title: A study of snake-like locomotion through the analysis of a flexible robot model.
abstract: We examine the problem of snake-like locomotion by studying a system consisting of a planar inextensible elastic rod with adjustable spontaneous curvature, which provides an internal actuation mechanism that mimics muscular action in a snake. Using a Cosserat model, we derive the equations of motion in two special cases: one in which the rod can only move along a prescribed curve, and one in which the rod is constrained to slide longitudinally without slipping laterally, but the path is not fixeda priori(free-path case). The second setting is inspired by undulatory locomotion of snakes on flat surfaces. The presence of constraints leads in both cases to non-standard boundary conditions that allow us to close and solve the equations of motion. The kinematics and dynamics of the system can be recovered from a one-dimensional equation, without any restrictive assumption on the followed trajectory or the actuation. We derive explicit formulae highlighting the role of spontaneous curvature in providing the driving force (and the steering, in the free-path case) needed for locomotion. We also provide analytical solutions for a special class of serpentine motions, which enable us to discuss the connection between observed trajectories, internal actuation and forces exchanged with the environment.
authors.affiliation: SISSA , International School for Advanced Studies , via Bonomea 265, 34136 Trieste, Italy.
authors.forename: Giancarlo
authors.initials: G
authors.lastname: Cicconofri
authors.affiliation: SISSA , International School for Advanced Studies , via Bonomea 265, 34136 Trieste, Italy.
authors.forename: Antonio
authors.initials: A
authors.lastname: DeSimone
keywords: Cosserat rod models; bioinspired robots; limbless locomotion; snake locomotion; soft robotics; undulatory locomotion