Steering laws and continuum models for planar formations
Justh, E.W.; Krishnaprasad, P.S.
Decision and Control, 2003. Proceedings. 42nd IEEE Conference on
Volume 4, Issue , 9-12 Dec. 2003 Page(s): 3609 - 3614 vol.4
Digital Object Identifier   10.1109/CDC.2003.1271708
Summary: We consider a Lie group formulation for the problem of control of formations. Vehicle trajectories are described using the planar Frenet-Serret equations of motion, which capture the evolution of both vehicle position and orientation for unit-speed motion subject to curvature (steering) control. The Lie group structure can be exploited to determine the set of all possible (relative) equilibria for arbitrary G-invariant curvature controls, where G=SE(2) is a symmetry group for the control law. The main result is a convergence result for n vehicles (for finite n), using a Lyapunov function which for n=2, has been previously shown to yield global convergence. A continuum formulation of the basic equations is also presented.

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