Abstract
This paper presents a set of fundamental properties of the velocity of a snake robot conducting lateral undulation on a planar surface. In particular, the derived properties state that the average forward velocity of the snake robot 1) is proportional to the squared amplitude of the sinusoidal motion of each joint of the robot, 2) is proportional to the angular frequency of the sinusoidal motion of each joint, 3) is proportional to a particular function of the constant phase shift between the joints, and 4) is maximized by the phase shift between the joints that also maximizes the particular phase shift function. The paper presents simulation results that support the validity of the derived properties