Controlling a rigid formation from a triangle

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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.

Original languageEnglish (US)
Title of host publication2016 IEEE 55th Conference on Decision and Control, CDC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781509018376
StatePublished - Dec 27 2016
Event55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States
Duration: Dec 12 2016Dec 14 2016

Publication series

Name2016 IEEE 55th Conference on Decision and Control, CDC 2016


Other55th IEEE Conference on Decision and Control, CDC 2016
Country/TerritoryUnited States
CityLas Vegas

ASJC Scopus subject areas

  • Artificial Intelligence
  • Decision Sciences (miscellaneous)
  • Control and Optimization


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