Rendezvous control design for the Cucker-Smale model on the unit sphere

Abstract

In this paper, we investigate a rendezvous problem for the Cucker-Smale model on the n-dimensional unit sphere. We design a feedback control law with the help of covariant derivative, parallel transport, and geodesic on the n-dimensional unit sphere and show that the proposed feedback control law enables all agents to convergeto a static target on the n-dimensional unit sphere under some a priori conditions. Meanwhile, a numerical simulation is provided to verify and illustrate the theoretical results.