3-D Snake Robot Motion: Nonsmooth Modeling, Simulations, and Experiments

Abstract

A nonsmooth (hybrid) 3-D mathematical model of a snake robot (without wheels) is developed and experimentally validated in this paper. The model is based on the framework of nonsmooth dynamics and convex analysis that allows us to easily and systematically incorporate unilateral contact forces (i.e., between the snake robot and the ground surface) and friction forces based on Coulomb's law of dry friction. Conventional numerical solvers cannot be employed directly due to set-valued force laws and possible instantaneous velocity changes. Therefore, we show how to implement the model for numerical treatment with a numerical integrator called the time-stepping method. This method helps to avoid explicit changes between equations during simulation even though the system is hybrid. Simulation results for the serpentine motion pattern lateral undulation and sidewinding are presented. In addition, experiments are performed with the snake robot "Aiko" for locomotion by lateral undulation and sidewinding, both with isotropic friction. For these cases, back-to-back comparisons between numerical results and experimental results are given.

A survey on snake robot modeling and locomotion

“…109 However, a choice of minimal coordinates and a compliant contact force model renders the resulting set of equations of motion stiff and cumbersome to solve numerically. This is solved in parts by introducing nonminimal coordinates for a nonsmooth 3D model 110 where contact forces are modeled in a rigid-body setting and velocities are allowed to change instantaneously. This model is suited for simulation, but not for analytical considerations.…”

Modeling and path-following for a snake robot with active wheels

“…The nonsmooth model for simulation presented in this paper can be extended to describe 3-D motion. This can be achieved by, e.g., employing techniques developed for a simulation model of a 3-D snake robot without wheels in [14].…”

Pedundulatory robotic locomotion: Centipede and polychaete modes in unstructured substrates

“…When μ N /μ T 1, the undulatory system moves in the direction opposite to that of the wave propagation, so that forward propulsion is by retrograde (head-to-tail) body waves (see, e.g., [4], [9]- [12], [21]- [23]). By contrast, when μ N /μ T < 1, or when μ N /μ T 1 (as is the case in our system), the overall locomotion is along the body wave direction, so that forward motion is by direct (tail-to-head) waves (for analysis and relevant robotic implementations, see [1]- [3], [6], [8]). …”

“…These works consider purely undulatory robots, i.e., ones without parapodia, mostly investigating polychaetelike tail-to-head body undulations. Relevant work includes other research efforts on non-wheeled undulatory locomotion (e.g., [6]- [12]), as well as the salamander-like robot [13], which employs for land locomotion a standing body wave, combined with the coordinated movement of its four limbs.…”