In this paper, position control problem of a two-degree-of-freedom underactuated manipulator is considered and a state feedback control structure with energy-based switching is proposed. The mechanism has two revolute joints that move the two links on horizontal plane. Difficulties in system control arise with the fact that the manipulator has less control input signals than system degrees of freedom, and has complex nonholonomic structure. Furthermore, in horizontal operational conditions, position control of the system is a challenging work since free joint is not affected by the gravity. The system has only one actuator at the shoulder joint and the elbow joint is completely free. Therefore, the system cannot be stabilized around any equilibrium point by a linear state feedback control method. In this study, a control system that utilizes two stabilizing state feedback controllers and an energy-based supervisory switching mechanism is proposed. Stabilizing controllers are obtained utilizing the partial feedback linearization method. Proposed control is tested by computer simulations. First the open-loop plant dynamic model is obtained by Euler-Lagrange formulation and state-space modeling approach. Then, a simulation model of the system in closed loop with proposed control scheme is developed using the dynamic model and control law. Simulation tests are performed with respect to three different initial conditions. Performance of the control system is observed and revealed via simulations.

State feedback control,Switching control; Underactuated manipulator; Partial feedback linearization

- [1] Oriolo, G., Nakamura, Y. 1991. Control of mechanical systems with second-order nonholonomic constraints: Underactuated manipulators. Proceedings of the 30th IEEE Conference on Decision and Control, 11-13 December, Brighton, 2398-2403.
- [2] Ratajczak, A., Janiak, M. 2011. Motion planning of the underactuated manipulators with friction in constrained state space. Journal of Automation Mobile Robotics and Intelligent Systems, 5, 33-40.
- [3] Brockett, R. W. 1983. Asymptotic stability and feedback stabilization. Differential geometric control theory, 27(1), 181-191.
- [4] Arai, H., Tachi, S. 1991. Position control of manipulator with passive joints using dynamic coupling. IEEE transactions on Robotics and Automation, 7(4), 528-534.
- [5] Arai, H. 1996. Controllability of a 3-DOF manipulator with a passive joint under a nonholonomic constraint. Journal of the Robotics Society of Japan, 14(5), 751-758.
- [6] Bergerman, M. 1996. Dynamics and control of underactuated manipulators. Doctoral dissertation, Carnegie Mellon University, Pennsylvania.
- [7] Scherm, N., & Heimann, B. 2000. Dynamics and control of underactuated manipulation systems: A discrete-time approach. Robotics and Autonomous Systems, 30(3), 237-248.
- [8] Izumi, K., Kamada, Y., Ichida, K., Watanabe, K. 2008. A switching control of underactuated manipulators by introducing a definition of monotonically decreasing energy. 6th IEEE International Conference on Industrial Informatics, 13-16 July, Daejeon, 383-388.
- [9] Tian, Z., Wu, H., Feng, C. 2010. Hierarchical adaptive backstepping sliding mode control for underactuated space robot. 2nd International Asia Conference on Informatics in Control, Automation and Robotics (CAR), 6-7 May, Hong Kong, 500-503.
- [10] Knoll, C., Röbenack, K. 2011. Control of an underactuated manipulator using similarities to the double integrator. IFAC Proceedings Volumes, 44(1), 11501-11507.
- [11] Seifried, R. 2012. Integrated mechanical and control design of underactuated multibody systems. Nonlinear Dynamics, 67(2), 1539-1557.
- [12] Xia, Q. X., Yu, Y. Q., Liu, Q. B. 2013. Fuzzy Control for Underactuated Manipulator. Applied Mechanics and Materials, 397, 1490-1493.
- [13] Spong, M. W. 1998. Underactuated mechanical systems. ss. 135-150. Sicilliano, B., Valavanis, K. P., ed. 1998. Control problems in robotics and automation, Springer Berlin Heidelberg, England, 298s.
- [14] Mahindrakar, A. D., Rao, S., Banavar, R. N. 2006. Point-to-point control of a 2R planar horizontal underactuated manipulator. Mechanism and Machine Theory, 41(7), 838-844.
- [15] Ichida, K., Watanabe, K., Izumi, K., Uchida, N. 2006. Fuzzy switching control of underactuated manipulators with approximated switching regions. IEEE/RSJ International Conference on Intelligent Robots and Systems, 9-15 October, Beijing, 586-591.
- [16] He, G. P., Wang, Z. L., Zhang, J., Geng, Z. Y. 2016. Characteristics analysis and stabilization of a planar 2R underactuated manipulator. Robotica, 1-17.

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Bibtex | ```
@ { sdufenbed382201,
journal = {Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi},
issn = {},
address = {Süleyman Demirel Üniversitesi},
year = {2017},
volume = {21},
pages = {703 - 710},
doi = {10.19113/sdufbed.88605},
title = {State Feedback Switching Control of an Underactuated Planar Manipulator with Partial Feedback Linearization},
key = {cite},
author = {KARA, Tolgay and ARICI, Mehmet}
}
``` |

APA | KARA, T , ARICI, M . (2017). State Feedback Switching Control of an Underactuated Planar Manipulator with Partial Feedback Linearization. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 21 (3), 703-710. Retrieved from http://dergipark.gov.tr/sdufenbed/issue/34610/382201 |

MLA | KARA, T , ARICI, M . "State Feedback Switching Control of an Underactuated Planar Manipulator with Partial Feedback Linearization". Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 21 (2017): 703-710 <http://dergipark.gov.tr/sdufenbed/issue/34610/382201> |

Chicago | KARA, T , ARICI, M . "State Feedback Switching Control of an Underactuated Planar Manipulator with Partial Feedback Linearization". Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 21 (2017): 703-710 |

RIS | TY - JOUR T1 - State Feedback Switching Control of an Underactuated Planar Manipulator with Partial Feedback Linearization AU - Tolgay KARA , Mehmet ARICI Y1 - 2017 PY - 2017 N1 - DO - T2 - Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi JF - Journal JO - JOR SP - 703 EP - 710 VL - 21 IS - 3 SN - -1308-6529 M3 - UR - Y2 - 2018 ER - |

EndNote | %0 Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi State Feedback Switching Control of an Underactuated Planar Manipulator with Partial Feedback Linearization %A Tolgay KARA , Mehmet ARICI %T State Feedback Switching Control of an Underactuated Planar Manipulator with Partial Feedback Linearization %D 2017 %J Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi %P -1308-6529 %V 21 %N 3 %R %U |