Equilibria and steering laws for planar formations

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 veh...

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Bibliographic Details
Published in:Systems & control letters 2004-05, Vol.52 (1), p.25-38
Main Authors: Justh, E.W., Krishnaprasad, P.S.
Format: Article
Language:English
Subjects:
Applied sciences
Computer science
control theory
systems
Control theory. Systems
Exact sciences and technology
Formations
Moving frames
Relative equilibria
Stability
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Summary: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.
ISSN:0167-6911
1872-7956
DOI:10.1016/j.sysconle.2003.10.004