On the metrics and co-ordinate-system-induced sensitivity in computational kinematics

International Journal for Numerical Methods in Engineering

Volumn 42, Issue 4, 1998, Pages 729-747

  Jovanovic, Vojin T ^a   Kazerounian, Kazem ^b  

^a T Sendzimir Inc   (United States)

^b UNIVERSITY OF CONNECTICUT   (United States)

Author keywords

Basins of attraction; Chaos; Fractals; Newton Raphson method; Sensitivity; Singularity

Indexed keywords

CHAOS THEORY; COMPUTATIONAL METHODS; EQUATIONS OF MOTION; FRACTALS; ITERATIVE METHODS;

COMPUTATIONAL KINEMATICS; NEWTON-RAPHSON METHOD;

KINEMATICS;

EID: 0032099051     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19980630)42:4<729::AID-NME387>3.0.CO;2-J     Document Type: Article

References (11)

1. W. C. Rheinboldt, Methods for Solving Systems of Nonlinear Equations, SIAM Philadelphia, PA, 1974.
2. R. L. Devaney, An Introduction to Chaotic Dynamical Systems, 2nd ed., Addison-Wesley, Redwood City, CA, 1989.
3. K. C. Gupta, 'Computational kinematics', chapter of the book: The First 40 years of Modern Kinematics, A. Erdman (ed.), Wiley, New York, 1993.
4. V. T. Jovanovic and K. Kazerounian, 'Using chaos to obtain global solutions in computational kinematics', Proceedings of the 1996 ASME Design Eng. Tech. Conferences, 18-22 August, 1996, Irvine, California. Also to appear in ASME J. Mech. Des.
5. V. T. Jovanovic and K. Kazerounian, 'Using chaos to obtain global solutions in computational kinematics', Proceedings of the 1996 ASME Design Eng. Tech. Conferences, 18-22 August, 1996, Irvine, California. Also to appear in ASME J. Mech. Des.
6. V. Jovanovic, 'Identifying, utilizing and improving chaotic numerical instabilities in computational kinematics', Ph.D. Thesis, The University of Connecticut, 1997.
7. D. E. Orin and W. W. Schrader, 'Efficient computation of the Jacobian for robot manipulators', Int. J. Robotics Res., 3(4), 66-75 (1984).
8. P. J. Lanzkron, D. J. Rose and J. T. Wilkes, 'An analysis of approximate non-linear elimination', SIAM J. Sci. Comp., 17(2), 538-559 (March 1996).
9. S. L. S. Jacoby, J. S. Kowalik and J. T. Pizzo, Iterative methods for Nonlinear Optimization Problems, Prentice-Hall, Englewood Cliffs, N.J., 1972.
10. L.-W. Tsai and A. P. Morgan, 'Solving the kinematics of the most general six- and five-degree-of-freedom manipulators by continuation methods', ASME J. Mechanisms, Transmissions, Autom. in Design, 107, 189-200 (1985).
11. V. T. Jovanovic and K. Kazerounian, 'Chaos in computational kinematics', Proceedings of 4th National Applied Mechanisms and Robotics Conference, Ohio, Cincinnati, December 1995.