Robust rendezvous for multi-robot system with random node failures: an optimization approach

In this paper, we consider the problem of designing distributed control algorithms to solve the rendezvous problem for multi-robot systems with limited sensing, for situations in which random nodes may fail during execution. We first formulate a distributed solution based upon averaging algorithms that have been reported in the consensus literature. In this case, at each stage of execution a one-step sequential optimal control (i.e., näive greedy algorithm) is used. We propose a distributed stochastic optimal control algorithm that minimizes a mean–variance cost function for each stage, given that the probability distribution for possible node failures is known a priori, as well as a minimax version of the problem when the prior probability distribution is not known. We demonstrate via extensive numerical simulations that our proposed algorithm provides statistically better rendezvous task performance than contemporary algorithms in cases for which failures occur.