Toward a Coherent Framework for the Control of Planar Biped Locomotion

Toward a Coherent Framework for the Control of Planar Biped Locomotion by Eric R. Westervelt Co-Chairs: Jessy W. Grizzle and Daniel E. Koditschek Planar, underactuated, biped walkers form an important domain of application for hybrid dynamical systems. This dissertation presents the design of controllers that induce exponentially stable dynamic walking for general planar biped robots that have one degree of freedom greater than the number of available actuators during the single support phase. The within-step control action creates an attracting invariant set—a two-dimensional zero dynamics submanifold of the full hybrid model—whose restriction dynamics admits a scalar linear time invariant return map. Exponentially stable periodic orbits of the zero dynamics correspond to exponentially stabilizable orbits of the full model. Thus, walking controllers may be designed via the two-dimensional zero dynamics. A convenient parameterization of the hybrid zero dynamics is imposed through the choice of a class of output functions. Parameter optimization is used to tune the hybrid zero dynamics in order to achieve closed-loop, exponentially stable walking with low energy consumption, while meeting natural kinematic and dynamic constraints. Two additional control features are developed: 1) the ability to compose controllers that induce walking at a fixed average walking rate to obtain walking at several, discrete average walking rates with guaranteed stability during the transitions; and 2) the ability to regulate the average walking rate to a continuum of values. The general theory developed in the dissertation is experimentally verified on a five-link prototype walker, consisting of a torso and two legs with knees. c © Eric R. Westervelt 2003 All Rights Reserved In loving memory of my grandmother, Annette Focarelli.