Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-04T19:01:15.019Z Has data issue: false hasContentIssue false
  • English
  • Français

Adaptive vector sliding mode fault-tolerant control of the uncertain Stewart platform based on position measurements only

Published online by Cambridge University Press:  02 September 2014

Qiang Meng ,
Tao Zhang ,
Jing-feng He  and
Jing-yan Song
Qiang Meng
Affiliation:
Department of Automation, School of Information and Technology, Tsinghua University, Beijing 100084, P. R. China Division of Control Science and Engineering, Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, P. R. China National Computer Network Emergency Response Technical Team/Coordination Center of China (CNCERT/CC), Beijing 100029, P. R. China
Tao Zhang
Affiliation:
Department of Automation, School of Information and Technology, Tsinghua University, Beijing 100084, P. R. China Division of Control Science and Engineering, Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, P. R. China
Jing-feng He*
Affiliation:
School of Mechatronic Engineering, Harbin Institute of Technology, Harbin 150001, P. R. China
Jing-yan Song
Affiliation:
Department of Automation, School of Information and Technology, Tsinghua University, Beijing 100084, P. R. China Division of Control Science and Engineering, Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, P. R. China
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

This paper investigates the trajectory tracking of a Stewart platform, which is a typical multi-input multi-output nonlinear system, with unmodeled dynamics, parameter uncertainties, friction, and unpredictable actuator faults. An adaptive vector sliding mode fault-tolerant control law is derived to ensure the system is insensitive to uncertainties and drive the state variable errors of the closed-loop system to converge to the origin. Moreover, novel adaptive laws are proposed to update the upper boundary of uncertainty according to the actual system state, which greatly reduces the chattering of sliding mode control. Furthermore, velocity signals are estimated by introducing a simple nonlinear observer, resulting in the proposed controller requiring position measurements only. Finally, numerical simulations illustrate the effectiveness of the proposed control scheme.

Keywords

Adaptive vector sliding mode controlFault-tolerant controlStewart platformUncertaintiesVelocity estimation
Type
Articles
Information
Robotica , Volume 34 , Issue 6 , June 2016 , pp. 1297 - 1321
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Koekebakker, S. H., Model Based Control of a Flight Simulation Motion SystemPh.D. Dissertation (The Netherlands: Delft University of Technology, 2001).Google Scholar
2.Jafari, F. and Mclnroy, J. E., “Orthogonal Gough-Stewart platforms for micromanipulation,” IEEE Trans. Robot. Autom. 19 (4), 595–603 (2003).CrossRefGoogle Scholar
3.Mclnroy, J. E. and Jafari, F., “Finding symmetric orthogonal Gough-Stewart platforms,” IEEE Trans. Robot. 22 (5), 880–889 2006.Google Scholar
4.Su, Y. X., Duan, B. Y. and Zheng, C. H., “Genetic design of kinematically optimal fine tuning Stewart platform for large spherical radio telescope,” Mechatronics 11 (7), 821–835 (2001).CrossRefGoogle Scholar
5.Lu, Y. J., Zhu, W. B. and Ren, G. X., “Feedback control of a cable-driven Gough-Stewart platform,” IEEE Trans. Robot. 22 (1), 198–202 (2006).Google Scholar
6.Bamberger, H. and Shoham, M., “A novel six degrees-of-freedom parallel robot for MEMS fabrication,” IEEE Trans. Robot. 23 (2), 189–195 (2007).Google Scholar
7.Dasgupta, B. and Mruthyunjaya, T. S., “The Stewart platform manipulator: a review,” Mech. Mach. Theory 35 (1), 15–40 (2000).CrossRefGoogle Scholar
