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

Abstract

A traveling wave rectilinear gait for elongated, continuous bodies is modeled as a cyclically-varying backbone curve. The gait shapes are represented as planar deviations relative to an average body curve and an associated, rigidly-attached body frame. Body-ground contact patterns and other geometric properties integral to computation of external forcing are conveniently defined with respect to this average body curve. Introducing a body-ground rolling friction model permits the controlled equations of motion to be derived in closed form. Incorporating a constant curvature into the average body realizes turning movements, and hence turning control. Repeated numerical integration of the system dynamics facilitates construction of a control-to-action mapping, characterizing steady system behavior with respect to the gait’s parameter space. The control-to-action map reduces this complex dynamical system to a kinematic unicycle model for which feedback tracking strategies are well understood. To illustrate its utility, it is applied in a trajectory planning and tracking framework for locomotion around obstacles. Using the framework, a robotic snake exercising the traveling wave rectilinear gait successfully plans feasible trajectories and traverses non-trivial obstacle arrangements to reach specified goal positions.