Control of Locomotion with Shape-Changing Wheels

We present a novel approach to controlling the locomotion of a wheel by changing its shape, leading to applications to the synthesis and closed-loop control of gaits for modular robots. A dynamic model of a planar, continuous deformable ellipse in contact with a ground surface is derived. We present two alternative approaches to controlling this system and a method for mapping the gaits to a discrete rolling polygon. Mathematical models and dynamic simulation of the continuous approximation and the discrete n-body system, and experimental results obtained from a physical modular robot system illustrate the accuracy of the dynamic models and the validity of the approach.