Sidewinding on slopes

Sidewinding is an efficient translation gait used by snakes over flat ground. When implemented on snake robots, it retains its general effectiveness, but becomes unstable on sloped surfaces. Flattening the sidewinding motion along the surface to provide a more stable base corrects for this instability, but degrades other performance characteristics, such as efficiency and handling of rough terrain. In this paper, we identify stability conditions for a sidewinder on a slope and find a solution for the minimum aspect ratio of the sidewinding pattern needed to maintain stability. Our theoretical results are supported by experiments on snake robots. In constructing our stability analysis, we present a new, tread-based model for sidewinding that is both consistent with previous models and provides new intuition regarding the kinematics of the gait. This new interpretation of sidewinding further admits a symmetry-based model reduction that simplifies its analysis. Additionally, an intermediate stage of the theoretical work contains a comprehensive analysis of the behavior of an ellipse in rolling contact with a sloped surface.