8.Merlet, J. P., “Solving the forward kinematics of a Gough-type parallel manipulator with interval analysis,” Int. J. Robot. Res. 23 (3), 221–235 (2004).Google Scholar
9.Ji, P. and Wu, H. T., “A closed-form forward kinematics solution for the 6–6(p) Stewart platform,” IEEE Trans. Robot. Autom. 17 (4), 522–526 (2001).Google Scholar
10.Gao, X. S., Lei, D. L., Liao, Q. Z. and Zhang, G. F., “Generalized Stewart-Gough platforms and their direct kinematics,” IEEE Trans. Robot. 21 (2), 141–151 (2005).Google Scholar
11.Wang, Z. L., He, J. J. and Gu, H., “Forward kinematics analysis of a six-degree-of-freedom Stewart platform based on independent component analysis and Nelder-Mead algorithm,” IEEE Trans. Syst. Man Cybern. A 41 (3), 589–597 (2011).Google Scholar
12.Husty, M. L., “An algorithm for solving the direct kinematics of general Stewart-Gough platforms,” Mech. Mach. Theory 31 (4), 365–379 (1996).CrossRefGoogle Scholar
13.Innocenti, C. and Parenti-Castelli, V., “Direct position analysis of the Stewart platform mechanism,” Mech. Mach. Theory 25 (6), 611–621 (1990).Google Scholar
14.Liu, M. J., Li, C. X. and Li, C. N., “Dynamic analysis of the Gough–Stewart platform manipulator,” IEEE Trans. Robot. Autom. 16 (1), 94–98 (2000).Google Scholar
15.Yang, C. F., Han, J. W., Zheng, S. T. and Peter, O. O., “Dynamic modeling and computational efficiency analysis for a spatial 6-DOF parallel motion system,” Nonlinear Dyn. 67 (2), 1007–1022 (2012).Google Scholar
16.Gallardo, J., Rico, J., Frisoli, A.et al., “Dynamics of parallel manipulators by means of screw theory,” Mech. Mach. Theory 38 (11), 1113–1131 (2003).CrossRefGoogle Scholar
17.Armstronghelouvry, B., Dupont, P. and Dewit, C. C., “A survey of models, analysis tools and compensation methods for the control of machines with friction,” Automatica 30 (7), 1083–1138 (1994).Google Scholar
18.Yang, C. F., Huang, Q. T. and Han, J. W., “Decoupling control for spatial six-degree-of-freedom electro-hydraulic parallel robot,” Robot. Compu.-Integr. Manuf. 28 (1), 14–23 2012.Google Scholar
19.Davliakos, I. and Papadopoulos, E., “Model-based control of a 6-DOF electrohydraulic Stewart–Gough platform,” Mech. Mach. Theory 43 (11), 1385–1400 (2008).Google Scholar
20.Davliakos, I. and Papadopoulos, E., “Impedance model-based control for an electrohydraulic Stewart platform,” Eur. J. Control 15 (5), 560–577 (2009).Google Scholar
21.Nguyen, C. C., Antrazi, S. S. and Zhou, Z. L., “Adaptive control of a Stewart platform-based manipulator,” J. Robot. Syst. 10 (5), 657–687 (1993).Google Scholar
22.Chen, S. H. and Fu, L. C., “Output feedback sliding mode control for a Stewart platform with a Nonlinear observer-based forward kinematics solution,” IEEE Trans. Control Syst. Technol. 21 (1), 176–185 (2013).Google Scholar
23.Gao, W. B. and Hung, J. C.. “Variable structure control of nonlinear systems: A new approach,” IEEE Trans. Ind. Electron. 40 (1), 45–55 (1993).Google Scholar
24.Slotine, J. J. E. and Li, W. P., “On the adaptive control of robot manipulator,” Int. J. Robot. Res. 6 (3), 49–59 (1987).Google Scholar
25.Ren, L., Mills, J. K. and Sun, D., “Experimental comparison of control approaches on trajectory tracking control of a 3-DOF parallel robot,” IEEE Trans. Control Syst. Technol. 15 (5), 982–988 (2007).Google Scholar
26.Su, Y. X., Sun, D., Ren, L. and Mills, J. K., “Integration of saturated PI Synchronous control and PD feedback for control of parallel manipulators,” IEEE Trans. Robot. 22 (1), 202–207 (2006).Google Scholar
27.Sun, D., Lu, R., Mills, J. K. and Wang, C., “Synchronous tracking control of parallel manipulators using cross-coupling approach,” Int. J. Robot. Res. 25 (11), 1137–1147 (2006).Google Scholar
28.Zhang, Y. M. and Jiang, J., “Bibliographical review on reconfigurable fault-tolerant control systems,” Annu. Rev. Control 32 (2), 229–252 (2008).Google Scholar
