A collisionless singular Cucker-Smale model with decentralized formation control

TL;DR

This paper develops decentralized control laws for a singular Cucker-Smale model to achieve consensus and formation patterns, extending existing 1D control strategies to higher dimensions with theoretical analysis and numerical validation.

Contribution

It introduces a multidimensional decentralized control approach for singular Cucker-Smale systems, addressing consensus, collision avoidance, and formation control.

Findings

Successful consensus emergence demonstrated

Collision avoidance achieved in simulations

Formation patterns validated in multiple dimensions

Abstract

We address the design of decentralized feedback control laws inducing consensus and prescribed spatial patterns over a singular interacting particle system of Cucker-Smale type. The control design consists of a feedback term regulating the distance between each agent and pre-assigned subset of neighbours. Such a design represents a multidimensional extension of existing control laws for 1d platoon formation control. For the proposed controller we study consensus emergence, collision-avoidance and formation control features in terms of energy estimates for the closed-loop system. Numerical experiments in 1, 2 and 3 dimensions assess the different features of the proposed design.