Tracking Control and Vibration Reduction of Flexible Cable-Suspended Parallel Robots using a Robust Input Shaper

Document Type : Article


Robotic Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran


The control of flexible cable-driven parallel robots usually requires not only the feedback from the joints, but the feedback from the end-effector pose or cable tension. This paper presents a new approach for reducing the vibration of flexible cable-suspended robots, using only the feedback from the joints. First, the dynamic equations of a 6DOF cable-suspended parallel robot with elastic cables were derived by Gibbs-Appel formulation. Subsequently, three different control approaches were investigated based on the computation load and required sensors. As a result, a feedback linearization method based on the rigid model of the system was selected. In order to reduce the vibration, a robust input shaping method was employed to prevent excitation of natural modes. Simulation results revealed that the proposed approach leads to a noticeable vibration and settling time reduction in cases of low and high cable stiffness, respectively. Moreover, another simulation compares the presented approach with a composite controller, which uses the feedbacks from the end-effector and actuators. Thereafter, the performance of the approach in vibration reduction is quantitatively shown. Finally, experimental validation of the approach was accomplished by frequency analysis of the vibration obtained from the IMU sensor, attached to the end-effector.


Main Subjects


1. Diao, X. and Ma, O. \Vibration analysis of cabledriven parallel manipulators", Multibody Syst. Dyn., 21(4), pp. 347-360 (2009).
2. Korayem, M.H., Tourajizadeh, H. and Bamdad, M. \Dynamic load carrying capacity of
exible cable suspended robot: robust feedback linearization control approach", J. Intell. Robot. Syst., 60(3), pp. 341-363 (2010).
3. Korayem, M.H., Taherifar, M. and Tourajizadeh, H. \Compensating the  exibility uncertainties of a cable suspended robot Using SMC approach", Robotica, 33(3), pp. 578-598 (2015).
4. Laroche, E., Chellal, R., Cuvillon, L. and Ganglo ,
J. \A preliminary study for control of parallel cabledriven
manipulators", In Cable-Driven Parallel Robots,
12, pp. 353-369, Springer, Berlin, Heidelberg (2013).
5. Meunier, G., Boulet, B. and Nahon, M. \Control of
an overactuated cable-driven parallel mechanism for a
radio telescope application", IEEE Trans. on Control
Systems Technology, 17(5), pp. 1043-1054 (2009).
6. Caverly, R.J. and Forbes, J.R. \Dynamic modeling and
noncollocated control of a
exible planar cable-driven
manipulator", IEEE Trans. on Robotics, 30(6), pp.
1386-1397 (2014).
7. Shao, Z.F., Tang, X., Wang, L.P. and Chen, X.
\Dynamic modeling and wind vibration control of the
feed support system in FAST", Nonlinear Dyn., 67(2),
pp. 965-985 (2012).
8. Liu, Z., Tang, X. and Wang, L. \Research on the
dynamic coupling of the rigid-
exible manipulator",
Robot. Comput. Integr. Manufac., 32, pp. 72-82
9. Khosravi, M.A. and Taghirad, H.D. \Dynamic analysis
and control of fully-constrained cable robots with
elastic cables: variable sti ness formulation", In Cable-
Driven Parallel Robots, Springer International Publishing,
pp. 161-177 (2015).
10. Ozgoli, S. and Taghirad, H.D. \A Survey on the control
exible joint robots", Asian Journal of Control,
8(4), pp. 332-344 (2006).
11. Singer, N., Singhose, W. and Seering, W. \Comparison
of ltering methods for reducing residual vibration",
European Journal of Control, 5(2-4), pp. 208-218
12. Luo, L., Wang, S., Mo, J. and Cai, J. \On the
modeling and composite control of
exible parallel
mechanism", Int. J. Adv. Manuf. Technol., 29(7), pp.
786-793 (2006).
13. Hu, Q. \Robust integral variable structure controller
and pulse-width pulse-frequency modulated input
shaper design for
exible spacecraft with mismatched
uncertainty/disturbance", ISA Transactions, 46(4),
pp. 505-518 (2007).
250 M.H. Korayem et al./Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 230{252
14. Zhang, Q., Mills, J.K., Cleghorn, W.L., Jin, J. and
Zhao, C. \Trajectory tracking and vibration suppression
of a 3-PRR parallel manipulator with
links", Multibody Syst. Dyn., 33(1), pp. 27-60 (2015).
15. Zhang, Q., Mills, J.K., Cleghorn, W.L., Jin, J. and
Sun, Z. \Dynamic model and input shaping control of a

exible link parallel manipulator considering the exact
boundary conditions", Robotica, 33(06), pp. 1201-1230
16.  Oltjen, J., Kotlarski, J. and Ortmaier, T. \Reduction
of end e ector oscillations of a parallel mechanism
with modi ed motion pro les", IEEE 10th Conf. on
Industrial Electronics and Applications, pp. 823-829
17. Li, W.P., Luo, B. and Huang, H. \Active vibration
control of
exible joint manipulator using input shaping
and adaptive parameter auto disturbance rejection
controller", JSV, 363, pp. 97-125 (2016).
18. Blackburn, D.F. \Command shaping for vibration
reduction in nonlinear cabled systems", M.S. Thesis,
School of Mechanical Engineering, Georgia Institute
of Technology (2006).
19. Park, J., Kwon, O. and Park, J.H. \Anti-sway trajectory
generation of incompletely restrained wiresuspended
system", JMST, 27(10), pp. 3171-3176
20. Thalapil, J. \Input shaping for sway control in gantry
cranes", Journal of Mechanical and Civil Engineering,
1(2), pp. 36-46 (2012).
21. Garrido, S., Abderrahim, M., Gimenez, A. and Diez,
R. \Anti-swinging input shaping control of an automatic
construction crane", IEEE Trans. Autom. Sci.
Eng., 5(3), pp. 549-557 (2008).
22. Elbadawy, A.A. and Shehata, M.M.G. \Anti-sway
control of marine cranes under the disturbance of a
parallel manipulator", Nonlinear Dyn., 82(1), pp. 415-
434 (2015).
23. Fatehi, M.H., Eghtesad, M. and Amjadifard, R. \Using
singular perturbation method for controlling a crane
system with a
exible cable and large swing angle",
Journal of Low Frequency Noise, Vibration and Active
Control, 34(3), pp. 361-383 (2015).
24. Kokotovic, P., Khalil, H.K. and O'Reilly, J., Singular
Perturbation Methods in Control: Analysis and Design,
25, Siam (1999).
25. Singhose, W. \Command shaping for
exible systems:
A review of the rst 50 years", Int. J. Precis. Eng.
Manuf., 10(4), pp. 153-168 (2009).
26. Vaughan, J., Yano, A. and Singhose, W. \Comparison
of robust input shapers", JSV, 315(4), pp. 797-815
27. Kozak, K., Ebert-Upho , I. and Singhose, W. \Locally
linearized dynamic analysis of parallel manipulators
and application of input shaping to reduce vibrations",
J. Mech. Des., 126(1), pp. 156-168 (2004).