Robotic tasks with intermittent dynamics

Abstract

This thesis concerns the modeling, analysis, and synthesis of intermittent dynamical robotic tasks. The chief focus is the task domain of robot juggling, which was inspired by the success of Raibert's work in dynamically stable legged locomotion. My formal analysis of his elegant control strategy proves it to be correct when implemented on a simplified version of his one-legged hopping robot. This result and my subsequent work exploits the specific properties of periodic intermittent dynamical tasks, allowing for model and task encoding formulations which are parsimonious, expressive and suitable for analysis. A new family of purely feedback-based control laws--mirror algorithms--forms the basis of all juggling implementations. Local linear analysis establishes the correctness of the mirror algorithms for controlling a juggling task with one object. The intrinsic inability of this analysis to predict the domain of validity motivated the development of new analytical tools which derived from recent results in nonlinear dynamical systems theory. They narrow the gap between theory and practice and permit strong global predictions for a large class of discrete maps, including Raibert's hopper and a simple juggler. For implementation purposes, a planar juggling apparatus and a new associated distributed control computer tailored for general robotics applications was constructed. Experimental data validates the models and shows gratifying correspondence to the analytical predictions. The insight gained into intermittent dynamical robotic tasks led to the first successful implementation of a robot juggling and catching. Generalizations derived from this work promise to be applicable to other intermittent dynamical tasks as well.