3-RPS Parallel Manipulator Dynamical Modelling and Control Based on SMC and FL Methods

Document Type : Research Article

Authors

1 Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran

2 Department of Mechanical Engineering, Maleke-Ashtar University of Technology, Tehran, Iran

Abstract

In this paper, a dynamical model-based SMC (Sliding Mode Control) is proposed for
trajectory tracking of a 3-RPS (Revolute, Prismatic, Spherical) parallel manipulator. With ignoring small
inertial effects of all legs and joints compared with those of the end-effector of 3-RPS, the dynamical model of
the manipulator is developed based on Lagrange method. By removing the unknown Lagrange multipliers, the
distribution matrix of control input vector disappears from the dynamical equations. Therefore, the calculation
of the aforementioned matrix is not required for modeling the manipulator. It in trun results in decreased
mathematical manipulation and low computational burden. As a robust nonlinear control technique, a SMC
system is designed for the tracking of the 3-RPS manipulator. According to Lyapunov’s direct method, the
asymptotic stability and the convergence of 3-RPS manipulator to the desired reference trajectories are
proved. Based on computer simulations, the robust performance of the proposed SMC system is evaluated
with respect to FL (feedback linearization) method. The proposed model and control algorithms can be
extended to different kinds of holonomic and non-holonomic constrained parallel manipulators.

Highlights

[1] P. Nanua, K.J. Waldron, V. Murthy, Direct kinematic solution of a Stewart platform, IEEE Transactions on Robotics and Automation, 6(4) (1990) 438-444.

[2] P. Ji, H. Wu, A closed-form forward kinematics solution for the 6-6/sup p/Stewart platform, IEEE Transactions on robotics and automation, 17(4) (2001) 522-526.

[3] J. Schadlbauer, D. Walter, M. Husty, The 3-RPS parallel manipulator from an algebraic viewpoint, Mechanism and Machine Theory, 75 (2014) 161-176.

[4] J.-P. Merlet, Parallel robots, Springer Science & Business Media, 2006.

[5] J.-P. Merlet, Direct kinematics of parallel manipulators, IEEE transactions on robotics and automation, 9(6) (1993) 842-846.

[6] C.-f. Yang, S.-t. Zheng, J. Jin, S.-b. Zhu, J.-w. Han, Forward kinematics analysis of parallel manipulator using modified global Newton-Raphson method, Journal of Central South University of Technology, 17(6) (2010) 1264-1270.

[7] W.-H. Ding, H. Deng, Q.-M. Li, Y.-M. Xia, Control-orientated dynamic modeling of forging manipulators with multi-closed kinematic chains, Robotics and Computer-Integrated Manufacturing, 30(5) (2014) 421-431.

[8] S.-H. Lee, J.-B. Song, W.-C. Choi, D. Hong, Position control of a Stewart platform using inverse dynamics control with approximate dynamics, Mechatronics, 13(6) (2003) 605-619.

[9] M.-J. Liu, C.-X. Li, C.-N. Li, Dynamics analysis of the Gough-Stewart platform manipulator, IEEE Transactions on Robotics and Automation, 16(1) (2000) 94-98.

[10] W. Khalil, S. Guegan, Inverse and direct dynamic modeling of Gough-Stewart robots, IEEE Transactions on Robotics, 20(4) (2004) 754-761.

[11] H. Pendar, M. Vakil, H. Zohoor, Efficient dynamic equations of 3-RPS parallel mechanism through Lagrange method, in:  Robotics, Automation and Mechatronics, 2004 IEEE Conference on, IEEE, 2004, pp. 1152-1157.

[12] E. Özgür, N. Andreff, P. Martinet, Linear dynamic modeling of parallel kinematic manipulators from observable kinematic elements, Mechanism and Machine Theory, 69 (2013) 73-89.

[13] M. Diaz-Rodriguez, A. Valera, V. Mata, M. Valles, Model-based control of a 3-DOF parallel robot based on identified relevant parameters, IEEE/ASME Transactions on Mechatronics, 18(6) (2013) 1737-1744.

