Robust trajectory tracking control of robotic manipulators based on model-free PID-SMC approach
Abstract
In this paper, a robust controller based on proportional-derivative control and sliding mode
control for trajectory tracking problem of a nonlinear robotic manipulator is presented. Actuator
dynamics is taken into account in tracking control simulations for verification of good precision
trajectory tracking. A low pass filter is employed for the elimination of chattering, high frequency
components, and noises. The proposed control scheme combines the simplicity feature of the
proportional-integral-derivative (PID) controller and the robustness feature of the sliding mode
control (SMC). There is no need to know the dynamic model of controlled systems, unlike most
robust controllers, and only the upper bound of the dynamic system is required in the proposed
method. Lyapunov’s stability method is used to prove robustness of the proposed controller for the
robot manipulator subjected to system uncertainties and external disturbance. The performance of
the proposed controller is simulated by MATLAB-Simulink environment and is compared with
other control schemes to verify its efficiency with various control methods commonly preferred in
robotic manipulators. Robustness tests of the proposed controller against uncertainties in robot and
actuator dynamics and external disturbance are illustrated.
References
Abdollahi, F., Talebi, H. & Patel, R. 2006. A stable neural network-based observer with application to
flexible-joint manipulators. IEEE Transactions on Neural Networks, 17: 118–129.
Amera, A.F., Sallamb, E.A. & Elawadyb, W. M. 2011. Adaptive fuzzy sliding mode control using supervisory
fuzzy control for 3 DOF planar robot manipulators. Applied Soft Computing, 11:4943–4953.
Bartolini, G., Ferrara, A., Usai, E. & Utkin, V.I. 2000. On Multi-input Chattering-free Second-order Sliding
Mode Control. IEEE Transactions on Automatic Control, 45:1711–1717.
Bingul, Z & Karahan, O. 2012. Fractional PID controllers tuned by evolutionary algorithms for robot
trajectory control. TurkJ Electr Eng ComputSci, 20:1123–36.
Chern, T.L. & Wu, Y.C. 1993. Design of brushless DC position servo systems using integral variable
structure approach. IEE Proc. Electr. Power Appl., 140:27–34.
Craig, J.J. 2005. Introduction to robotics: mechanics and control. Vol. 3, Pp. 48 - 70. Prentice Hall, Upper
Saddle River.
De, J.B. & Banens, J. 1994. Experimental evaluations of robot controllers. Proceedings of the 33rd conference
on decision and control, Lake Buena Vista, Fl, USA, 363–368.
Debbarma, S., Saikia L. & Sinha, N. 2014. Automatic generation control using two degree of freedom
fractional order PID controller. Electr Power Energy Syst., 58:120–129.
Dehghan, S.A., Danesh, M., Sheikholeslam, F. & Zekri, M. 2015. Adaptive force–environment estimator
for manipulators based on adaptive wavelet neural network. Applied Soft Computing, 28:527–540.
Eker, I. 2006. Sliding mode control with PID sliding surface and experimental application to an
electromechanical plant. ISA Trans., 45:109–118.
Fallaha, C.J., Saad, M., Kanaan, H.Y. & Kamal, A. H. 2011. Sliding-mode robot control with exponential
reaching law. IEEE Trans. Ind. Electron., 58:600–610.
Fateh, M. M. & Fateh, S. 2012. Decentralized direct adaptive fuzzy control of robots using voltage control
strategy. Nonlinear Dyn., 70:1919–1930.
Ghosh, A., Krishan, T., Tejaswy, P., Mandal, A., Pradhan, J. & Ranasingh, S. 2014. Design and
implementation of a 2-DOF PID compensation for magnetic levitation systems. ISA Transactions,
:1216–1222.
Ghosh, B.B., Sarkar, B.K. & Saha, R. 2015. Real time performance analysis of different combinations
of fuzzy–PID and bias controllers for a two degree of freedom electro hydraulic parallel manipulator.
Robotics and Computer-Integrated Manufacturing, 34:62–69.
Ho, H.F., Wong, Y.K. & Rad, A.B. 2007. Robust fuzzy tracking control for robotic manipulators. Simul.
