Approximate Probabilistic Security for Networked Multi-Robot Systems

In this paper, we formulate a combinatorial optimization problem that aims to maximize the accuracy of a lower bound estimate of the probability of security of a multi-robot system (MRS), while minimizing the computational complexity involved in its calculation. Security of an MRS is defined using the well-known control theoretic notion of left invertiblility, and the probability of security of an MRS can be calculated using binary decision diagrams (BDDs). The complexity of a BDD depends on the number of disjoint path sets considered during its construction. Taking into account all possible disjoint paths results in an exact probability of security, however, selecting an optimal subset of disjoint paths leads to a good estimate of the probability while significantly reducing computation. To deal with the dynamic nature of MRSs, we introduce two methods: (1) multi-point optimization, a technique that requires some a priori knowledge of the topology of the MRS over time, and (2) online optimization, a technique that does not require a priori knowledge, but must construct BDDs while the MRS is operating. Finally, our approach is validated on an MRS performing a rendezvous objective while exchanging information according to a noisy state agreement process.