Traveling Wave Locomotion of Snake Robot along Symmetrical and Unsymmetrical body shapes

In this paper, kinematics and dynamics of traveling wave locomotion of a snake robot with two types of body shapes are developed. The body shape, also called body curve, is the actual geometrical shape in the plane in which the robot can assume during its progression. The snake can then travel along this curve. Two types of body curves, symmetrical and unsymmetrical, have been introduced for creeping locomotion, in horizontal plane. Kinematics and dynamic of traveling wave with symmetrical body curve has also been developed. These concepts are applied and kinematics and dynamics for traveling wave in vertical plane with unsymmetrical body shapes are obtained. In kinematics section, we first determine the joint relative angles using the body shape and curvature function. Next, position, velocity and acceleration of each link as well as center of gravity of the snake body are calculated. In Dynamic's section, force diagram of the i(exp th) link is shown. Using Newton principle, relative motion of the i(exp th) link with respect to the (i+1)(exp th) link is determined. Next, effects of friction coefficient, initial winding angle and the unsymmetrical factor on the joint torques are investigated. Results indicate that as the winding angle increases, joint torques decreases. Additionally, it is shown that the unsymmetrical factor, k, does not significantly affect torques. Finally, to validate our analysis, traveling wave locomotion is simulated in both Webots as well as MATLAB. It is shown that the traveling wave locomotion for both symmetrical and unsymmetrical body shapes is realized.