Global Saturated Regulator with Variable Gains for Robot Manipulators
Abstract
In this paper, we propose a set of saturated controllers with variable gains to solve the regulation problem for robot manipulators in joint space. These control schemes deliver torques inside the prescribed limits of servomotors. The gamma of variable gains is formed by continuous, smooth, and differentiable functions of the joint position error and velocity of the manipulator. A strict Lyapunov function is proposed to demonstrate globally asymptotic stability of the closed-loop equilibrium point. Finally, the functionality and performance of the proposal are illustrated via simulation results and comparative analysis against Proportional-Derivative (PD) control scheme on a two-degrees-freedom direct-drive robot manipulator.
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B. Sánchez-García, E. Rodríguez-Hernández, F. Reyes-Cortés, B. Al-Hadithi and O. Felix-Beltrán, “Desing and implementation of saturated regulators with variable gains for robot manipulators”, Devolvement with mechatronics fucus, Cap. 9, vol. 1, pp. 113–130, 2020.
F. Reyes-Cortes, Robotics: Control of robot manipulators, 1st ed., vol. 1. Grupo editor Alfa Omega, 2011, pp. 331-335.
R. Kelly, V. Santibáñez and F. Reyes-Cortés, “On a saturated-proportional derivative feedback with adaptive gravity compensation of robot manipulators,” International Journal of Adaptive Control and Signal Processing, vol. 10, pp. 465-479, 1996.
V. Santibáñez and R. Kelly, “Global regulation for robot manipulators under SP-SD feedback”, IEEE International Conference on Robotics and Automation, vol. 1, pp. 927-932, 1996.
V. Santibáñez, R. Kelly and F. Reyes-Cortés, “A new set-point controller with bounded torques for robot manipulators”, IEEE Transactions on Industrial Electronics, vol. 45, no. 1, 1998.
D. Lopéz-Araujo, A. Zavala-Rio, V. Santibáñez and F. Reyes-Cortés,” An SP-SD-type global adaptive tracking for robot manipulators with bounded torques”, XV1 Congreso latinoamericano de Control Automático, pp. 791-797, 2014.
V. Santibáñez and R. Kelly, “A class of nonlinear PID global regulators for robot manipulators”, IEEE International Conference on Robotics and Automation, vol 4, pp. 3601-3606, 1998.
D. Sun, S. Hu, X. Shao and C. Liu, “Global stability of a saturated nonlinear PID controller for robot manipulators” IEEE Transactions on Control Systems Technology, vol. 17, no. 4, pp. 892-899, 2009.
M. Takegaki and S. Arimoto, “A new feedback method for dynamic control of manipulators”, ASME Journal Dynamic System Measuring Control (103), pp. 119-125, 1981.
F. Reyes-Cortés, J. Barahona and L. Espinosa, “Trigonometric saturated controller for robot manipulators”, 2nd WSEAS International Conference on Instrumentation Measurement Control Circuits and Systems, pp. 356-362, 2002.
F. Reyes-Cortés, L. Espinosa and J. Barahona, “Family of saturated controllers for robot manipulators”, IASTED International Conference on Control and Applications, pp. 250-255, 2002.
F. Reyes-Cortés, J. Cid, M. A. Limón and M. Cervantes, “Square root-type control for robot manipulators”, International Journal of Advance Robotic Systems, vol. 10, no. 39, pp. 1-7, 2013.
F. Reyes-Cortés, O. Felix-Beltrán, J. Cid and G. Alonso, “A family of hyperbolic-type control schemes for robot manipulators”, Kybernetika, vol. 55, no. 3, pp. 561-585, 2019.
R. Kelly, R. Haber, R. Haber-Guerra and F. Reyes-Cortés, “Lyapunov stable control of robot manipulators: A fuzzy self-tuning procedure”, Intelligent Automation and Soft Computing, vol. 5, no.4, pp. 313-326, 1999.
