Model-based control and analysis of anthropomorphic walking.

Abstract

This dissertation proposes advanced feedback controllers that allow bipedal robots to perform anthropomorphic walking. The motion is confined to the sagittal plane and the robots possess at least two identical legs and a torso. Walking is composed of alternating single support and double support phases. A model of a planar, underactuated robot with point feet is extended in two ways to include two facets of walking with feet. An impulsive actuator is attached to the end of each leg to approximate the push-off observed in human walking just before double support is initiated and an additional link is attached to the end of the leg via a revolute joint with actuation to model a foot plus ankle during the single support phase. The robot with the impulsive actuator at each leg is modeled as an underactuated bipedal robot whose dynamics is governed by a set of Lagrangian differential equations during the single support phase. The double support phase is composed of two instantaneous subphases and described by an algebraic map. Key to the control-law design is the creation of a two-dimensional surface that is invariant under the Lagrangian dynamics and the combined impulsive forces from impact with the ground and the impulsive actuation. Simulation is conducted to show that the model with the impulsive action is more energy efficient than the robot without impulsive actuation. The robot model with the impulsive actuator is applied to study walking during load carrying, with the objective of partially explaining the extraordinary energy efficiency of women of the Luo and Kikyu tribes when carrying loads. A model of load carrying in the Luo style shows that the walking efficiency observed in these women is nearly energy optimal. Two models of walking with loads is proposed for an untrained group of walkers, and the results are compared to energy-optimal walking. It is found that with a light load, reducing energy consumption at the stance knee leads to a more energy efficient gait whereas reducing energy consumption at the hips is more beneficial when the load is heavy. The single support phase of a robot with feet and a revolute actuated ankle is composed of two subphases, each represented by sets of differential equations, and an instantaneous double support phase. The single support phase begins with a fully-actuated (flat-footed) phase followed by an underactuated (toe-rolling) phase. A two-dimensional invariant surface is created in each subphase. While the Zero Moment Point (ZMP) is applied to ensure that the stance foot does not rotate over the stance toe during the flat-footed phase, the stability of the robot's gait is proved using the Poincare return map on the invariant surfaces. A corollary of the analysis shows that the oft-used ZMP principle is not sufficient for a stable periodic orbit.