TY - JOUR

T1 - Avoiding collisions in cucker-smale flocking models under group-hierarchical multileadership

AU - Jonq, Juang

AU - Liang, Yu Hao

PY - 2018/1/1

Y1 - 2018/1/1

N2 - The Cucker-Smale (C-S) flocking model can be applied to design several mobile autonomous agent systems such as unmanned aerial vehicles and robot systems. In these applications, the problem of collision is usually a nonnegligible issue that should be addressed. In the literature, extra bonding/repulsive forces are added to solve the problem of collision. However, all the known results are limited to the symmetric coupling topology. In this paper, we address this problem under a group-hierarchical multileadership consisting of symmetric coupling topologies and the hierarchical leadership. We obtain the following three main results. First, we show that the augmented C-S model achieves asymptotic flocking provided, roughly, that the ratio between the rate of bounding force and communication rate is sufficiently large. Second, we prove that, for a given augmented C-S model, there exists a set of initial states, which can be explicitly described, such that their corresponding solutions maintain some minimum distance between them. Finally, we show that, for a given set of initial states, we can control the system so that its corresponding solution is collision free by suitably choosing bounding forces, which are independent of given initial states. This in turn suggests that the corresponding system can be collision free by having tolerance for error in their initial states.

AB - The Cucker-Smale (C-S) flocking model can be applied to design several mobile autonomous agent systems such as unmanned aerial vehicles and robot systems. In these applications, the problem of collision is usually a nonnegligible issue that should be addressed. In the literature, extra bonding/repulsive forces are added to solve the problem of collision. However, all the known results are limited to the symmetric coupling topology. In this paper, we address this problem under a group-hierarchical multileadership consisting of symmetric coupling topologies and the hierarchical leadership. We obtain the following three main results. First, we show that the augmented C-S model achieves asymptotic flocking provided, roughly, that the ratio between the rate of bounding force and communication rate is sufficiently large. Second, we prove that, for a given augmented C-S model, there exists a set of initial states, which can be explicitly described, such that their corresponding solutions maintain some minimum distance between them. Finally, we show that, for a given set of initial states, we can control the system so that its corresponding solution is collision free by suitably choosing bounding forces, which are independent of given initial states. This in turn suggests that the corresponding system can be collision free by having tolerance for error in their initial states.

KW - Collision avoidance

KW - Flocking

KW - Group-hierarchical multileadership

UR - http://www.scopus.com/inward/record.url?scp=85043786456&partnerID=8YFLogxK

U2 - 10.1137/16M1098401

DO - 10.1137/16M1098401

M3 - Article

AN - SCOPUS:85043786456

VL - 78

SP - 531

EP - 550

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 1

ER -