A New LQR Optimal Control for a Single-Link Flexible Joint Robot Manipulator Based on Grey Wolf Optimizer

Flexible manipulators are very commonly used in industries. In this paper a single-link flexible joint robot is modeled firstly by using Euler–Lagrange energy equation. An optimized Linear Quadratic Regulator is employed to control the manipulator. After that, a Linear Quadratic Regulator (LQR) controller is used for optimal control of the manipulator. For optimizing the LQR, the regulator term weighting of the LQR is achieved by using the newly introduced grey wolf optimizer technique. With the optimized LQR controller based on the proposed performance index, it is tried to have a system with the minimum overshoot and settling time. By considering the proposed performance index and comparing with the PSO-based controller as a popular algorithm, the superiority of the proposed LQR controller in improving the stability and performance of the manipulator is shown. The simulations are performed in MATLAB environment and the results confirm the efficiency of the proposed controller.

[1]  David Wang,et al.  Verification of a closed-loop shaped-input controller for a five-bar-linkage manipulator , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[2]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[3]  I. Schur,et al.  Neue Begründung der Theorie der Gruppencharaktere: Sitzungsberichte der Preussischen Akademie der Wissenschaften 1905, Physikalisch-Mathematische Klasse, 406 – 432 , 1973 .

[4]  Romeo Ortega,et al.  A class of output feedback globally stabilizing controllers for flexible joints robots , 1995, IEEE Trans. Robotics Autom..

[5]  Gene H. Golub,et al.  Matrix computations , 1983 .

[6]  Warren P. Seering,et al.  Three dynamic problems in robot force control , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[7]  Eckart Zitzler,et al.  Indicator-Based Selection in Multiobjective Search , 2004, PPSN.

[8]  Alin Albu-Schäffer,et al.  A Unified Passivity-based Control Framework for Position, Torque and Impedance Control of Flexible Joint Robots , 2007, Int. J. Robotics Res..

[9]  Zafer Bingul,et al.  PID and state feedback control of a single-link flexible joint robot manipulator , 2011, 2011 IEEE International Conference on Mechatronics.

[10]  An-Chyau Huang,et al.  Adaptive sliding control for single-link flexible-joint robot with mismatched uncertainties , 2004, IEEE Transactions on Control Systems Technology.

[11]  Navid Razmjooy,et al.  A New Meta-Heuristic Optimization Algorithm Inspired by FIFA World Cup Competitions: Theory and Its Application in PID Designing for AVR System , 2016 .

[12]  Romeo Ortega,et al.  An observer-based set-point controller for robot manipulators with flexible joints , 1993 .

[13]  Swinging-Up and Balancing Control of Double Furuta Pendulum by Using State-Dependent Riccati Equation , 2004 .

[14]  Eugene I. Rivin,et al.  Mechanical Design of Robots , 1987 .

[15]  Jurek Z. Sasiadek,et al.  Modeling and Direct Adaptive Control of a Flexible-Joint Manipulator , 2012 .

[16]  Rob Dekkers,et al.  Control of Robot Manipulators in Joint Space , 2005 .

[17]  Andrew Lewis,et al.  Grey Wolf Optimizer , 2014, Adv. Eng. Softw..

[18]  P. Tomei.  A simple PD controller for robots with elastic joints , 1991 .

[19]  Hoda A. ElMaraghy,et al.  Feedback linearization control of flexible joint robots , 1992 .

[20]  Hamid D. Taghirad,et al.  A SURVEY ON THE CONTROL OF FLEXIBLE JOINT ROBOTS , 2006 .