Robust Multiple-Path Orienteering Problem: Securing Against Adversarial Attacks

Abstract

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 multirobot routing tasks, such as exploring unknown environments and information gathering for environmental monitoring. In this article, 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> robots. We consider two versions of this problem: RMOP offline and RMOP online. In the offline version, there is no communication or replanning when robots execute their plans, and our main contribution is a general approximation scheme with a bounded approximation guarantee that depends on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> and the approximation factor for single-robot orienteering. In particular, we show that the algorithm yields a: 1) constant-factor approximation when the cost function is modular; 2) <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\log$</tex-math></inline-formula> factor approximation when the cost function is submodular; and 3) constant-factor approximation when the cost function is submodular, but the robots are allowed to exceed their path budgets by a bounded amount. In the online version, the RMOP is modeled as a two-player sequential game and solved adaptively in a receding horizon fashion based on Monte Carlo tree search. In addition to theoretical analysis, we perform simulation studies for ocean monitoring and tunnel information-gathering applications to demonstrate the efficacy of our approach.