Linear quadratic optimal controller for cable-driven parallel robots

Abstract

In recent years, various cable-driven parallel robots have been investigated for their advantages, such as low structural weight, high acceleration, and large workspace, over serial and conventional parallel systems. However, the use of cables lowers the stiffness of these robots, which in turn may decrease motion accuracy. A linear quadratic (LQ) optimal controller can provide all the states of a system for the feedback, such as position and velocity. Thus, the application of such an optimal controller in cable-driven parallel robots can result in more efficient and accurate motion compared to the performance of classical controllers such as the proportional-integral-derivative controller. This paper presents an approach to apply the LQ optimal controller on cable-driven parallel robots. To employ the optimal control theory, the static and dynamic modeling of a 3-DOF planar cable-driven parallel robot (Feriba-3) is developed. The synthesis of the LQ optimal control is described, and the significant experimental results are presented and discussed.

Keywords

cable-driven parallel robot / linear quadratic optimal control / accuracy

References

[1] Abdolshah S, Rosati G. First experimental testing of a dynamic minimum tension control (DMTC) for cable driven parallel robots. In: Pott A, Bruckmann T, eds. Cable-Driven Parallel Robots. Springer International Publishing, 2015,239–248

[2] Riechel A T, Bosscher P, Lipkin H, . Concept paper: Cable-driven robots for use in hazardous environments. In: Proceedings of the 10th International Topical Meeting on Robotics and Remote Systems for Hazardous Environments. 2004

[3] Cone L L. Skycam: An aerial robotic camera system. Byte, 1985, 10(10): 122–132

[4] Rosati G, Gallina P, Masiero S. Design, implementation and clinical tests of a wire-based robot for neurorehabilitation.  IEEE Transactions on Neural Systems and Rehabilitation Engineering, 2007, 15(4): 560–569 doi:10.1109/TNSRE.2007.908560

[5] Rosati G, Zanotto D, Secoli R, . Design and control of two planar cable-driven robots for upper-limb neurorehabilitation. In: Proceedings of IEEE International Conference on Rehabilitation Robotics, ICORR<Date>2009</Date>. Kyoto: IEEE, 2009, 560–565 doi:10.1109/ICORR.2009.5209551

[6] Kawamura S, Kino H, Won C. High-speed manipulation by using parallel wire-driven robots. Robotica, 2000, 18(01): 13–21 doi:10.1017/S0263574799002477

[7] Yang G, Mustafa S K, Yeo S H, . Kinematic design of an anthropomimetic 7-DOF cable-driven robotic arm. Frontiers of Mechanical Engineering, 2011, 6(1): 45–60 

[8] Bamdad M. Analytical dynamic solution of a flexible cable-suspended manipulator. Frontiers of Mechanical Engineering, 2013, 8(4): 350–359

[9] Pott A, Bruckmann T, Mikelsons L. Closed-form force distribution for parallel wire robots. Computational Kinematics, 2009, 26(1): 25–34

[10] Gallina P, Rosati G. Manipulability of a planar wire driven haptic device. Mechanism and Machine Theory, 2002, 37(2): 215–228

[11] Lamaury J, Gouttefarde M. Control of a large redundantly actuated cable-suspended parallel robot. In: Proceedings of 2013 IEEE International Conference on Robotics and Automation (ICRA). Karlsruhe: IEEE, 2013, 4659–4664 doi:10.1109/ICRA.2013.6631240

[12] Kino H, Yahiro T, Takemura F, . Robust PD control using adaptive compensation for completely restrained parallel-wire driven robots: Translational systems using the minimum number of wires under zero-gravity condition. IEEE Transactions on Robotics, 2007, 23(4): 803–812

[13] Qi L, Zhang H, Duan G. Task-space position/attitude tracking control of FAST fine tuning system. Frontiers of Mechanical Engineering in China, 2008, 3(4): 392–399

[14] Khosravi M A, Taghirad H D. Experimental performance of robust PID controller on a planar cable robot. In: Bruckmann T, Pott A, eds. Cable-Driven Parallel Robots. Berlin: Springer, 2013, 337–352

[15] Zi B, Duan B, Du J,. Dynamic modeling and active control of a cable-suspended parallel robot. Mechatronics, 2008, 18(1): 1–12

[16] Alp A B, Agrawal S K. Cable suspended robots: Feedback controllers with positive inputs. In: Proceedings of the 2002 American Control Conference. Volume 1. IEEE, 2002, 815–820 

[17] Alikhani A, Vali M. Modeling and robust control of a new large scale suspended cable-driven robot under input constraint. In: Proceedings of 2011 8th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI). Incheon: IEEE, 2011, 238–243 doi:10.1109/URAI.2011.6145969

[18] Laroche E, Chellal R, Cuvillon L, . A preliminary study for H_∞ control of parallel cable-driven manipulators. In: Bruckmann T, Pott A, eds. Cable-Driven Parallel Robots. Berlin: Springer, 2013, 353–369

[19] Korayem M, Tourajizadeh H. Maximum DLCC of spatial cable robot for a predefined trajectory within the workspace using closed loop optimal control approach. Journal of Intelligent & Robotic Systems, 2011, 63(1): 75–99

[20] Gallina P, Rosati G, Rossi A. 3-d.o.f. wire driven planar haptic interface. Journal of Intelligent & Robotic Systems, 2001, 32(1): 23–36

[21] Anderson B D O, Moore J B. Optimal Control: Linear Quadratic Methods. Upper Saddle River: Prentice-Hall, 2007

Acknowledgments

We would like to express our sincerest thanks to Prof. Giulio Rosati from the Department of Management and Engineering at the University of Padua (Italy) for his comments and support in providing facilities for this work. We would also like to thank Prof. Alessandro Gasparetto from the Department of Electrical Management and Mechanical Engineering at the University of Udine (Italy) for his support and guidance.

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg