Shape-centric modeling of traveling wave rectilinear locomotion for snake-like robots

Abstract

A traveling wave rectilinear gait for elongated, continuous bodies is modeled as planar deviations along a baseline average body and with respect to an average body frame. This framework enables intuitive and convenient formulation of the gait as a cyclically-varying backbone curve as well as contact patterns and other elements of the model which are integral in computing external forcing. A rolling friction model is introduced to describe interactions with the environment. The equations of motion of the dynamical system are derived in closed form along with the steady-state velocity for a straight-line average body. We demonstrate that control objectives such as turning can be conveniently achieved by introducing a constant radius of curvature into the average body, without any change to the gait formulation.