Paper abstract

 Title:  Geometric Perspectives on the Mechanics and Control of
         Robotic Locomotion
 Authors:  Jim Ostrowski and Joel Burdick
 In:   Preprints of the 7th Int. Symp. on Robotics Research,
       Herrsching Germany, 1995.

ABSTRACT:

This paper uses geometric methods to study basic problems in locomotion. We consider in detail the case of ``undulatory locomotion,'' which is a type of locomotion that is generated by a coupling of internal shape changes to external nonholonomic constraints. We show that such locomotion can be modeled as a connection on a principal fiber bundle. The properties of connections allow us to establish simplified results for both the dynamics and controllability of locomotion systems. Using recent results from geometric mechanics, we introduce a special form the dynamical equations of motion which takes into account the kinematic constraints and dynamic symmetries that are inherent to problems of locomotion. We also consider the issue of controllability. We demonstrate the utility of this approach on two examples: a novel ``Snakeboard'' and a multi-segmented serpentine robot which is modeled after Hirose's Active Cord Mechanism.