M. A. Llama, R. Kelly and V. Santibáñez, “A stable motion control system for robot manipulators via fuzzy self-tuning”, Fuzzy Sets and Systems, Elsevier, vol. 124, pp. 133-154, 2001.
J. L. Meza, V. Santibáñez, R. Soto and M. A. Llama, “Fuzzy self-tuning PID semiglobal regulator for robot manipulator”, IEEE Transactions on Industrial Electronics, vol 59, no. 6, pp. 2709-2717, 2012.
M. Van, X. Do and M. Mavrovouniotis,” Self-tuning fuzzy PID-nonsingular fast terminal sliding mode control for robust fault tolerant control of robot manipulators”, ISA Transactions, Elsevier, no. 96, pp. 60-68, 2019.
K. Zhang and X. An, “Design of multivariable self-tuning PID controllers via quasi-diagonal recurrent wavelet neural network”, Second International Conference on Intelligent Human-Machine Systems and Cybernetics, pp. 95-99, 2010.
S. Al-Khayyt, “Tuning PID Controller by neural network for robot manipulators trajectory tracking”, Al-khwarizmi Engineering Journal, 2013, vol. 9, no.1, pp. 19-28, 2013.
N.Jaisumroum, P.Chotiprayanakul and S. Limnararat, “Self-tuning control with neural network for robot manipulator”, 16th International Conference on Control Automation and Systems (ICCAS), pp. 1073-1076, 2016.
H. Nohooji, “Constrained neural adaptive PID control for robot manipulators”, Journal of the Franklin Institute, Elsevier, vol. 357, no. 7, pp. 3907-3923, 2020.
F. Reyes-Cortés and B. Al-Hadithi, “An asinh-type regulator for robot manipulators with global asymptotic stability”, Automatika, vol.61, no.4, pp. 574-586, 2020.
R. Kelly and R. Carelli, “A class a of nonlinear PD-type controllers for robot manipulators”, Journal of Robotic Systems, vol. 13, no 12, pp.793-802, 1996.
F. Reyes-Cortés, J. Cid, and C. Campuzano, “Development of an experimental platform with open architecture for robot manipulators”, IAESTED International Conference Modeling and Simulation, pp. 77-81, 1999.
F. Salas, V. Santibáñez and M. A. Llama, “Variable gains PD tracking control for robot manipulators: Satability analysis and simulation”, World Automation Congress, IEEE, pp. 1-6, 2012.
J. Sifuentes, J. L. Meza, “A global asymptotic stable quasi variable PID regulator for robot manipulators”, Congreso Nacional de Control Automático, pp. 233-238, 2012.
O. Ramos, F. Reyes-Cortés, M. A. Vargas and S. Vergara, “Variable control gains for PD controller for robot manipulators”, 2015 International, Conference on Mechatronics Electronics and Automotive Engineering, pp- 187-192, 2015.
M. A. Limón-Diaz, F. Reyes-Cortés and E. González-Galván, “Unbounded regulators with variable gains for a direct-drive robot manipulator”, Automaika: Journal for control Mensurament Electronics Computing and Communications, Kprema IFAC, vol. 57, no.2, pp. 484-495, 2016.
M. A. Limón-Diaz, F. Reyes-Cortés and E. González-Galván, “Saturated regulation with derivative gain for robot manipulators”, Revista Iberoamericana de Automática e Informática Industrial, RIAI Elsevier, no. 14, pp. 434-445, 2017.
F. Reyes-Cortés and R. Kelly, “Experimental evaluation of model-based controllers on a direct-drive robot arm”, Mechatronics 11, 2000 Elsevier Science, pp. 267-282, 2001.
R. Kelly, V. S. Davila, and A. Loria, “Control of robot manipulators in joint space”, Advanced Textbooks in Control and Signal Processing, 2005.
DOI: https://doi.org/10.18196/jrc.26139
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Copyright (c) 2021 Brandon Erick Sanchez, Fernando Reyes, Basil Al-Hadithi, Ernesto Rodriguez
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