Abstract
We seek to formulate control and motion planning algorithms for a class of dynamic robotic locomotion systems. We consider mechanical systems that involve some type of interaction with the environment and have dynamics that possess rotational and translational symmetries. Research in non-holonomic systems and geometric mechanics has led to a single, simplified framework that describes this class of systems. In this paper, we explore a hybrid systems approach to generating motion plans for systems of this type. We perform a dynamic analysis of the system to find a small set of periodic control inputs for momentum generation in desired directions. We then find a simplified, kinematic model which captures the fundamental nature of the locomotion system and we use this abstract model for motion planning. This approach is inherently modular, since broad classes of locomotion systems can be described by the same kinematic approximation. In this paper, we describe the application of such an approach to two examples: the snakeboard robot and an eel-like, underwater robot.