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(eng): This paper presents noniterative linearization-based controllers for nonlinear unconstrained systems, coined as extended Rauch–Tung–Striebel (ERTS) and unscented Rauch–Tung–Striebel (URTS) controllers, derived from the duality between optimal control and estimation. The proposed controllers use a Rauch–Tung–Striebel forward–backward smoother as an state estimator to compute the original optimal control problem. The new controllers are applied to trajectory-following problems of differential-drive mobile robots and compared with iterative linear quadratic regulator controller, nonlinear model predictive control, and approximate inference approaches. Simulations show that ERTS and URTS controllers produce almost optimal solutions with a significantly lower computing time, avoiding initialization issues in the other algorithms (in fact, they can be used to initialize them). This paper validates ERTS controller with an experiment of a Pioneer 3-DX mobile robot.