29.Yi, Y., Mclnroy, J. E. and Chen, Y. X., “Fault tolerance of parallel manipulators using task space and kinematic redundancy,” IEEE Trans. Robot. 22 (5), 1017–1021 (2006).Google Scholar
30.Wu, J., Wang, J. S. and Wang, L. P., “Dynamics and control of a planar 3-DOF parallel manipulator with actuation redundancy,” Mech. Mach Theory 44 (4), 835–849 (2009).Google Scholar
31.Taghirad, H. D. and Bedoustani, Y. B., “An analytic-iterative redundancy resolution scheme for cable-driven redundant parallel manipulators,” IEEE Trans. Robot. 27 (6), 1137–1143 (2011).Google Scholar
32.Ukidve, C. S., Mclnroy, J. E. and Jafari, F., “Orthogonal Gough-Stewart Platforms with Optimal Fault Tolerant Manipulability,” Proceedings of the IEEE International Conference on Robotics and Automation, Orlando, USA (May 15–19, 2006) pp. 3801–3806.Google Scholar
33.Ukidve, C. S., Mclnroy, J. E. and Jafari, F., “Using redundancy to optimize manipulability of Stewart platforms,” IEEE-ASME Trans. Mechatronics 13 (4), 475–479 (2008).Google Scholar
34.Mclnroy, J. E. and Jafari, F., “Finding symmetric orthogonal Gough–Stewart platforms,” IEEE Trans. Robot. 22 (5), 880–889 (2006).Google Scholar
35.Arteaga, M. A., “Robot control and parameter estimation with only joint position measurements,” Automatica 39 (1), 67–73 (2003).CrossRefGoogle Scholar
36.Su, Y. X., Zheng, C. H., Mueller, P. C. and Duan, B. Y., “A simple improved velocity estimation for low-speed regions based on position measurements only,” IEEE Trans. Control Syst. Technol. 14 (5), 937–942 (2006).Google Scholar
37.Parikh, P. J. and Lam, S. S. Y., “A hybrid strategy to solve the forward kinematics problem in parallel manipulators,” IEEE Trans. Robot. 21 (1), 18–25 (2005).Google Scholar
38.Meng, Q., Zhang, T., He, J. F. and Song, J. Y., “Dynamic modeling of a 6-degree-of-freedom Stewart platform driven by a permanent magnet synchronous motor,” J. Zhejiang Univ.-Sci. C-Comput. Electron. 11 (10), 751–761 (2010).Google Scholar
39.Genduso, F., Miceli, R., Rando, C. and Galluzzo, G. R., “Back EMF sensorless-control algorithm for high-dynamic performance PMSM,” IEEE Tran. Ind. Electron. 57 (6), 2092–2100 (2010).Google Scholar
40.Corley, M. J. and Lorenz, R. D., “Rotor position and velocity estimation for a salient-pole permanent magnet synchronous machine at standstill and high speed,” IEEE Trans. Ind. Appl. 34 (4), 784–789 (1998).Google Scholar
41.Su, Y. X., Duan, B. Y., Zheng, C. H., Zhang, Y. F., Chen, G. D. and Mi, J. W., “Disturbance-rejection high-precision motion control of a Stewart platform,” IEEE Trans. Control Syst. Technol. 12 (3), 364–374 (2004).Google Scholar
42.Fraguela, L., Fridman, L. and Alexandrov, V. V., “Output integral sliding mode control to stabilize position of a Stewart platform,” J. Franklin Inst.-Eng. Appl. Math. 349 (4), 1526–1542 (2012).Google Scholar
43.Berghuis, H. and Nijmeijer, H., “Global regulation of robots using only position measurements,” Syst. Control Lett. 21 (4), 289–293 (1993).CrossRefGoogle Scholar
44.Lee, S. H., Lasky, T. A. and Velinsky, S. A., “Improved velocity estimation for low-speed and transient regimes using low-resolution encoders,” IEEE-ASME Trans. Mechatronics 9 (3), 553–560 (2004).Google Scholar
45.Su, Y. X., Zheng, C. H., Sun, D. and Duan, B. Y., “A simple nonlinear velocity estimator for high-performance motion control,” IEEE Trans. Ind. Electron. 52 (4), 1161–1169 (2005).Google Scholar
46.Su, Y. X., Mueller, P. C. and Zheng, C. H., “Global asymptotic saturated PID control for robot manipulators,” IEEE Trans. Control Syst. Technol. 18 (6), 1280–1288 (2010).Google Scholar
47.Han, J. Q. and Wang, W., “Nonlinear tracking differentiator,” (in Chinese), J. Syst. Sci. Math. Sci. 14 (2), 177–183 (1994).Google Scholar
