Nonholonomic Virtual Constraints for Bipedal Locomotion



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This dissertation addresses nonholonomic virtual constraints (NHVCs) for application to bipedal locomotion. A NHVC is a general class of virtual constraints that depend on the configuration velocities of a mechanical system that does not physically exist, but can be emulated via feedback. Motivated by the goal to create a new paradigm in the control of bipedal robots and powered prostheses, this dissertation presents contributions in two major areas. First, we present a theoretical framework of NHVCs for the stabilization of periodic motion of underactuated robotic systems with one degree of underactuation. The framework presented covers a host of topics that includes a closed form expression of the robot zero dynamics, conditions that make the NHVCs invariant with respect to rigid impacts with the ground, and a reduced dimensionality test, which is independent of the number of degrees of freedom of the robot, is proposed for checking existence and exponential stability of hybrid periodic orbits under NHVCs. The second contribution explores the application of NHVCs to bipedal robots and powered transfemoral prostheses. To this end, we present a novel method for designing NHVCs for bipedal robots that addresses the problem of walking over variable-inclined terrain disturbances. Additionally, we extend the notion of NHVCs and present experimental results for the application of NHVCs to powered prostheses for the first time.



Bipedalism, Robots -- Motion, Prosthesis