Abstract
In full-knowledge multi-robot adversarial patrolling, a group of robots have to detect an adversary who knows the robots' strategy. The adversary can easily take advantage of any deterministic patrolling strategy, which necessitates the employment of a randomised strategy. While the Markov decision process has been the dominant methodology in computing the penetration detection probabilities, we apply enumerative combinatorics to characterise the penetration detection probabilities. It allows us to provide the closed formulae of these probabilities and facilitates characterising optimal random defence strategies. Comparing to iteratively updating the Markov transition matrices, our methods significantly reduces the time and space complexity of solving the problem. We use this method to tackle four penetration configurations.
Highlights
Multi-robot adversarial patrolling is a well-established problem with numerous security applications including crime prevention [An et al, 2017], stopping piracy, defending critical infrastructure [Oliva et al, 2019], protecting animals, natural reserves, or the environment [Basilico et al, 2017]
The problem has many characteristics and has been considered with different approaches; we focus on the important setting of finding optimal random strategies for defending polyline graphs against full-knowledge adversaries
We present a novel approach to model all possible paths of a robot’s random strategy as lattice paths
Summary
Multi-robot adversarial patrolling is a well-established problem with numerous security applications including crime prevention [An et al, 2017], stopping piracy, defending critical infrastructure [Oliva et al, 2019], protecting animals, natural reserves, or the environment [Basilico et al, 2017]. We use the lattice path representation to count the number of paths which immediately allow us to explicitly state the probability of catching the adversary in different segments. This removes the first step of calculating the functions, such that the remaining step of solving the system of equations can be done efficiently. We highlight connections between the parameter and the resulting probabilities
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