Locomotion is the means by which systems use internal shape changes to move through the world, and is one of the most fundamental actions performed by robots and living organisms.
Geometric mechanics is the application of differential geometry to problems in classical mechanics. By studying locomotion with geometric tools, we can make rigorous statements about systems’ motion capabilities.
The three-link kinematic snake, shown in the image, propels itself by using shape changes (changes to the internal joint angles) to push against the passive wheels on the links. These wheels act as nonholonomic constraints that prevent lateral translation while allowing free longitudinal and rotational motion of each link. Using the framework of geometric mechanics, this locomotory effect can be quantified and qualified, leading to the identification of patterns of motion that produce a desired net displacement.
This project focuses on two aspects of geometric mechanics in locomotion: improving approachability of the material to non-specialists and optimally choosing the coordinates used in these analyses.