Extended Rauch-Tung-Striebel controller

This paper presents a novel controller for nonlinear unconstrained systems, coined as Extended Rauch-Tung-Striebel (ERTS) controller. The controller is derived from a general framework based on the duality between optimal control and estimation established by Todorov. The proposed controller uses Rauch-Tung-Striebel smoother that predicts (filters) future states by linearizing the nonlinear system around predicted states and then applies a backward smoothing. The new controller is applied to solve path following problems of non-holonomic vehicles and compared with the standard LQR controller linearizing the model around the desired trajectory and the iterative LQR (iLQR) controller. The main advantages of ERTS controller with respect to the alternative techniques are good control performance and computational efficiency.