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Stable Motions of Vehicle Formations
Mathematics and Statistics Faculty Publications and Presentations
  • Anca Williams, Portland State University
  • Gerardo Lafferriere, Portland State University
  • J. J. P. Veerman, Portland State University
Document Type
Publication Date
  • Control theory -- Mathematical models,
  • Multiagent systems -- Stability,
  • Feedback control systems,
  • Laplacian matrices

We investigate stable maneuvers for a group of autonomous vehicles while moving in formation. The allowed decentralized feeback laws are factored through the Laplacian matrix of the communication graph. We show that such laws allow for stable circular or elliptical motions for certain vehicle dynamics. We find necessary and sufficient conditions on the feedback gains and the dynamic parameters for convergence to formation. In particular, we prove that for undirected graphs there exist feedback gains that stabilize rotational (or elliptical) motions of arbitrary radius (or eceentricity). In the directed graph case we provide necessary and sufficient conditions on the curvature that guarantee stability for a given choice of feedback gains. We also investigate stable motions involving reorientation of the formation along the direction of motion.


This is the author’s version of a work that was accepted for publication in Proceedings of the 44th IEEE Conference on Decision and Control. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication.

A definitive version was subsequently published in Proceedings of the 44th IEEE Conference on Decision and Control and can be found online at:

Persistent Identifier
Citation Information
Anca Williams, Gerardo Lafferriere and J. J. P. Veerman. "Stable Motions of Vehicle Formations" (2005)
Available at: