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.

中文翻译：

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稳健的多路径定向问题：抵御对抗性攻击

多路径定向运动问题要求一组机器人的路径最大化收集的总奖励，同时满足路径长度的预算约束。该问题模拟了许多多机器人路由任务，例如探索未知环境和环境监控信息收集。在本文中，我们专注于如何使机器人团队在对抗性环境中运行时对故障具有鲁棒性。我们引入了鲁棒多路径定向问题 (RMOP)，在该问题中，我们寻求最坏情况保证，以对抗最多能够攻击 $\alpha$ 机器人的对手。我们的主要贡献是具有有限近似保证的一般近似方案，该保证取决于 $\alpha$ 和单个机器人定向运动的近似因子。特别是，我们表明，当成本函数是模块化时，该算法会产生 (i) 常数因子近似值；(ii) 当成本函数是子模时的 $\log$ 因子逼近；(iii) 当成本函数是次模的但允许机器人超出其路径预算有界时的常数因子近似。除了理论分析外，我们还对海洋监测应用进行了模拟研究，以证明我们方法的有效性。