The Mechanics and Control of Undulatory Robotic Locomotion

Jim Ostrowski, Mechanical Engineering, California Institute of Technology

In this dissertation, we examine the problem of undulatory robotic locomotion within the framework of mechanical systems with nonholonomic constraints and symmetries. Using tools from geometric mechanics, we study the underlying structure found in general problems of locomotion. In doing so, we decompose locomotion into two basic components: internal shape changes and net changes in position and orientation. This decomposition has a natural mathematical interpretation in which the relationship between shape changes and locomotion can be described using connections on trivial principal fiber bundles. We demonstrate how the Lie group symmetries which are present across many forms of locomotion can be used to reduce the governing equations necessary to describe these types of problems. We show that the presence of symmetries can be used to reduce the necessary calculations to simple matrix manipulations. Furthermore, the use of connections leads us naturally to methods for testing controllability and for developing intuition regarding the generation of various locomotive gaits. As such, we explore the application of this theory to several examples, including the snakeboard and Hirose snake robot.