Stepping Towards Control of Systems Undergoing Impact for Legged Locomotion

Abstract

This dissertation focuses on bringing control theory to mechanical systems subject to uni- lateral constraints, with the focus on legged locomotion. The key feature of these systems is the impact that occurs, causing a sudden change in the velocity of the object and a potential change in its underlying vector fields. The primary challenge for such systems arises from constraint activation, in other words, when a leg transitions from moving through the air to the ground. Throughout this dissertation, the dynamics are captured using the modelling paradigm of hybrid dynamical systems. In the language of hybrid dynamical systems, a reset occurs causing instantaneous change in the systems velocity. In addition, when a constraint activates or deactivates, the underlying vector field discontinuously changes. Such discontinuities violate continuity and smoothness assumptions many classical control techniques impose. This dissertation focuses on developing three aspects of control for legged locomotion: developing a control law about a desired trajectory undergoing simultaneous constraint activation, such as a pronk gait, determining the complete state, both discrete and continuous, of the system from noisy measurements, and finding a control law to track a desired trajectory through contact.