TY - GEN

T1 - Controlling a rigid formation from a triangle

AU - Chen, Xudong

AU - Belabbas, Mohamed Ali

AU - Basar, M Tamer

PY - 2016/12/27

Y1 - 2016/12/27

N2 - Consider a formation control problem in which agents in Euclidean space are tasked with stabilizing their positions at prescribed target distances from each other, and for which these distances are described by a rigid graph. There is a mismatch in target distances if there is a pair of neighboring agents i and j such that agent i aims to stabilize from agent j at a distance dij, but agent j from agent i at a slightly different distance d′ij. A mismatch in target distances results in a mismatch in the associated interaction laws. It was shown in a recent paper [1] that when there is a small mismatch in the interaction laws, the entire formation undergoes a constant rigid motion. In this work, we build on this observation to establish a controllability result. Specifically, given that there is a selected subset of agents that can control the mismatches in interactions among them, we show that if these agents are fully connected and form a nondegenerate triangle (or more generally, a nondegenerate k-simplex in the k-dimensional case), then it is possible to control an arbitrary rigid motion of the entire formation.

AB - Consider a formation control problem in which agents in Euclidean space are tasked with stabilizing their positions at prescribed target distances from each other, and for which these distances are described by a rigid graph. There is a mismatch in target distances if there is a pair of neighboring agents i and j such that agent i aims to stabilize from agent j at a distance dij, but agent j from agent i at a slightly different distance d′ij. A mismatch in target distances results in a mismatch in the associated interaction laws. It was shown in a recent paper [1] that when there is a small mismatch in the interaction laws, the entire formation undergoes a constant rigid motion. In this work, we build on this observation to establish a controllability result. Specifically, given that there is a selected subset of agents that can control the mismatches in interactions among them, we show that if these agents are fully connected and form a nondegenerate triangle (or more generally, a nondegenerate k-simplex in the k-dimensional case), then it is possible to control an arbitrary rigid motion of the entire formation.

UR - http://www.scopus.com/inward/record.url?scp=85010774007&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85010774007&partnerID=8YFLogxK

U2 - 10.1109/CDC.2016.7798246

DO - 10.1109/CDC.2016.7798246

M3 - Conference contribution

AN - SCOPUS:85010774007

T3 - 2016 IEEE 55th Conference on Decision and Control, CDC 2016

SP - 57

EP - 62

BT - 2016 IEEE 55th Conference on Decision and Control, CDC 2016

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 55th IEEE Conference on Decision and Control, CDC 2016

Y2 - 12 December 2016 through 14 December 2016

ER -