Steering left-invariant control systems on matrix Lie groups

Generalizes a technique for eliminating the drift from the description of a control system on a matrix Lie group with left-invariant vector fields. A diffeomorphism of the state space together with an affine input transformation are used in order to put the system into an equivalent left-invariant drift-free form. Techniques developed for steering drift-free control systems may then be applied. The authors apply this method to the Lie group of the rigid rotations SO(3) as in the authors' previous work (Walsh, Sarti,and Sastry, 1993), and to a new example, the rigid motions SE(3).<
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