Abstract
Model predictive control strategies refer to a set of methods relying on a process model to determine an optimal control signal by minimising a cost function. This paper reports on the application of predictive control strategies to a wheeled mobile robot. As a first step, friction forces originating from the motor gearboxes and wheels were estimated and a feedforward compensation was applied. Step response tests were then carried out to identify a linear model to design several simple control strategies, such as the Proportional-Integral-Derivative (PID) controller. The PID response constitutes the reference to assess the efficiency of two predictive control strategies: the generalised predictive control (GPC) and the linear quadratic model predictive control (LQMPC) algorithms. These control strategies were tested in simulation with Matlab and EasyDyn (a C++ library for multibody system simulations) and in real life experiments. All three control strategies offer satisfactory reference tracking but MPC allows a reduction of the energy consumption of up to 70 % as a result of set-point anticipation. LQMPC is the best in terms of input activity reduction.
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Lages, W.F., Kühne, F., Gomes da Silva Jr., J.M.: Model Predictive Control of a Mobile Robot Using Linearization. Proc. of the IEEE Mechatronics and Robotics 4, 525–530 (2004). Germany
Pacheco, L., Cufi, X., Luo, N.: Using Model Predictive Control for Local Navigation of Mobile Robots. Advanced Model Predictive Control, Dr. Tao ZHENG 1, 292–308 (2011)
Boucher, P., Dumur, D.: La Commande Prédictive, Méthodes et pratiques de l’ingénieur, Edition Technip, vol. 8, Paris (1996)
Bemporad, A., Borrelli, F., Morari, M.: Model Predictive Control Based on Linear Programming - The Explicit Solution. IEEE Transaction On Automatic Control 47(12), 1974–1985 (2002). doi:10.1109/TAC.2002.805688
Mayne, D.Q., Rawlings, J.B., Rao, C.V., Scokaert, P.O.M.: Constrained model predictive control: Stability and optiMality. Automatica (Elsevier) 36, 789–814 (2000)
Di Ruscio, D.: Model Predictive Control and optimization, Lecture notes, System and Control Engineering, Department of Technology, Telemark University College (2010)
Rossiter, J.A.: Model-Based Predictive Control: A Practical Approach, Taylor and Francis Group CRC Press (2003)
Clarke, D.W., Mohtadi, C., Tuffs, P.S.: Generalized predictive control - Part I. The basic algorithm. Automatica, Pergamon 23(2), 137–148 (1987)
Mosca, E.: Optimal, Predictive and Adaptive Control. Prentice-Hall, Inc (1995)
Rossiter, J.A.: Videos on modelling, control and analysis: Model Predictive Control, University of Sheffield: Department of Automatic Control and System Engineering. https://sites.google.com/a/sheffield.ac.uk/video-lectures-on-modelling-analysis-and-control/ (2014)
Scokaert, P.O.M., Rawlings, J.B.: Infinite horizon linear quadratic control with constraints. In: Proceedings, IFAC World Congress, pp. 109–114, San Francisco (1996)
Verlinden, O., Kouroussis, G., Conti, C.: EasyDyn: a framework based on free symbolic and numerical tools for teaching multibody systems. In: ECCOMAS Thematic Conference Multibody Dynamics 2005, Madrid, Spain, pp. 21–24 (2005)
MATLAB Release: The Mathworks, Inc., Natick, Massachusetts, United States (2011a)
Verlinden, O., Ben Fékih, L., Kouroussis, G.: Symbolic generation of the kinematics of multibody systems in EasyDyn: From MuPAD to Xcas/Giac. Theor. Appl. Mech. Lett. 3, 013012 (2013). doi:10.1063/2.13013012
Gwanghun, G.: Vehicle dynamic simulation with a comprehensive model for pneumatic tires, PhD Thesis, University Libraries, University of Arizona (1988)
Renotte, C., Vande Wouwer, A., Remy, M.: A Simple Frequency Domain Approach to the Tuning of PID Controllers - Design of an Interactive Software Tool. Journal A. Benelux Quaterly Journal on Automatic Control 42(3), 23–27 (2001)
Gilbert, E.G., Tan, K.T.: Linear systems with state and control constraints: the theory and application of maximal output admissible sets. IEEE Trans. Autom. Control 36(9), 1008–1020 (1991). doi:10.1109/9.83532
Kerrigan, E.C., Maciejowski, J.M.: Invariant sets for constrained nonlinear discrete-time systems with application to feasibility in model predictive control, Conference on Decision and Control (2000)
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Huynh, H.N., Verlinden, O. & Vande Wouwer, A. Comparative Application of Model Predictive Control Strategies to a Wheeled Mobile Robot. J Intell Robot Syst 87, 81–95 (2017). https://doi.org/10.1007/s10846-017-0500-2
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DOI: https://doi.org/10.1007/s10846-017-0500-2