The Theory of Tetrapod Locomotion on Granular Substrates

Abstract

We need robots to extend our reach into dirty and dangerous environments. To do so, mobile robots must be able to locomote in messy unstructured terrains. Conventional mobile robots have not begun to display the multi-functionality of organisms that inhabit natural terrains. This is because mobile robots have been created in, and their models mainly validated on, clean hard laboratory floors, whereas biological organisms have evolved to contend with heterogeneous, dirty and unpredictable environments. One important example of such real world complex terrain, often overlooked by our community despite its ubiquity, involves loose granular materials commonly found in deserts, disaster sites, containers, and caves. Therefore creation of the next level of mobility to traverse dirty environments requires simultaneous advances in both robotics and physics, particularly regarding the interactions associated with desired behaviors.

The proposed work is built on a foundation of geometric mechanics, granular physics of intrusion and biological inspiration from desert-dwelling snakes. We use geometric mechanics, a field that applies principles from differential geometry to problems in classical mechanics, to design gaits for biologically inspired robots. We bring the benefits of the geometric tools to bear on granular environments: in even these mathematically "messy" systems, we can begin to efficiently analyze gaits. The key concept in this effort is that systems with complicated, nonlinear low-level physics often exhibit much "cleaner" high-level motion, often approximated by a kinematic relationship. Development of such high-level motion controllers will be aided by our ability to discover basic biological principles of locomotion in granular media. We will therefore develop computationally efficient analysis tools for granular materials and will develop techniques to study the locomotion of systems on the surface of granular media.