Multi‐vehicle coordination for double‐integrator dynamics under fixed undirected/directed interaction in a sampled‐data setting

Abstract

This paper studies the convergence of two coordination algorithms for double‐integrator dynamics under fixed undirected/ directed interaction in a sampled‐data setting. The first algorithm guarantees that a team of vehicles achieves coordination on their positions with a zero final velocity while the second algorithm guarantees that a team of vehicles achieves coordination on their positions with a constant final velocity. We show necessary and sufficient conditions on the sampling period, the control gain, and the communication graph such that coordination is achieved using these two algorithms under, respectively, an undirected interaction topology and a directed interaction topology. Tools like matrix theory, bilinear transformation, and Cauchy theorem are used for convergence analysis. Coordination equilibria for both algorithms are also given. Simulation results are presented as a proof of concept. Copyright © 2009 John Wiley & Sons, Ltd.