[14] M. Zeinali, L. Notash, Adaptive sliding mode control with uncertainty estimator for robot manipulators, Mechanism and Machine Theory, 45(1) (2010) 80-90.

[15] J. Cazalilla, M. Vallés, V. Mata, M. Díaz-Rodríguez, A. Valera, Adaptive control of a 3-DOF parallel manipulator considering payload handling and relevant parameter models, Robotics and Computer-Integrated Manufacturing, 30(5) (2014) 468-477.

[16] M.R. Sirouspour, S.E. Salcudean, Nonlinear control of hydraulic robots, IEEE Transactions on Robotics and Automation, 17(2) (2001) 173-182.

[17] I. Davliakos, E. Papadopoulos, Model-based control of a 6-dof electrohydraulic Stewart–Gough platform, Mechanism and machine theory, 43(11) (2008) 1385-1400.

[18] M.A. Khosravi, H.D. Taghirad, Robust PID control of fully-constrained cable driven parallel robots, Mechatronics, 24(2) (2014) 87-97.

[19] J.-M. Yang, J.-H. Kim, Sliding mode control for trajectory tracking of nonholonomic wheeled mobile robots, IEEE Transactions on robotics and automation, 15(3) (1999) 578-587.

[20] M.A. Hussain, P.Y. Ho, Adaptive sliding mode control with neural network based hybrid models, Journal of Process Control, 14(2) (2004) 157-176.

[21] P. Doostdar, J. Keighobadi, Design and implementation of SMO for a nonlinear MIMO AHRS, Mechanical Systems and Signal Processing, 32 (2012) 94-115.

[22] K.-M. Lee, D.K. Shah, Kinematic analysis of a three-degrees-of-freedom in-parallel actuated manipulator, IEEE Journal on Robotics and Automation, 4(3) (1988) 354-360.

[23] J.J. Craig, Introduction to robotics: mechanics and control, Pearson Prentice Hall Upper Saddle River, 2005.

[24] X. Yang, H. Wu, Y. Li, B. Chen, A dual quaternion solution to the forward kinematics of a class of six-DOF parallel robots with full or reductant actuation, Mechanism and Machine Theory, 107 (2017) 27-36.

[25] K.H. Harib, Dynamic modeling, identification and control of Stewart platform-based machine tools, The Ohio State University, 1997.

[26] L.-W. Tsai, Robot analysis: the mechanics of serial and parallel manipulators, John Wiley & Sons, 1999.

[27] F.L. Lewis, C.T. Abdallah, D.M. Dawson, Control of robot manipulators, Macmillan New York, 1993.

