Locomotive, principally kinematic system of snakelike robot mathematical model with variable segment length

In this work, we focused on the principle of locomotion and its description using the formalism of geometric mechanics, applied to a specific robotic mechanism. By applying non-holonomic constraints to the mechanism, we know that the speed at which the entire system can move is sideways limited, but without changing the configuration environment. By expressing the language of differential geometry, the nonholonomic constraint is defined by the function on the system’s configuration tangent bundle TQ. Although the non-holonomic constraints prevent us from performing a certain type of movement, in the end it is still true that the mechatronic system can reach a defined point of the manifold $\mathcal{S}E(2)$ when performing a certain combination of possible movements. Among other things, the existing two types of configuration variables affecting the overall locomotion of the mechanism were presented in the work. The first type of configuration variables are the so-called shape variables and the second type are positional variables or also group variables. The work shows that the specific locomotion of a snake-like robot is the result of a suitable combination of changes in shape and position variables.