Toward a formal framework for open -loop stabilization of rhythmic tasks.

Recent collaborations between engineers and biologists have led to the identification of a family of biologically-inspired control principles for legged locomotion. It was shown that the passive mechanical musculoskeletal system plays a crucial part in the control of legged locomotion. In fact, in some extreme cases the active control takes the form of a purely feed-forward excitation of this passive mechanical system. RHex---a highly dexterous autonomous hexapod robot---has demonstrated that task-level open-loop control can in fact give rise to exceptional performance over rough surfaces and may be the key to the eventual development of real world products. From an engineering point of view, open-loop controllers are very desirable solutions due to their significantly simpler structure which does not require sensors or related infrastructure. In essence, the ability to control legged locomotion by feed forward controllers brings ease of control---a feature typically attributed to wheeled vehicles---into the field of legged robotics. Unfortunately, to this date the design of open-loop controllers is still a black art in which the intuition of the researcher acts as the only design tool. This thesis marks the beginning of a formal framework to design and verify open-loop controllers for dynamical legged locomotion. To this end we consider a very simple open-loop controlled dynamical model---a clock driven 1-DOF hopper---to investigate the basic principles of open-loop control with the overarching goal of identifying sufficient (and hopefully necessary) conditions for stable locomotion. We present an analysis which allows us to study arbitrary excitation patterns. We discuss a computational algorithm for the design of open-loop controllers based on these analytic results. Furthermore, we introduce a family of hierarchical stride-to-stride adaptation laws that take advantage of this open-loop setup. Our numerical studies suggest that some key ideas discovered in this simple illustrative model indeed extend to a wide family of physically relevant setups.Ph.D.Applied SciencesElectrical engineeringSystems scienceUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/124713/2/3150238.pd