Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-25T22:16:58.288Z Has data issue: false hasContentIssue false
  • English
  • Français

Tip-contact force control of a single-link flexible arm using feedback and parallel compensation approach

Published online by Cambridge University Press:  13 February 2013

Liang-Yih Liu  and
Hsiung-Cheng Lin
Liang-Yih Liu
Affiliation:
Automation Engineering, Chienkuo Technology University, Chung Hua, Taiwan
Hsiung-Cheng Lin*
Affiliation:
Electronic Engineering, National Chin-Yi University of Technology, Taichung, Taiwan
*
*Corresponding author. E-mail: [email protected]; [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

In this paper, the force control of a constrained one-link flexible arm is investigated using a feedback parallel compensation algorithm based on a linear distributed parameter model with internal damping of Kelvin–Voigt type. Generally, the non-collocation of the joint torque input and the tip contact force output comes along with the non-minimum phase in nature. To overcome this inherent limitation, a new input induced by the measurement of root-bending moment and its derivative, and a virtual contact force output generated by a parallel compensator are defined. Therefore, the transfer function from the new input to the virtual contact force output is proved not only strictly minimum phase but also in a stable condition. A PD controller then improves the performance of the overall closed-loop system. Furthermore, the perfect asymptotic tracking of a desired contact force trajectory with internal stability can be achieved accurately. The exact solutions of the infinite-dimensional system are obtained using the infinite product formulation. The proposed system promises stability robustness to parameter uncertainties, also free of spillover problems. Numerical simulations are provided to verify the effectiveness of the proposed approach.

Keywords

Constrained flexible armParallel compensatorMinimum phase systemInfinite-dimensional system
Type
Articles
Information
Robotica , Volume 31 , Issue 5 , August 2013 , pp. 825 - 835
Copyright
Copyright © Cambridge University Press 2013 

