Resilient multi-robot target pursuit

Abstract

We consider the problem of networked agents cooperating together to perform a task of optimizing the parameters of a global cost function. Agents receive linearly correlated noisy streaming data that can be used to learn the target parameters via Least-Mean-Squares (LMS) approaches. Diffusion scheme is incorporated such that at each step after agents adapt the parameters by the current received data, a combination step is included for agents to aggregate the information coming from its one-hop neighbors. It has been demonstrated that by introducing the aggregation step, diffusion algorithms greatly improve the learning accuracy of the parameters measured by the network Mean-Square-Deviation (MSD) [1]. However, the aggregation step is susceptible to attacks. In the presence of Byzantine agents, the aggregation of Byzantine information can easily disrupt the convergence of normal robots and even one Byzantine agent can drive its normal neighbors to converge to some point desired by the attacker [2]. To address this, we propose a resilient aggregation rule based on the notion of centerpoint [3], which is a generalization of median in the higher dimensional Euclidean space. We show that if a normal robot implements the centerpoint based aggregation rule for distributed diffusion, then it can guarantee the aggregated result to lie inside the convex hull of its normal neighbors, given at most [EQUATION] neighbors are Byzantine with n total negihbors and d-dimensional state vectors exchanged among agents. Further, we demonstrate all normal robots implementing centerpoint based distributed diffusion converge resiliently to the true target state. In addition, we demonstrate that widely adopted aggregation rules such as coordinate-wise median [4] and geometric median [5] based are not resilient under certain conditions. The main reason is that unlike centerpoint based aggregation, these rules do not guarantee the aggregation result to be inside the convex hull of the states of normal agents. We carried out experiments on Robotarium, a multirobot testbed developed at the Georgia Institute of Technology to demonstrate the cases where diffusion with coordinate-wise median and geometric median based aggregation rules fail to converge to the true target state, whereas diffusion with centerpoint based rule resiliently converge to the true target state in the same scenario.