Geometric Phases and Robotic Locomotion

Scott Kelly, Mechanical Engineering, Caltech

Robotic locomotion is often based upon cyclic changes in the shape of a robot mechanism. Certain variations in shape exploit the constrained nature of a robot's interaction with its environment to generate net motion. Tools from the geometry of trivial principal fiber bundles, in particular the notion of holonomy, lend themselves to an insightful formulation of the modeling and control of locomotion systems. This talk will provide an overview of the mathematics leading up to several characterizations of controllability, peppered with sample calculations for a variety of physical systems.