Departmental Papers (ESE)


We study the problem of flocking and velocity alignment in a group of kinematic nonholonomic agents in 2 and 3 dimensions. By analyzing the velocity vectors of agents on a circle (for planar motion) or sphere (for 3-D motion), we develop a geodesic control law that minimizes a misalignment potential and results in velocity alignment and flocking. The proposed control laws are distributed and will provably result in flocking when the underlying proximity graph which represents the neighborhood relation among agents is connected. We further show that flocking is possible even when the topology of the proximity graph changes over time, so long as a weaker notion of joint connectivity is preserved.

Document Type

Journal Article

Subject Area


Date of this Version

April 2007


Copyright 2007 IEEE. Reprinted from IEEE Transactions on Automatic Control, Volume 52, Issue 4, April 2007, pages 681-686. Publisher URL:

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cooperative control, distributed coordination, flocking, multiagent systems



Date Posted: 20 June 2007

This document has been peer reviewed.