Robust Multiple-Path Orienteering Problem: Securing Against Adversarial Attacks

The multiple-path orienteering problem asks for paths for a team of robots that maximize the total reward collected while satisfying budget constraints on the path length. This problem models many multi-robot routing tasks such as exploring unknown environments and information gathering for environmental monitoring. In this paper, we focus on how to make the robot team robust to failures when operating in adversarial environments. We introduce the Robust Multiple-path Orienteering Problem (RMOP) where we seek worst-case guarantees against an adversary that is capable of attacking at most $\alpha$ robots. Our main contribution is a general approximation scheme with bounded approximation guarantee that depends on $\alpha$ and the approximation factor for single robot orienteering. In particular, we show that the algorithm yields a (i) constant-factor approximation when the cost function is modular; (ii) $\log$ factor approximation when the cost function is submodular; and (iii) constant-factor approximation when the cost function is submodular but the robots are allowed to exceed their path budgets by a bounded amount. In addition to theoretical analysis, we perform simulation study for an ocean monitoring application to demonstrate the efficacy of our approach.