This research studies the geometric aspects of motion generation and control for a large class of locomotion systems involving cyclic internal shape changes (often called undulatory). Particular emphasis is placed on the geometry and dynamics of robotic swimming motions, with models derived from the basic locomotion mechanisms found in eels, fish, and paramecia. This requires investigating continuous (in terms of shape and actuation) dynamic systems and addressing the associated design and control theoretic challenges. Optimal control theory is also employed to study both the optimality of gaits found in biological systems and to design more efficient forms of aquatic robotic locomotion. Swimming robotic mechanisms offer many potential advantages over rotor-driven devices, including increased efficiency, flexibility, and agility, and can be used in underwater search and rescue to enter areas that are not easily accessible by traditional vehicles. In this work, theoretical results will be tightly coupled with experimental verification and the development of robotic systems. This research also builds a foundation for future work in areas such as dynamic analyses of biological gaits and group swimming patterns, underwater surveillance and detection, and micro- locomotion. A long-term goal of this research is to fabricate locomotion devices on the cellular biological scale using MEMS technology.
