Nonlinear dynamics and chaotic motions in feedback-controlled two- and three-degree-of-freedom robots

International Journal of Robotics Research

Volumn 18, Issue 1, 1999, Pages 93-108

  Ravishankar, A S ^a   Ghosal, Ashitava ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); CHAOS THEORY; DEGREES OF FREEDOM (MECHANICS); FEEDBACK CONTROL; MANIPULATORS; MOTION CONTROL; NONLINEAR EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS; ROBOTIC ARMS;

GAUSSIAN CURVATURE; POINCARE MAPS; RIEMANNIAN CURVATURE;

ROBOTICS;

EID: 0032759588     PISSN: 02783649     EISSN: None     Source Type: Journal    
DOI: 10.1177/02783649922066088     Document Type: Article

References (33)

1. Armstrong, B., Khatib, O., and Burdick, J. W. 1986. The explicit dynamic model and inertial parameters of the PUMA 560 arm. Proc. of the Int. Conf. on Robot. and Automat. Los Alamitos, CA: IEEE, pp. 510-517.
2. Arnold, V. I. 1989. Mathematical Methods in Classical Mechanics, 2nd ed. New York: Springer-Verlag.
3. Asada, H., and Slotline, J.-J.E. 1986. Robot Analysis and Control. New York: Wiley.
4. Bühler, M., and Koditschek, D. E. 1991. Analysis of a simplified hopping robot. Int. J. Robot. Res. 10(6):587-605.
5. Craig, J. J. 1988. Adaptive Control of Mechanical Manipulators. Reading, MA: Addison-Wesley.
6. Craig, J. J. 1989. Introduction to Robotics: Mechanics and Control, 2nd ed. Reading, MA: Addison-Wesley.
7. D'Humieres, D., Beasely, M. R., Huberman, B. A., and Lichaber, A. 1982. Chaotic states and routes to chaos in a forced pendulum. Physics Rev. Lett. 65(4):3211-3214.
8. Dowell, E. H., and Pezeshki, C. 1986. On the understanding of chaos in Duffing's equation including a comparison with experiment. ASME J. Appl. Mech. 53(3):5-9.
9. Gordon, M. K., and Shampine, L. F. 1975. Computer Solutions of Ordinary Differential Equations: The Initial Value Problem. San Francisco: W. H. Freeman.
10. Guckenheimer, J., and Holmes, P. 1983. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. New York: Springer-Verlag.
11. Hübinger, B., Doerner, R., Heng, H., and Martienssen, W. 1994a. Approaching nonlinear dynamics by studying the motion of a pendulum: I. Observing trajectories in phase space. Int. J. Bifurcation Chaos 4(4):751-760.
12. Hübinger, B., Doerner, R., Heng, H., and Martienssen, W. 1994b. Approaching nonlinear dynamics by studying the motion of a pendulum. II. Analyzing chaotic motions. Int. J. Bifurcation Chaos 4(4):761-771.
13. Hübinger, B., Doerner, R., Heng, H., and Martienssen, W. 1994c. Approaching nonlinear dynamics by studying the motion of a pendulum. III. Predictability and control of chaotic motion. Int. J. Bifurcation Chaos 4(4):773-784.
14. Kawakami, H. 1984. Bifurcations of periodic responses in forced dynamic nonlinear circuits: Computation of bifurcation values of the system parameters. IEEE Trans. Circuits Systems 31(4):248-260.
15. Khosla, P. K. 1986. Real-time control and identification of direct-drive manipulators. PhD thesis, Department of Electrical and Computer Engineering, Carnegie-Mellon University, USA.
16. Mahout, V. 1994. Recurrences and complex behaviours within robotics in the context of repetitive tasks - application to a SCARA manipulator. PhD thesis, INSA de Toulouse. (Available as Technical Report 267.)
17. Mahout, V., Lopez, P., Carcassés, J. P., and Mira, C. 1993. Complex behaviours of a two-revolute-joint robot: Harmonic, subharmonic, higher harmonic, fractional harmonic, chaotic responses. Proc. of the Int. Conf. on Sys., Man and Cybernet., vol. 5. Los Alamitos, CA: IEEE, pp. 201-205.
18. M'Closkey, R. T., and Burdick, J. W. 1993. Periodic motions of a hopping robot with vertical and forward motion. Int. J. Robot. Res. 12(6):197-218.
19. Moon, F. C. 1987. Chaotic Vibrations: An Introduction for Applied Scientists and Engineers. New York: Wiley.
20. Parker, T. S., and Chua, L. O. 1989. Practical Numerical Algorithms for Chaotic Systems. New York: Springer-Verlag.
21. Paul, R. P. 1981. Robot Manipualtors: Mathematics, Programming and Control. Cambridge, MA: MIT Press.
22. Sekar, P., and Narayanan, S. 1995. Chaos in mechanical systems: A review. Sadhana 20(2-4):529-582.
23. Shrinivas, L., and Ghosal, A. 1996. Possible chaotic motions in a feedback controlled 2-R robot. Proc. of the IEEE Conf. on Robot. and Automat. Washington, DC: IEEE, pp. 1241-1246.
24. Spong, M. W. 1992. Remark on robot dynamics: Canonical transformations and Riemannian geometry. Proc. of the Int. Conf. on Robot. and Automat. Los Alamitos, CA: IEEE, pp. 554-559.
25. Stoker, J. J. 1969. Differential Geometry. New York: Wiley.
26. Streit, D. A., Krousgrill, C. M., and Bajaj, A. K. 1986. A preliminary investigation of the dynamic stability of flexible manipulators performing repetitive tasks. Trans. ASME J. Dyn. Sys. Meas. Control 108(6):206-214.
27. Tongue, B. H. 1986. On necessary and sufficient conditions for chaos in Duffing's equation: A heuristic approach. J. Sound Vibration 110(1):59-78.
28. Vakakis, A. F., and Burdick, J. W. 1990. Chaotic motions in the dynamics of a hopping robot. Proc. of the IEEE Int. Conf. on Robot. and Automat. Los Alamitos, CA: IEEE, pp. 1464-1469.
29. Vakakis, A. F., and Burdick, J. W. 1991. An "interesting" strange attractor in the dynamics of a hopping robot. Int. J. Robot. Res. 10(6):606-618.
30. Varghese, M., Fuchs, A., and Mukundan, R. 1991. Chaotic zero dynamics in kinematically redundant robots. IEEE Trans. Aerospace Electronic Sys. 27(5):784-796.
31. Wolf, A., Swift, J. B., Swinney, H. A., and Vastano, J. A. 1985. Determining Lyapunov exponents from a time series. Physica 16D:285-317.
32. Zak, M. 1985a. Criteria for chaos in nonlinear mechanics. Int. J. Nonlinear Mech. 21(3):175-182.
33. Zak, M. 1985b. Two types of chaos in nonlinear mechanics. Int. J. Nonlinear Mech. 20(4):297-308.