Distributed Attack-Robust Submodular Maximization for Multi-Robot Planning

In this paper, we design algorithms to protect swarm-robotics applications against sensor denial-of-service (DoS) attacks on robots. We focus on applications requiring the robots to jointly select actions, e.g., which trajectory to follow, among a set of available ones. Such applications are central in large-scale robotic applications, such as multi-robot motion planning for target tracking. But the current attack-robust algorithms are centralized. In this paper, we propose a general-purpose distributed algorithm towards robust optimization at scale, with local communications only. We name it Distributed Robust Maximization (DRM). DRM proposes a divide-and-conquer approach that distributively partitions the problem among cliques of robots. Then, the cliques optimize in parallel, independently of each other. We prove DRM achieves a close-to-optimal performance. We demonstrate DRM's performance in both Gazebo and MATLAB simulations, in scenarios of active target tracking with swarms of robots. In the simulations, DRM achieves computational speed-ups, being 1-2 orders faster than the centralized algorithms; yet, it nearly matches the tracking performance of the centralized counterparts. Since, DRM overestimates the number of attacks in each clique, in this paper we also introduce an Improved Distributed Robust Maximization (IDRM) algorithm. IDRM infers the number of attacks in each clique less conservatively than DRM by leveraging 3-hop neighboring communications. We verify IDRM improves DRM's performance in simulations.