Geometric Phases and Robotic Locomotion
Scott D. Kelly and Richard M. Murray
J. Robotic Systems, 12(6):417-431, 1995
CDS Technical Report 94-014
Robotic locomotion is based in a variety of instances 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. This is true for legged
robots, snakelike robots, and wheeled mobile robots undertaking maneuvers such as parallel
parking. In this paper we explore the use of tools from differential geometry to model and
analyze this class of locomotion mechanisms in a unified way. In particular, we describe
locomotion in terms of the geometric phase associated with a connection on a principal
bundle, and address issues such as controllability and choice of gait. We also provide an
introduction to the basic mathematical concepts which we require and apply the theory to
numerous example systems.
CDS
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Richard Murray (murray@cds.caltech.edu)
Last modified: Tue Aug 30 07:42:21 2005