Feedback control of an underactuated planar bipedal robot with impulsive foot action

A planar underactuated bipedal robot with an impulsive foot model is considered. The analysis extends previous work on a model with unactuated point feet of Westervelt et al. 1 to include the actuator model of Kuo 2. The impulsive actuator at each leg end is active only during the double support phase, which results in the model being identical to the model with unactuated point feet for the single support phase. However, the impulsive foot actuation results in a different model for the double support map. Conditions for the existence of a hybrid zero dynamics for the robot with foot actuation are studied. A feedback design method is proposed that integrates actuation in the single and double support phases. A stability analysis is performed using a Poincaré return map. As in Kuo’s model 2, a more efficient gait is demonstrated with an impulsive foot action. I

Feedback Control of a Bipedal Walker and Runner with Compliance.

This dissertation contributes to the theoretical foundations of robotic bipedal locomotion and advances the experimental state of the art as well. On the theoretical side, a mathematical formalism for designing provably stable, walking and running gaits in bipedal robots with compliance is presented. A key contribution is a novel method of force control in robots with compliance. The theoretical work is validated experimentally on MABEL, a planar bipedal testbed that contains springs in its drivetrain for the purpose of enhancing both energy efficiency and agility of dynamic locomotion. While the potential energetic benefits of springs are well documented in the literature, feedback control designs that effectively realize this potential are lacking. The methods of virtual constraints and hybrid zero dynamics, originally developed for rigid robots with a single degree of underactuation, are extended and applied to MABEL, which has a novel compliant transmission and multiple degrees of underactuation. A time-invariant feedback controller is designed such that the closed-loop system respects the natural compliance of the open-loop system and realizes exponentially stable walking gaits. A second time-invariant feedback controller is designed such that the closed-loop system not only respects the natural compliance of the open-loop system, but also enables active force control within the compliant hybrid zero dynamics and results in exponentially stable running gaits. Several experiments are presented that highlight different aspects of MABEL and the feedback design method, ranging from basic elements such as stable walking, robustness under perturbations, energy efficient walking to a bipedal robot walking speed record of 1.5 m/s (3.4 mph), stable running with passive feet and with point feet. On MABEL, the full hybrid zero dynamics controller is implemented and was instrumental in achieving rapid walking and running, leading upto a kneed bipedal running speed record of 3.06 m/s (6.8 mph).Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/89801/1/koushils_1.pd