Duality-Based Nonlinear Quadratic Control: Application to Mobile Robot Trajectory-Following

Abstract

Leopoldo Armesto; Girbés, V.; Sala, A.; Miroslav Zima; Václav mídl (2015). Duality Abstract-This paper presents non-iterative linearization-based controllers for nonlinear unconstrained systems, coined as Extended Rauch-Tung-Striebel (ERTS) and Unscented RauchTung-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 in order 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 iLQR 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). The paper validates ERTS controller with an experiment of a Pioneer 3DX mobile robot. I. INTRODUCTIONOptimal control is widely used in control practice due to its advantages regarding the individual tuning of actuator amplitudes and control goals for each output, with wellknown solutions for the linear case, both unconstrained (LQR) and constrained [1], [2]. However, it is limited to a narrow spectrum of applications because many systems in practice are inherently nonlinear. Nonlinear optimal control strategies are computationally more demanding, see [3]-[5] for some modelbased approaches to handling it.The goal of model-based optimal control is designing a stabilizing control while minimizing a given performance criterion, usually in a quadratic form, assuming a deterministic plant model is available. Closed-loop solutions can not be found analytically in a general nonlinear case since it involves obtaining the solution of the corresponding Hamilton JacobiBellman equations [6]. One approach to avoid this problem is the iterative solution of a finite-horizon optimal control problem for a given state with a receding horizon implementation; control approaches using this strategy are referred to as model predictive control (MPC,[1]) and nonlinear model predictive control (NMPC,[5]). These approaches can deal with the unconstrained and constrained problems, where both states and control inputs must satisfy particular conditions. MPC is restricted to quadratic cost functions, linear systems and linear constraints, while NMPC can optimize non-quadratic

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