Level sets and stable manifold approximations for perceptually driven non-holonomically constrained navigation
This paper addresses problems of robot navigation in the presence of non-holonomic motion constraints arising from kinematics as well as holonomic constraints arising from perception. We consider the theoretical problem of visually registering a unicycle with respect to camera images of a known, persistent landmark. We propose a general hybrid procedure that adapts to this constrained motion setting the standard feedback controller arising from a navigation function in the fully actuated case. The algorithm switches back and forth between moving down and across the associated gradient field toward the stable manifold it induces in the constrained dynamics. Guaranteed to avoid obstacles in all cases, after the introduction of some technical (and not easily verified) additional assumptions, the algorithm can be readily shown to converge to an arbitrarily small neighborhood of the goal. We then introduce a more realistic, 'relaxed' version of the algorithm that appears to result in asymptotic convergence to the goal. Illustrative simulations are provided for two different perceptual models appropriate to environments with visual beacons.
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