Abstract
In this paper, the problem of path following for underactuated snake robots is investigated by using approximate dynamic programming and neural networks (NNs). The lateral undulatory gait of a snake robot is stabilized in a virtual holonomic constraint manifold through a partial feedback linearizing control law. Based on a dynamic compensator and Line-of-Sight guidance law, the path-following problem is transformed to a regulation problem of a nonlinear system with uncertainties. Subsequently, it is solved by an infinite horizon optimal control scheme using a single critic NN. A novel fluctuating learning algorithm is derived to approximate the associated cost function online and relax the initial stabilizing control requirement. The approximate optimal control input is derived by solving a modified Hamilton-Jacobi-Bellman equation. The conventional persistence of excitation condition is relaxed by using experience replay technique. The proposed control scheme ensures that all states of the snake robot are uniformly ultimate bounded which is analyzed by using the Lyapunov approach, and the tracking error asymptotically converges to a residual set. Simulation results are presented to verify the effectiveness of the proposed method.