48.Su, Y. X., Duan, B. Y. and Zheng, C. H., “Nonlinear PID control of a six-DOF parallel manipulator,” IEEE Proc., Control Theory Appl. 151 (1), 95–102 (2004).Google Scholar
49.Young, K. D., Utkin, V. I. and Ozguner, U., “A control engineer's guide to sliding mode control,” IEEE Trans. Control Syst. Technol. 7 (3), 328–342 (1999).Google Scholar
50.Levant, A., “Higher-order sliding modes, differentiation and output-feedback control,” Int. J. Control 76 (9–10), 924–941 (2003).Google Scholar
51.Feng, Y., Yu, X. H. and Man, Z. H., “Non-singular terminal sliding mode control of rigid manipulator,” Automatica 38 (12), 2159–2167 (2002).Google Scholar
52.Chen, M. S., Hwang, Y. R. and Tomizuka, M., “A state-dependent boundary layer design for sliding mode control,” IEEE Trans. Autom. Control 47 (10), 1677–1681 (2002).Google Scholar
53.Huang, C. I. and Fu, L. C., “Smooth Sliding Mode Tracking Control of the Stewart Platform,” Proceedings of the IEEE International Conference on Control Applications, Toronto, Canada (Aug. 28–31, 2005) pp. 43–48.Google Scholar
54.Zhao, D. Y., Li, S. Y and Feng, G., “Continuous Finite Time Control for Stewart Platform with Terminal Sliding Mode,” Proceedings of the 26th Chinese Control Conference, Hunan, China (Jun. 31–Jul. 26, 2007) pp. 27–30.Google Scholar
55.Negash, D. S. and Mitra, R., “Integral Sliding Mode Controller for Trajectory Tracking Control of Stewart Platform Manipulator,” Proceedings of the 5th International Conference on Industrial and Information Systems, Mangalore, India (Jul. 29–Aug. 1, 2010) pp. 650–654.Google Scholar
56.Kumar, P. R. and Bandyopadhyay, B., “Stabilization of Stewart Platform Using Higher Order Sliding Mode Control,” Proceedings of the 7th International Conference on Electrical and Computer Engineering (ICECE), Dhaka, Bangladesh (Dec. 20–22, 2012) pp. 945–948.Google Scholar
57.Fraguela, L., Fridman, L. and Alexandrov, V. V., “Position Stabilization of a Stewart Platform: High-Order Sliding Mode Observer Based Approach,” Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), Orlando, USA (Dec. 12–15, 2011) pp. 5971–5976.Google Scholar
58.Chen, S. H., Lin, C. T. and Fu, L. C., “Second Order Sliding Mode Control on Task-Space of a 6-DOF Stewart Platform,” Proceedings of the 38th Annual Conference on IEEE Industrial Electronics Society, Montreal, Canada (Oct. 25–28, 2012) pp. 2482–2487.Google Scholar
59.Zhu, Z., Xia, Y. Q. and Fu, M. Y., “Adaptive sliding mode control for attitude stabilization with actuator saturation,” IEEE Trans. Ind. Electron. 58 (10), 4898–4907 (2011).Google Scholar
60.Hu, Q. L., “Robust adaptive sliding mode attitude maneuvering and vibration damping of three-axis-stabilized flexible spacecraft with actuator saturation limits,” Nonlinear Dyn. 55 (4), 301–321 (2009).Google Scholar
61.Wai, R. J., “Fuzzy sliding mode control using adaptive tuning technique,” IEEE Trans. Ind. Electron. 54 (1), 586–594 (2007).Google Scholar
62.Efe, M. O., “Fractional fuzzy adaptive sliding-mode control of a 2-DOF direct-drive robot arm,” IEEE Trans. Syst. Man Cybern. B 38 (6), 1561–1570 (2008).Google Scholar
63.Slotine, J. E. and Li, W., Applied Nonlinear Control (Prentice-Hall, Englewood Cliffs, New Jersey, 1991).Google Scholar
64.Yang, C. F., Huang, Q. T., Jiang, H. Z.et al., “PD control with gravity compensation for hydraulic 6-DOF parallel manipulator,” Mech. Mach. Theory 45 (4), 666–677 (2010).Google Scholar
65.Ge, S. S., Hang, C. C. and Woon, L. C., “Adaptive neural network control of robot manipulators in task space,” IEEE Trans. Ind. Electron. 44 (6), 746–752 (1997).Google Scholar
66.Liang, X. W., Huang, X. H., Wang, M. and Zeng, X. J., “Adaptive task-space tracking control of robots without task-space- and joint-space-velocity measurements,” IEEE Trans. Robot. 26 (4), 733–742 (2010).Google Scholar