Biped Locomotion Control

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The objective of this project is to develop a coherent mathematical framework in which asymptotically stabilizing feedback controllers for biped systems may be rigorously analyzed and synthesized. Feedback control is an integral part of both biological and mechanical biped locomotion. For the important cases of under actuated bipeds, none of the feedback controllers or stabilization mechanisms proposed in the literature has been proven to yield asymptotically stable motions. The lack of analytical progress is normally attributed to the inherent complexity of even the simplest biped models. The proposed work will be based on a recent breakthrough by Grizzle, Abba and Plestan. For the important special case of an under actuated biped with a torso and stiff legs (i.e., no knees), these researchers provided the first mathematical proof of the asymptotic stability of a feedback-controlled walking motion. This project will systematically explore feedback stabilization and design for a sequence of more realistic biped models. The models will be selected on the basis of their applicability to robotics, biomechanics and prosthetics, and will represent a wide range in the degree of (under) actuation.