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.Chodavarapu, P. A. and Spong, M. W., “On Noncollocated Control of a Single Flexible Link,” In: Proceedings of the IEEE International Conference on Robotics and Automation, Minneapolis, Minnesota (1996) pp. 1101–1106.CrossRefGoogle Scholar
2.Korayem, M. H., Nikoobin, A. and Azimirad, V., “Trajectory optimization of flexible link manipulators in point-to-point motion,” Robotica 27 (6), 825–840 (2009).CrossRefGoogle Scholar
3.Nguyen, V. B. and Morris, A. S., “Using a genetic algorithm to fully optimise a fuzzy logic controller for a two-link-flexible robot arm,” Robotica 27 (5), 677–687 (2009).CrossRefGoogle Scholar
4.Korayem, M. H., Haghighi, R., Korayem, A. H., Nikoobin, A. and Alamdari, A., “Determining maximum load carrying capacity of planar flexible-link robot: Closed-loop approach,” Robotica 28 (7), 959–973 (2010).CrossRefGoogle Scholar
5.Gümüsel, L. and Özmen, N. G., “Modelling and control of manipulators with flexible links working on land and underwater environments,” Robotica 29 (3), 461–470 (2011).CrossRefGoogle Scholar
6.Macchelli, A., Melchiorri, C. and Stramigioli, S., “Port-based modeling of a flexible link,” IEEE Trans. Robot. 23 (4), 650–660 (2007).CrossRefGoogle Scholar
7.Nguyen, T. D. and Egeland, O., “Infinite dimensional observer for a flexible robot arm with a tip load,” Asian J. Control 10 (4), 454–461 (2008).CrossRefGoogle Scholar
8.Wang, X. and Chen, D., “Output tracking control of a one-link flexible manipulator via causal inversion,” IEEE Trans. Control Syst. Technol. 14 (1), 141–148 (2006).CrossRefGoogle Scholar
9.Lee, S. Y. and Sheu, J. J., “Free vibration of a rotating inclined beam,” Trans. ASME J. Appl. Mech. 74 (3), 406–414 (2007).CrossRefGoogle Scholar
10.Garcia, A. and Feliu, V., “Force control of a single-link flexible robot based on a collision detection mechanism,” Proc. IEE, Control Theory Appl. 147 (6), 588–595 (2000).CrossRefGoogle Scholar
11.Payo, I., Feliu, V. and Moallem, M., “Force Control of a Single-Link Flexible Arm,” In: Proceedings of the IEEE 3rd International Conference on Mechatronics, Budapest (2006) pp. 575–580.Google Scholar
12.Becedas, J., Payo, I. and Feliu, V., “Generalised proportional integral torque control for single-link flexible manipulators,” IET Control Theory Appl. 4 (5), 773–783 (2010).CrossRefGoogle Scholar
13.Ma, O. and Wang, J., “Model order reduction for impact-contact dynamics simulations of flexible manipulators,” Robotica 25 (4), 397–407 (2007).CrossRefGoogle Scholar
14.Becedas, J., Payo, I. and Feliu, V., “Two-flexible-fingers gripper force feedback control system for its application as end effector on a 6-DOF manipulator,” IEEE Trans. Robot. 27 (3), 599–615 (2011).CrossRefGoogle Scholar
15.Ding, X. and Selig, J. M., “Dynamic modeling of a compliant arm with 6-dimensional tip forces using screw theory,” Robotica 21 (2), 193–197 (2003).CrossRefGoogle Scholar
16.Francis, M., Ching, C. and Wang, D., “Exact solution and infinite-dimensional stability analysis of a single flexible link in collision,” IEEE Trans. Robot. Autom. 19 (6), 1015–1020 (2003).Google Scholar
17.Chiou, B. C. and Shahinpoor, M., “Dynamic stability analysis of a one-link force-controlled flexible manipulator,” J. Robot. Syst. 5 (5), 443–451 (1988).CrossRefGoogle Scholar
18.Chiou, B. C. and Shahinpoor, M., “Dynamic stability analysis of a two-link force-controlled flexible manipulator,” ASME J. Dyn. Syst. Meas. Control 112 (4), 661–666 (1990).CrossRefGoogle Scholar
19.Li, D., “Tip-Contact Force Control of One-Link Flexible Manipulator: An Inherent Performance Limitation,” In: Proceedings of 1990 American Control Conference, San Diego, CA (1990) pp. 697–701.CrossRefGoogle Scholar
20.Matsuno, F., Sakawa, Y. and Asano, T., “Quasi-Static Hybrid Position/Force Control of a Flexible Manipulator,” In: Proceedings of 1991 IEEE International Conference on Robotics and Automation, Sacramento, CA (1991) pp. 2838–2842.CrossRefGoogle Scholar
21.Matsuno, F., Asano, T. and Sakawa, Y., “Quasi-static hybrid position/force control of constrained planar two-link flexible manipulators,” IEEE Trans. Robot. Autom. 10 (3), 287–297 (1994).CrossRefGoogle Scholar
22.Hu, F. L. and Ulsoy, A. G., “Force and motion control of a constrained flexible arm,” ASME J. Dyn. Syst. Meas. Control 116 (3), 336–343 (1994).CrossRefGoogle Scholar
23.Matsuno, F. and Yamamoto, K., “Dynamic hybrid position/force control of a two degree-of-freedom flexible manipulator,” J. Robot. Syst. 11 (5), 355–366 (1994).CrossRefGoogle Scholar
24.Yim, W. and Singh, S. N., “Inverse force and motion control of constrained elastic robots,” ASME J. Dyn. Syst. Meas. Control 117 (3), 374–383 (1995a).CrossRefGoogle Scholar
25.Yim, W. and Singh, S. N., “Sliding mode force, motion control, and stabilization of elastic manipulator in the presence of uncertainties,” J. Robot. Syst. 12 (5), 315–330 (1995b).Google Scholar
26.Lin, J. and Chiang, T. S., “A New Design of Hierarchical Fuzzy Hybrid Position/Force Control for Flexible Link Robot Arm,” In: Proceedings of 2003 American Control Conference, Denver, Colorado (2003) pp. 5239–5244.Google Scholar
