Snakes & Spiders, Robots & Geometry - Ross Hatton

Locomotion and perception are common threads between robotics and biology. Understanding these phenomena at a mechanical level involves nonlinear dynamics and the coordination of many degrees of freedom. In this talk, I will discuss geometric approaches to organizing this information in two problem domains: 1) Undulatory locomotion of snakes and swimmers; and 2) vibration propagation in spider webs.

In the first section, I will discuss how differential geometry and Lie Group Theory provide insight into the locomotion of undulating systems through a vocabulary of lengths, areas, and curvatures. In particular, a tool called the Lie Bracket combines these geometric concepts to describe the effects of cyclic changes in the locomotor’s shape, such as the gaits used by swimming or crawling systems. Building on these results, I will demonstrate that the geometric techniques are useful beyond the “clean” ideal systems on which they have traditionally been developed, and can provide insight into the motion of systems with considerably more complex dynamics, such as locomotors in granular media.