Scales and Locomotion: Non-Reversible Longitudinal Drag
This work addresses a gap in geometric mechanics for robotics and biology by modeling non-reversible drag from scales, but it is incremental as it focuses on foundational groundwork without direct applications.
The paper tackled the problem of understanding how snake scales affect locomotion by introducing a geometric model for a single-joint undulating system with scales, treating them as inducing a Finsler metric on the configuration space to lay groundwork for future research.
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.