Undirected rigid formations are problematic

S. Mou, A. S. Morse, M. A. Belabbas, B. D.O. Anderson

Research output: Contribution to journalConference article


By an undirected rigid formation of mobile autonomous agents is meant a formation based on graph rigidity in which each pair of 'neighboring' agents is responsible for maintaining a prescribed target distance between them. In a recent paper, a systematic method was proposed for devising gradient control laws for asymptotically stabilizing a large class of rigid, undirected formations in two-dimensional space assuming all agents are described by kinematic point models. The aim of this paper is to explain what happens to such formations if neighboring agents have slightly different understandings of what the desired distance between them is supposed to be, or equivalently, if neighboring agents have differing estimates of what the actual distance between them is. In either case, what one would expect would be a gradual distortion of the formation from its target shape as discrepancies in desired or sensed distances increase. While this is observed for the gradient laws in question, something else quite unexpected happens at the same time. It is shown that for any rigidity-based, undirected formation which is comprised of three or more agents, that if some neighboring agents have slightly different understandings of what the desired distances between them are suppose to be, then almost for certain, the trajectory of the resulting distorted but rigid formation will converge exponentially fast to a closed circular orbit in two-dimensional space which is traversed periodically at a constant angular speed.

Original languageEnglish (US)
Article number7039453
Pages (from-to)637-642
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Issue numberFebruary
StatePublished - Jan 1 2014
Event2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States
Duration: Dec 15 2014Dec 17 2014

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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