Rendezvous Control for a Double-Integrator Multiparticle System on Lorentz Group $SO(1,1)$

Abstract

In this article, we study the rendezvous problem for a double-integrator multiparticle system under a proximity-based communication topology on the Lorentz group $SO(1,1)$. With the help of the Riemannian manifold structure on the Lorentz group $SO(1,1)$, we design a rendezvous controller for particles by using the covariant derivative, parallel transport, and Riemannian logarithm map on $SO(1,1)$. We further show that the proposed controller can guarantee that the distance between each particle converges to zero and maintain the connectivity of the communication topology if the initial network is connected. Several numerical simulations are provided to verify and illustrate the theoretical results.