Optimal control of a planar robot manipulator based on the Linear Quadratic Inverse-Dynamics design


To ensure the correct positioning of the end-effector of robot manipulators is one of the most important objectives of the robotic systems control. Lack of reliability in tracking the reference trajectory, as well as in the desired final positioning compromises the quality of the task to be performed, even causing accidents. The purpose of this work was to propose an optimal controller with an inner loop based on the dynamic model of the manipulator and a feedback loop based on the Linear Quadratic Regulator, in order to ensure that the end effector is in the right place, at the right time. The controller was compared to the conventional PID, presenting better performance, both in the transient response, eliminating overshoot, and steady-state, eliminating the stationary error.


BAGHLI, F.; BAKKALI, L. E.; LAKHAL, Y.; NASRI, A.; GASBAOUI, B. Arm manipulator position control based on multi-input multi-output PID strategy. Journal of Automation, Mobile Robotics & Intelligent Systems, PIAP - Industrial ResearchInstitute for Automation and Measurements, v. 8, n. 2,p. 36–39, apr 2014.

CHATRAEI, A.; ZÁDA, V. Global optimal feedback-linearizing control of robot manipulators. Asian Journal of Control, Wiley, v. 15, n. 4, p.1178–1187, nov 2012.

CHEN, Y.; MA, G.; LIN, S.; NING, S.; GAO, J. Computed-torque plus robust adaptive compensation control for robot manipulator with structured and unstructured uncertainties. IMA Journal ofMathematical Control and Information, OxfordUniversity Press (OUP), v. 33, n. 1, p. 37–52, jul 2014.

COSTA, T. L.; LARA-MOLINA, F. A.; JUNIOR,A. A. C.; TAKETA, E. Robust h∞computed torque control for manipulators. IEEE Latin America Transactions, Institute of Electrical and Electronics Engineers (IEEE), v. 16, n. 2, p. 398–407, Feb. 2018.

CRAIG, J. J.Introduction to Robotics: Mechanics and Control. 3. ed. [S.l.]: Pearson Prentice Hall, 2012.

DELAVARI, H.; GHADERI, R.; RANJBAR, A.;HOSSEINNIA, H.; MOMANI, S. Adaptive fractional pid controller for robot manipulator. In: The 4th FAC Workshop Fractional Differentiation and its Applications. Badajoz, Spain: FDA, 2012.

FATEH, M.; AZARGOSHASB, S. Discrete time robust control of robot manipulators in the task space using adaptive fuzzy estimator. Journal of Artificial Intelligence and Data Mining, International DigitalOrganization for Scientific Information (IDOSI), v. 3,n. 1, 2015.

GRANT, C. P.Thoery of Ordinary Differential Equations. Utah: CreateSpace Independent Publishing Platform, 2007. ISBN 9781502911407.

HALL, A. C. The Analysis and Synthesis of Linear Servomechanisms. Tese (Doutorado), 1943.

HASAN, A. T. Under-actuated robot manipulator positioning control using artificial neural network inversion technique. Advances in Artificial Intelligence, Hindawi Limited, v. 2012, p. 1–6, 2012.

JAHED, A.; PILTAN, F.; REZAIE, H.; BOROOMAND, B. Design computed torque controller with parallel fuzzy inference system compensator tocontrol of robot manipulator. International Journal of Information Engineering and Electronic Business, MECS Publisher, v. 5, n. 3, p. 66–77, Sep. 2013.

KALMAN, R. E. Contributions to the theory ofoptimal control. Bol. Soc. Mexicana, p. 102–119,1960.

KHAIRUDIN, M.; MOHAMED, Z.; HUSAIN, A. R. Dynamic model and robust control of flexible link robot manipulator. TELKOMNIKA (Telecommunication Computing Electronics and Control), Universitas Ahmad Dahlan, v. 9, n. 2, p. 279, Aug. 2011.

KUMAR, E.; JEROME, J. Algebraic riccati equation based q and r matrices selection algorithm for optimal lqr applied to tracking control of 3rd order magnetic levitation system. Archives of electrical engineering, v. 65, p. 151–168, 2016.

LAMMERTS, I. Adaptive computed reference computed torque control of flexible manipulators. Tese (Doutorado), 1993.

LEWIS, F.; M., D. D.; ABDALLAH, C.Robot Manipulator Control Theory and Practice. NewYork: Prentice-Hall, 1993.

MOOLAM, R. K. Dynamic Modeling and Control of Flexible Manipulators. Tese (Doutorado), 2013.
How to Cite
MOSCONI, Denis; SIQUEIRA, Adriano Almeida Gonçalves; FONSECA, Everthon Silva. Optimal control of a planar robot manipulator based on the Linear Quadratic Inverse-Dynamics design. Journal of Mechatronics Engineering, [S.l.], v. 2, n. 2, p. 2 - 10, july 2019. ISSN 2595-3230. Available at: <http://jme.ojs.galoa.net.br/index.php/jme/article/view/25>. Date accessed: 21 oct. 2020. doi: https://doi.org/10.21439/jme.v2i2.25.