Probabilistic guarantees for rendezvous under noisy measurements

This paper studies the performance of consensus-based rendezvous algorithms when the agent location measurements are subject to noise. In our previous work [1] we provided worst-case bounds on the convergence radius in the case of noisy location estimates. Even though worst-case results are tight, they are conservative. The aim of this paper is thus to investigate typical realizations of consensus-based rendezvous algorithms. We show that while the expected value of the convergence radius is finite, it is bounded by the noise covariance.We also show that there is a natural trade-off between the speed of convergence and the radius of convergence to rendezvous. The results are illustrated with simulations.