Flocking formation and stabilizer of boosted cooperative control on a sphere

TL;DR

This paper analyzes flocking formations of second-order systems on a sphere using a Cucker-Smale type operator and cooperative control, proving convergence to specific configurations and demonstrating stabilization effects through numerical simulations.

Contribution

It introduces a new flocking control law on a sphere, classifies possible asymptotic formations, and shows how a boost term stabilizes the system.

Findings

Solutions converge to asymptotic spherical configurations.

The flocking operator stabilizes the cooperative control laws.

Numerical simulations confirm convergence and formation stability.

Abstract

The purpose of this paper is to consider flocking formations of a second order dynamic system on a sphere with a Cucker-Smale type flocking operator and cooperative control. The flocking operator consists of a weighted control parameter and a natural relative velocity. The cooperative control law is given by a combination of attractive and repulsive forces. We prove that the solution to this system converges to an asymptotic spherical configuration depending on the control parameters of the cooperative control law. All possible asymptotic configurations for this system are classified and sufficient conditions for rendezvous, deployment, and local deployment, respectively, are presented. In addition, we provide several numerical simulations to confirm our analytic results. We numerically verify that the solution to this system converges to a formation flight with a nonzero constant speed if we add a boost term. The flocking operator acts as a stabilizer on the spherical cooperative control laws.