoretic framework for stochastic surveillance and provides optimal strategies for star, complete, and line graphs, including performance bounds.

Findings

Universal upper bound on capture probability derived

Optimal strategies identified for complete graphs

Dominant and optimal strategies characterized for star and line graphs

Abstract

This paper studies a stochastic robotic surveillance problem where a mobile robot moves randomly on a graph to capture a potential intruder that strategically attacks a location on the graph. The intruder is assumed to be omniscient: it knows the current location of the mobile agent and can learn the surveillance strategy. The goal for the mobile robot is to design a stochastic strategy so as to maximize the probability of capturing the intruder. We model the strategic interactions between the surveillance robot and the intruder as a Stackelberg game, and optimal and suboptimal Markov chain based surveillance strategies in star, complete and line graphs are studied. We first derive a universal upper bound on the capture probability, i.e., the performance limit for the surveillance agent. We show that this upper bound is tight in the complete graph and further provide suboptimality guarantees for a natural design. For the star and line graphs, we first characterize dominant strategies for the surveillance agent and the intruder. Then, we rigorously prove the optimal strategy for the surveillance agent.