Journal
SYSTEMS & CONTROL LETTERS
Volume 52, Issue 1, Pages 25-38Publisher
ELSEVIER
DOI: 10.1016/j.sysconle.2003.10.004
Keywords
moving frames; formations; relative equilibria; stability
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This paper presents a Lie group setting for the problem of control of formations, as a natural outcome of the analysis of a planar two-vehicle formation control law. The vehicle trajectories are described using the planar Frenet-Serret equations of motion, which capture the evolution of both the vehicle position and orientation for unit-speed motion subject to curvature (steering) control. The set of all possible (relative) equilibria for arbitrary G-invariant curvature controls is described (where G = SE(2) is a symmetry group for the control law), and a global convergence result for the two-vehicle control law is proved. An n-vehicle generalization of the two-vehicle control law is also presented, and the corresponding (relative) equilibria for the n-vehicle problem are characterized. Work is on-going to discover stability and convergence results for the n-vehicle problem. (C) 2003 Elsevier B.V. All rights reserved.
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