Modeling and optimal torque control of a snake-like robot based on the fiber bundle theory

For the snake-like robot with passive wheels, the side constraint force provides the required thrust which is less than the maximum static friction. Minimizing the side constraint force can reduce possibility of skidding which is important to ensure stable and efficient motion of the robot. In this paper we model the snake- like robot based on the fiber bundle theory. This method can reduce the complexity of the dynamics and derive the exact analytical solution for the side constraint force which is linear to the redundant torque. Using the linear relation, we can derive directly the optimal torque by minimizing the side constraint force. Additionally the nonholonomic constraint can be used for constructing the connection of the fiber bundle. Using the connection, we can select the gait of the snake-like robot. The position and orientation of the head can be described in terms of the special Euclidean group SE（2） which is also the structure group of the fiber bundle. Using the symmetry of the structure group, we can reduce the dynamics equations and derive the analytical solution for the side constraint force. Kinematics and dynamics simulations validate the proposed methods.