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 fixed a 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.

Contest-Driven Soft-Robotics Boost: The RoboSoft Grand Challenge

“…This discipline is steeply growing, and from the seminal review paper of Trivedi et al (2008) the field was subject to several evolutions; to date, the most recent review paper on soft robotics (Rus and Tolley, 2015) identifies four possible application domains for soft robots: locomotion, manipulation, wearable, and soft cyborgs. This review agrees with our survey on the most relevant domains influenced by soft robotic, which identified three niches: (1) the terrestrial locomotion, where a great number of bio-inspired (Belanger et al, 2000;Mezoff et al, 2004;Lin et al, 2013;Umedachi et al, 2016) (inspired by worms, caterpillars, and their gaits) (Jayaram and Full, 2016) (insects) (Chrispell et al, 2013;Cicconofri and DeSimone, 2015) (snakes) or build from scratch robots (Kim et al, 2014;Li et al, 2016) are under development; (2) the underwater locomotion (Fiazza et al, 2010), mainly inspired by fishes (Clark et al, 2015), turtles (Song et al, 2016), crabs (Calisti et al, 2016), chephalopods (Arienti et al, 2013;Cianchetti et al, 2015), rays (Urai et al, 2015), or other aquatic animals; and (3) manipulation, either at the level of grippers (Manti et al, 2015;Fakhari et al, 2016;Shintake et al, 2016), arms Elango and Faudzi, 2015;Katzschmann et al, 2015;Deashapriya et al, 2016;Sun et al, 2016), or other devices (Deng et al, 2016).…”

Serpentine locomotion through elastic energy release

“…The presented theoretical results represent an extension and a clarification based on the concept of configurational force of the mathematical models introduced by Gray [1–3] and developed in several later contributions [5,7,13,15,30]. …”

“…Therefore, friction at the contact between the snake's skin and the ground is strongly orthotropic, as shown in [5–7]. The model considered in the present article can be viewed as the extreme situation of orthotropy in which longitudinal and transverse friction are, respectively, null and infinite.…”

Partial Constraint Singularities in Elastic Rods

“…respectively. Both of these equations are consequences of (12), which henceforth will be assumed to be valid. Note that (21) could also be obtained by splitting the kinematic quantities in (5) into invariant and non-invariant parts.…”