Probabilistic Security for Multirobot Systems

Abstract

In this article, we formulate and solve the probabilistic security problem, defined as the probability that a multirobot system (MRS) with probabilistic interaction graphs has realizations that are secure from adversarial attacks. The concept of security is based on the control-theoretic notion of left invertibility, which depends on the existence of disjoint paths and subcuts in the topology describing robot interactions. To model uncertainties in interactions, we associate the existence of edges with a probability distribution. We, then, derive a probability expression based on disjoint paths and subcuts that defines the probability of security of the MRS. The exact probability is computed using the concept of binary decision diagrams (BDDs), a graphical method used to represent Boolean functions. To improve computational complexity, we formulate a combinatorial optimization problem that aims to bound the probability of security. Since MRSs are inherently dynamic, we leverage the graphical properties of BDDs to adapt to any topological changes. To demonstrate the validity of our results, we first track the probability of security of an MRS performing an environmental monitoring task, with Monte Carlo simulations as a baseline for comparison. Finally, we study the behavior of a probabilistic MRS when under attack in three different scenarios.