27.Lin, J., “Hierarchical fuzzy logic controller for a flexible link robot arm performing constrained motion tasks,” Proc. IEE Control Theory Appl. 150 (4), 355–364 (2003).CrossRefGoogle Scholar
28.Kilicaslan, S., Ozgoren, M. K. and Ider, S. K., “Control of Constrained Spatial Three-Link Flexible Manipulators,” In: Proceedings of the 2007 Mediterranean Conference on Control and Automation, Athens, Greece (2007) pp. 1–6.Google Scholar
29.Matsuno, F. and Kasai, S., “Modeling and robust force control of constrained one-link flexible arms,” J. Robot. Syst. 15 (8), 447–464 (1998).3.0.CO;2-L>CrossRefGoogle Scholar
30.Bazaei, A. and Moallem, M., “Force transmission through a structurally flexible beam: dynamic modeling and feedback control,” IEEE Trans. Control Syst. Technol. 17 (6), 1245–1256 (2009).CrossRefGoogle Scholar
31.Matsuno, F., Umeyama, S. and Kasai, S., “Experimental Study on Robust Force Control of a Flexible Arm with a Symmetric Rigid Tip Body,” In: Proceedings of 1997 IEEE International Conference on Robotics and Automation, Albuquerque, New Mexico (1997) pp. 3136–3141.Google Scholar
32.Morita, Y., Kobayashi, Y., Kando, H., Matsuno, F., Kanzawa, T. and Ukai, H., “Robust force control of a flexible arm with a nonsymmetric rigid body,” J. Robot. Syst. 18 (5), 221–235 (2001).CrossRefGoogle Scholar
33.Bazaei, A. and Moallem, M., “Improving force control bandwidth of flexible-link arms through output redefinition,” IEEE/ASME Trans. Mechatronics 16 (2), 380–386 (2011).CrossRefGoogle Scholar
34.Endo, T. and Matsuno, F., “Dynamics Based Force Control of One-Link Flexible Arm,” In: Proceedings of the SICE 2004 Annual Conference, Sapporo (2004) pp. 2736–2741.Google Scholar
35.Morita, Y., Matsuno, F., Ikeda, M., Ukai, H. and Kando, H., “Experimental Study on PDS Force Control of a Flexible Arm Considering Bending and Torsional Deformation,” In: Proceedings of the 7th International Workshop on Advanced Motion Control, Maribor, Slovenia (2002) pp. 408–413.Google Scholar
36.Liu, L. Y. and Yuan, K., “Force control of a constraint one-link flexible arm: A distributed parameter modeling approach,” J. Chin. Inst. Eng. 26 (4), 443–454 (2003).CrossRefGoogle Scholar
37.Spong, M. W., Khorasani, K. and Kokotovic, P. V., “An integral manifold approach to the control of robot manipulators with flexible joints,” IEEE J. Robot. Autom. 3 (4), 291–300 (1987).CrossRefGoogle Scholar
38.Spong, M. W., “Modeling and control of elastic joint robots,” Trans. ASME J. Dyn. Syst. Meas. Control 109, 310–319 (1987).CrossRefGoogle Scholar
39.Spong, M. W., “On the force control problem for flexible joint manipulators,” IEEE Trans. Autom. Control 34 (1), 107–111 (1989).CrossRefGoogle Scholar
40.Ghorbel, F. and Spong, M. W., “Integral manifolds of singularly perturbed systems with application to rigid-link flexible-joint multibody systems,” Int. J. Nonlinear Mech. 34, 33–155 (2000).Google Scholar
41.Yigit, A. S., “On the use of an elastic-plastic contact law for the impact of a single flexible link,” J. Dyn. Syst. Meas. Control 117 (4), 527–533 (1995).CrossRefGoogle Scholar
42.Zhang, Y. N. and Sharf, I., “Validation of nonlinear viscoelastic contact force models for low speed impact,” J. Appl. Mech. 76 (5), 9–20 (2009).CrossRefGoogle Scholar
43.Yigit, S., Christoforou, A. P. and Majeed, M. A., “A nonlinear visco-elastoplastic impact model and the coefficient of restitution,” Nonlinear Dyn. 66 (4), 509–521 (2011).CrossRefGoogle Scholar
44.Doulgeri, Z. and Iliadis, G., “Contact stability analysis of a one degree-of-freedom robot using hybrid system stability theory,” Robotica 23 (5), 607–614 (2005).CrossRefGoogle Scholar
45.Stanisic, R. Z. and Fernández, A. V., “Simultaneous velocity, impact and force control,” Robotica 27 (7), 1039–1048 (2009).CrossRefGoogle Scholar
46.Anderson, R. J. and Spong, M. W., “Hybrid impedance control of robots”, IEEE J. Robot. Autom. 4 (5), 549–556 (1988).CrossRefGoogle Scholar
47.Yuan, K. and Hu, C. M., “Nonlinear modeling and partial linearizing control of a slewing timoshenko-beam manipulator,” ASME J. Dyn. Syst. Meas. Control 118 (1), 75–83 (1996).CrossRefGoogle Scholar
48.Sakawa, Y. and Luo, Z. H., “Modeling and control of coupled bending and torsional vibrations of flexible beams,” IEEE Trans. Autom. Control 34 (9), 970–977 (1989).CrossRefGoogle Scholar
49.Geniele, H., Potel, R. V. and Khorasani, K., “End-point control of a flexible-link manipulator: Theory and experiments,” IEEE Trans. Control Syst. Technol. 5 (6), 556–570 (1997).CrossRefGoogle Scholar
50.Wang, D. and Vidyasagar, M., “Passive control of a stiff flexible link,” Int. J. Robot. Res. 11 (6), 572–578 (1992).CrossRefGoogle Scholar
51.Doyle, J. C., Francis, B. A. and Tannenbaum, A. R., Feedback Control Theory (Macmillan, New York, 1992).Google Scholar
52.Luo, Z. H., “Direct Strain Feedback Control of Flexible Robot Arms: New Theoretical and Experimental Results” IEEE Trans. Autom. Control 38, 1610–1622 (1993).Google Scholar
53.Yuan, K. and Liu, L. Y., “Achieving minimum phase transfer function for a non-collocated single-link flexible manipulator,” Asian J. Control 2 (3), 179–191 (2000).CrossRefGoogle Scholar