Stabilization of planar collective motion: All-to-all communication

Rodolphe Sepulchre, Derek A. Paley, Naomi Ehrich Leonard

Research output: Contribution to journalArticlepeer-review

442 Scopus citations


This paper proposes a design methodology to stabilize isolated relative equilibria in a model of all-to-all coupled identical particles moving in the plane at unit speed. Isolated relative equilibria correspond to either parallel motion of all particles with fixed relative spacing or to circular motion of all particles with fixed relative phases. The stabilizing feedbacks derive from Lyapunov functions that prove exponential stability and suggest almost global convergence properties. The results of the paper provide a low-order parametric family of stabilizable collectives that offer a set of primitives for the design of higher-level tasks at the group level.

Original languageEnglish (US)
Pages (from-to)811-824
Number of pages14
JournalIEEE Transactions on Automatic Control
Issue number5
StatePublished - May 2007

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


  • Cooperative control
  • Geometric control
  • Multi-agent systems
  • Stabilization


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