| Local Controllability And Motion Planning For Some Classes Of Systems With Drift (1991) | |||||||||||||||||
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| We explain how some recent results on the design of controls for nonoholomic systems without drift can be extended to some classes of sytems with drift. In particular, we show that a dynamic extension of a driftless system that satisfies the Lie algebra rank condition necessary satisfies algebraic sufficient conditions for small-time local controllability at all its equilibrium points. 1. Introduction. Many mechanical systems can be modelled as control systems of the form \Sigma : x = f 0 (x) + u 1 f 1 (x) + : : : + um f m (x) ; (1) where the f i are smooth vector fields on a smooth connected manifold M . The motion planning problem (MPP) is the problem of designing reasonable algorithms that, for any given pair (p; q) of points in M (or in some subset S of M ), produce a control that steers p to q. Various such designs have been proposed in work by Brockett [2], Hauser-Sastry-Kokotovic [6], Murray-Sastry [13], [14], Sastry-Li [15], Fernandes-Gurvits-Li [4], Lafferriere [10], Laffe... | |||||||||||||||||
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