  Locomotion requires that an animal or robot be able to move itself forward
farther than it moves backward in each gait cycle (formally, that it be able to
break the symmetry of its interactions with the world). Previous work has
established that a difference between lateral and longitudinal drag provides
sufficient conditions for locomotion to be possible. The geometric mechanics
community has used this principle to build a geometric framework for describing
the effectiveness and efficiency of undulatory locomotion. Researchers in
biology and robotics have observed that structures such as snake scales
additionally provide a difference between forward and backward longitudinal
drag. As yet, however, the impact of scales on the geometric features relevant
to locomotion effectiveness and efficiency have not yet been explored. We
present a geometric model for a single-joint undulating system with scales and
identify the features needed to understand its motion. Mathematically, the
scales can be treated as inducing a "Finsler metric" on the configuration
space, and this paper lays the groundwork for further research into application
of such Finsler metrics to robotic locomotion.
