Non-smooth 3D Modeling of a Snake Robot with Frictional Unilateral Constraints

A non-smooth 3D mathematical model of the dynamics of a snake robot (without wheels) is developed in this paper. The model is based on the framework of non-smooth dynamics and convex analysis which allows us to easily incorporate unilateral contact forces and friction forces based on Coulomb´s law of dry friction. Impact and stick-slip transitions are modeled as instantaneous. A numerical integrator on impulse- velocity level, the time-stepping method, is used for simulation, which helps avoid an explicit switch between equations of motion during simulation. Numerical results are presented for a snake robot with 26 degrees of freedom and 22 possible contact points along its body. Simulation results of the snake motion pattern ´lateral undulation´ are shown.