Reachable and stabilizable area of an underactuated manipulator without state feedback control

IEEE/ASME Transactions on Mechatronics

Volumn 10, Issue 4, 2005, Pages 397-403

  Yabuno, Hiroshi ^a   Matsuda, Takashi ^a   Aoshima, Nobuharu ^a  

^a UNIVERSITY OF TSUKUBA   (Japan)

Author keywords

Bifurcation control; High frequency excitation; Motion control; Nonlinear systems; Pitchfork bifurcation; Underactuated manipulators

Indexed keywords

BIFURCATION (MATHEMATICS); FEEDBACK CONTROL; MOTION CONTROL; NONLINEAR CONTROL SYSTEMS; STATE FEEDBACK; SYSTEM STABILITY;

BIFURCATION CONTROL; HIGH FREQUENCY EXCITATION; PITCHFORK BIFURCATION; UNDERACTUATED MANIPULATORS;

MANIPULATORS;

EID: 27144491623     PISSN: 10834435     EISSN: None     Source Type: Journal    
DOI: 10.1109/TMECH.2005.852450     Document Type: Article

References (15)

1. P. L. Kapitza, "Dynamical stability of a pendulum when its point of suspension vibrates, and pendulum with a vibrating suspension," in Collected Papers of P. L. Kapitza, D. T. Haar, Ed. London, U.K.: Pergamon, 1965, vol. 2, pp. 714-737.
2. A. Stephenson, "On a new type of dynamical stability," Mem. Proc. Manch. Lit. Phil. Soc., vol. 52, pp. 1-10, 1908.
3. S. M. Meerkov, "Principle of vibrational control: Theory and applications," IEEE Trans. Autom. Control, vol. 25, no. 4, pp. 755-762, Aug. 1980.
4. R. E. Bellman, J. Bentsman, and S. M. Meerkov, "Vibrational control of nonlinear vibrational stability," IEEE Trans. Autom. Control, vol. 31, no. 8, pp. 710-716, Aug. 1986.
5. J. M. Schmitt and P. V. Bayly, "Bifurcations in the mean angle of a horizontally shaken pendulum: Analysis and experiment," Nonlinear Dynam., vol. 15, pp. 1-14, 1998.
6. B. Shapiro and B. T. Zinn, "High-frequency nonlinear vibration control," IEEE Trans. Autom. Control, vol. 42, no. 1, pp. 83-90, Jan. 1997.
7. S. Weibel, T. J. Kaper, and J. Baillieul, "Global dynamics of a rapid forced cart and pendulum," Nonlinear Dynam., vol. 13, pp. 313-170, 1996.
8. H. Yabuno, M. Miura, and N. Aoshima, "Bifurcation in an inverted pendulum with tilted high-frequency excitation," J. Sound Vibration, vol. 273, pp. 493-513, 2004.
9. H. Arai, K. Tanie, and N. Shiroma, "Nonholonomic control of a three-DOF planar underactuated manipulator," IEEE Trans. Robot. Autom., vol. 14, no. 5, pp. 681-695, Oct. 1998.
10. K. S. Hong, "An open-loop control for underactuated manipulators using oscillatory inputs: Steering capability of an unactuated joint," IEEE Trans. Contr. Syst. Technol., vol. 10, no. 3, pp. 469-480, May 2002.
11. T. Suzuki and Y. Nakamura, "Anti-gravity control of free-joint manipulators by vibrational input," in Proc. 2002 IEEE Int. Conf. Robot. Autom., Washington, DC, May 2002.
12. H. Yabuno, K. Goto, and N. Aoshima, "Swing-up and stabilization of an underactuated manipulator without state feedback of free joint," IEEE Trans. Robot. Autom., vol. 20, no. 2, pp. 399-365, Apr. 2004.
13. E. H. Abed and J. H. Fu, "Local feedback stabilization and bifurcation control," Syst. Control Lett., vol. 8, pp. 467-473, 1987.
14. H. Yabuno, "Bifurcation control of parametrically excited duffing systems by a combined linear-plus-nonlinear feedback control," Nonlinear Dynam., vol. 12, pp. 263-374, 1997.
15. A. H. Nayfeh, Perturbation Methods. New York: Wiley, 1979.