Keywords

References

[1] P. Nanua, K.J. Waldron, V. Murthy, Direct kinematic solution of a Stewart platform, IEEE Transactions on Robotics and Automation, 6(4) (1990) 438-444.
[2] P. Ji, H. Wu, A closed-form forward kinematics solution for the 6-6/sup p/Stewart platform, IEEE Transactions on robotics and automation, 17(4) (2001) 522-526.
[3] J. Schadlbauer, D. Walter, M. Husty, The 3-RPS parallel manipulator from an algebraic viewpoint, Mechanism and Machine Theory, 75 (2014) 161-176.
[4] J.-P. Merlet, Parallel robots, Springer Science & Business Media, 2006.
[5] J.-P. Merlet, Direct kinematics of parallel manipulators, IEEE transactions on robotics and automation, 9(6) (1993) 842-846.
[6] C.-f. Yang, S.-t. Zheng, J. Jin, S.-b. Zhu, J.-w. Han, Forward kinematics analysis of parallel manipulator using modified global Newton-Raphson method, Journal of Central South University of Technology, 17(6) (2010) 1264-1270.
[7] W.-H. Ding, H. Deng, Q.-M. Li, Y.-M. Xia, Control-orientated dynamic modeling of forging manipulators with multi-closed kinematic chains, Robotics and Computer-Integrated Manufacturing, 30(5) (2014) 421-431.
[8] S.-H. Lee, J.-B. Song, W.-C. Choi, D. Hong, Position control of a Stewart platform using inverse dynamics control with approximate dynamics, Mechatronics, 13(6) (2003) 605-619.
[9] M.-J. Liu, C.-X. Li, C.-N. Li, Dynamics analysis of the Gough-Stewart platform manipulator, IEEE Transactions on Robotics and Automation, 16(1) (2000) 94-98.
[10] W. Khalil, S. Guegan, Inverse and direct dynamic modeling of Gough-Stewart robots, IEEE Transactions on Robotics, 20(4) (2004) 754-761.
[11] H. Pendar, M. Vakil, H. Zohoor, Efficient dynamic equations of 3-RPS parallel mechanism through Lagrange method, in:  Robotics, Automation and Mechatronics, 2004 IEEE Conference on, IEEE, 2004, pp. 1152-1157.
[12] E. Özgür, N. Andreff, P. Martinet, Linear dynamic modeling of parallel kinematic manipulators from observable kinematic elements, Mechanism and Machine Theory, 69 (2013) 73-89.
[13] M. Diaz-Rodriguez, A. Valera, V. Mata, M. Valles, Model-based control of a 3-DOF parallel robot based on identified relevant parameters, IEEE/ASME Transactions on Mechatronics, 18(6) (2013) 1737-1744.
[14] M. Zeinali, L. Notash, Adaptive sliding mode control with uncertainty estimator for robot manipulators, Mechanism and Machine Theory, 45(1) (2010) 80-90.
[15] J. Cazalilla, M. Vallés, V. Mata, M. Díaz-Rodríguez, A. Valera, Adaptive control of a 3-DOF parallel manipulator considering payload handling and relevant parameter models, Robotics and Computer-Integrated Manufacturing, 30(5) (2014) 468-477.
[16] M.R. Sirouspour, S.E. Salcudean, Nonlinear control of hydraulic robots, IEEE Transactions on Robotics and Automation, 17(2) (2001) 173-182.
[17] I. Davliakos, E. Papadopoulos, Model-based control of a 6-dof electrohydraulic Stewart–Gough platform, Mechanism and machine theory, 43(11) (2008) 1385-1400.
[18] M.A. Khosravi, H.D. Taghirad, Robust PID control of fully-constrained cable driven parallel robots, Mechatronics, 24(2) (2014) 87-97.
[19] J.-M. Yang, J.-H. Kim, Sliding mode control for trajectory tracking of nonholonomic wheeled mobile robots, IEEE Transactions on robotics and automation, 15(3) (1999) 578-587.
[20] M.A. Hussain, P.Y. Ho, Adaptive sliding mode control with neural network based hybrid models, Journal of Process Control, 14(2) (2004) 157-176.
[21] P. Doostdar, J. Keighobadi, Design and implementation of SMO for a nonlinear MIMO AHRS, Mechanical Systems and Signal Processing, 32 (2012) 94-115.
[22] K.-M. Lee, D.K. Shah, Kinematic analysis of a three-degrees-of-freedom in-parallel actuated manipulator, IEEE Journal on Robotics and Automation, 4(3) (1988) 354-360.
[23] J.J. Craig, Introduction to robotics: mechanics and control, Pearson Prentice Hall Upper Saddle River, 2005.
[24] X. Yang, H. Wu, Y. Li, B. Chen, A dual quaternion solution to the forward kinematics of a class of six-DOF parallel robots with full or reductant actuation, Mechanism and Machine Theory, 107 (2017) 27-36.
[25] K.H. Harib, Dynamic modeling, identification and control of Stewart platform-based machine tools, The Ohio State University, 1997.
[26] L.-W. Tsai, Robot analysis: the mechanics of serial and parallel manipulators, John Wiley & Sons, 1999.
[27] F.L. Lewis, C.T. Abdallah, D.M. Dawson, Control of robot manipulators, Macmillan New York, 1993.
AUT Journal of Modeling and Simulation
Volume 49, Issue 2
December 2017
Pages 217-226

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