Path Following Control of a Planar Snake Robot with an Exponentially Stabilizing Joint Control Law

This paper considers the problem of path following control of a planar snake robot without sideslip constraints. We use Lagrangian mechanics to derive the dynamical equations of motion of the system. The possibility of controlling the orientation of the robot in the absence of external dissipative forces is investigated. An exponentially stabilizing joint control law for the actuated shape dynamics of the robot is presented. We analytically design a guidance-based path following control law for the snake robot, and we show that the trajectories of the heading error dynamics are ultimately bounded with a bound that can be made arbitrarily small. The efficiency of the control design is shown with simulations.