Modell. Pract. Theory, 15:801–816.
Hoseini, S.M., Farrokhi, M. & Koshkouei, A.J. 2008. Robust adaptive control of uncertain non-linear
systems using neural networks. International Journal of Control, 81:1319 - 1330 .
Huang, C.Q., Xie, L.F. & Liu, Y.L. 2012. PD plus error-dependent integral nonlinear controllers for robot
manipulators with an uncertain Jacobian matrix. ISA Transactions, 51:792–800.
Islam, S. & Liu, X.P. 2011. Robust sliding mode control for robot manipulators. IEEE Trans. Ind. Electron.,
:2444–2453.
Laghrouche, S., Plestan, F. & Glumineau, A. 2007. Higher Order Sliding Mode Control Based on Integral
Sliding Surface. Automatica, 43:531–537.
Levant, A. 2007. Principles of 2-sliding Mode Design. Automatica, 43:576–586.
Liu, F., Liang, L. & Gao, J. 2014. Fuzzy PID Control of Space Manipulator for Both Ground Alignment and
Space Applications. International Journal of Automation and Computing, 11:353 - 360.
Liu, H. & Zhang, T. 2013. Neural network-based robust finite-time control for robotic manipulators
considering actuator dynamics. Robotics and Computer-Integrated Manufacturing, 29(2), 301 - 308.
Plestan, F., Glumineau, A. & Laghrouche, S. 2008. A New Algorithm for High-order Sliding Mode Control.
International Journal of Robust and Nonlinear Control, 18:441– 453.
Richa, S., Rana, P. & Vineet, K. 2014. Performance analysis of fractional order fuzzy PID controllers
applied to a robotic manipulator. Expert Systems with Applications, 41:4274–4289.
Roopaei, M. & Jahromi, M.Z. 2009. Chattering-free fuzzy sliding mode control in MIMO uncertain
systems. Nonlinear Analysis, 71:4430–4437.
Sahu, R.K., Panda, S. & Rout, U.K. 2013. DE optimized parallel 2-DOF PID controller for load frequency
control of power system with governor dead-band nonlinearity. Electr Power Energy Syst., 49:19–33.
Schilling, R.J. 2003. Fundamentals of Robotics Analysis & Control. Prentice-Hall, New Delhi.
Sharma, R., Gaur, P. & Mittal, A.P. 2015. Performance analysis of two-degree of freedom fractional order
PID controllers for robotic manipulator with payload. ISA Transaction, 58:279–291.
Slotine, J. J. & Li, W. 1991. Applied nonlinear control (Vol. 199, No. 1). Prentice-Hall, Englewood Cliffs, NJ.
Slotine, J.J. & Li, W. 1987. On the adaptive control of robot manipulators. The International Journal of
Robotics Research, 6:49–59.
Tarn, T.J., Bejczy, A.K., Marth, G.T. & Ramadorai, A.K. 1993. Performance comparison of four
manipulator servo schemes. IEEE Control Systems, 13:22–29.
Tseng, M.-L. & Chen, M. S. 2010. Chattering reduction of sliding mode control by low-pass filtering the
control signal. Asian Journal of Control, 12(3):392–398.
Vega, V.P., Arimoto, S., Liu, Y., Hirzinger, G. & Akella, P. 2003. Dynamic Sliding PID Control for
Tracking of Robot Manipulators: Theory and Experiments. IEEE Transactions on Robotics and
Automation, 19:967–976.
Wai, R.J. 2007. Fuzzy sliding-mode control using adaptive tuning technique. IEEE Trans. Ind. Electron.,
:586–594.
Wai, R.J., Tu, C.Y. & Hsieh, K.Y. 2004. Adaptive tracking control of robot manipulator. International
Journal of System Science, 35(11):615- 27.
Wang Y.N., Mai, T.L. & Mao, J. X. 2014. Adaptive motion/force control strategy for non-holonomic mobile
manipulator robot using recurrent fuzzy wavelet neural networks. Engineering Applications of Artificial
Intelligence, 34:137–153.
Ye, J. 2014. Compound control of a compound cosine function neural network and PD for manipulators.
International Journal of Control, 87:2118–2129.
