Byzantine Resilience at Swarm Scale: A Decentralized Blocklist Protocol from Inter-robot Accusations

The Weighted-Mean Subsequence Reduced (W-MSR) algorithm, the state-of-the-art method for Byzantine-resilient design of decentralized multi-robot systems, is based on discarding outliers received over Linear Consensus Protocol (LCP). Although W-MSR provides theoretical guarantees relating network connectivity to the convergence of the underlying consensus, W-MSR comes with several limitations: the number of Byzantine robots, 𝐹 , to tolerate should be known a priori, each robot needs to maintain 2𝐹 + 1 neighbors, 𝐹 + 1 robots must independently make local measurements of the consensus property in order for the swarm's decision to change, and W-MSR is specific to LCP and does not generalize to applications not implemented over LCP. In this work, we propose a Decentralized Blocklist Protocol (DBP) based on inter-robot accusations. Accusations are made on the basis of locally-made observations of misbehavior, and once shared by cooperative robots across the network are used as input to a graph matching algorithm that computes a blocklist. DBP generalizes to applications not implemented via LCP, is adaptive to the number of Byzantine robots, and allows for fast information propagation through the multirobot system while simultaneously reducing the required network connectivity relative to W-MSR. On LCP-type applications, DBP reduces the worst-case connectivity requirement of W-MSR from (2𝐹 + 1)-connected to (𝐹 + 1)-connected and the minimum number of cooperative observers required to propagate new information from 𝐹 + 1 to just 1 observer. We demonstrate that our approach to Byzantine resilience scales to hundreds of robots on target tracking, time synchronization, and localization case studies.