Probabilistic guarantees for rendezvous under noisy measurements

Authors:
Carlos H. Caicedo-Núñez;Miloš Žefran
Affiliations:
Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, IL;Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, IL
Venue:
ACC'09 Proceedings of the 2009 conference on American Control Conference
Year:
2009

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Abstract

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.