Many animals and robots move through the world by coupling cyclical changes in shape called gaits to an interaction with the environment. Because mobility is an important aspect of such robots, a key metric when evaluating design and performance of mobile robots is the efficiency of their optimal gaits. The major contribution of this thesis is a set of geometric principles for understanding the geometry of optimal gaits for drag-dominated kinematic systems. We demonstrate these principles on a variety of system geometries (including Purcell's swimmer) and for optimization criteria that include maximizing displacement and efficiency of motion for both translation and turning motions. We also demonstrate how these principles can be used to simultaneously optimize a system's gait kinematics and physical design.
We present an analysis of how the shape of these optimal gaits are altered by the presence of passive elements like springs. We use frequency domain analysis to relate the motion of the passive joint to the motion of the actuated joint. We couple this analysis with elements of the geometric framework introduced in our first contribution, to identify speed-maximizing and efficiency-maximizing gaits for drag-dominated swimmers with a passive elastic joint.