This paper considers the lateral undulation motion of snake robots. The first contribution of the paper is a model of lateral undulation dynamics developed for control design and stability analysis purposes. The second contribution is an analysis of the simplified model that shows that any asymptotically stabilizing control law for the snake robot to an equilibrium point must be time varying. Furthermore, the analysis shows that a snake robot (with four links) is strongly accessible from almost any equilibrium point, except for certain singular configurations, and that the robot does not satisfy sufficient conditions for small-time local controllability. The third contribution is based on using averaging theory to prove that the average velocity of the robot during lateral undulation will converge exponentially fast to a steady-state velocity which is given analytically as a function of the gait pattern parameters. From the averaging analysis, we also derive a set of fundamental relationships between the gait parameters of lateral undulation and the resulting forward velocity of the snake robot. The paper presents simulation results and results from experiments with a physical snake robot that support the theoretical findings.

Nature has always inspired engineers. This research tries to understand the contribution of snake anatomy in its locomotion from engineering point of view to be adopted in the design of snake robots. Rib design and muscular structure of snake robots will have a great impact on snake robot flexibility, weight, and actuators' torque. It will help to eliminate wheels in snake robots during serpentine locomotion. The result of this research shows that snakes can establish the required peg points on smooth surfaces by deflecting the body and ribs. The results are verified by both field observations and simulation.