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A numerical algorithm for solving robot inverse kinematics

Published online by Cambridge University Press:  09 March 2009

K. C. Gupta  and
V. K. Singh
K. C. Gupta
Affiliation:
Department of Mechanical Engineering, University of Illinois at Chicago, Chicago, IL 60680 (U.S.A.)
V. K. Singh
Affiliation:
Department of Mechanical Engineering, University of Illinois at Chicago, Chicago, IL 60680 (U.S.A.)
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Summary

An extension of the inverse kinematics algorithm by Gupta and Kazerounian is presented. The robot kinematics is formulated by using the Zero Reference Position Method. Euler parameters and the related vector forms of the spatial rotation concatenation have been used to improve the efficiency of the velocity Jacobian computation. The joint rates are formally integrated by using a modified predictor-corrector method particularized to robot inverse kinematics – it is a strict descending, p(1)c(0 – n), variable step algorithm. The definitions of the rotational error and overall error measure have been revised. Depending upon the convergence criteria used, these modifications reduce the overall computational time by 20%.

Keywords

Inverse kinematicsIterative methodEuler parametersRobotsNumerical algorithm.
Type
Research Article
Information
Robotica , Volume 7 , Issue 2 , April 1989 , pp. 159 - 164
Copyright
Copyright © Cambridge University Press 1989

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References

1.Gupta, K.C. and Kazerounian, K., “Improved Numerical Solutions of Inverse Kinematics of Robots” Proc. IEEE Conf. Robotics and Automation. St. Louis743–748 (1985).Google Scholar
2.Orin, D.E. and Tsai, Y.T., “A Real Time Computer Architecture for Inverse Kinematics” Proc. IEEE COnf. Robotics and Automation.San Francisco 2, 843–850 (1986).Google Scholar
3.Gupta, K.C., “A Note on Position Analysis of Manipulators” Proc. 7th Applied Mechanisms Conf.,Kansas City3.1–3.3 (1981).Google Scholar
4.Bottema, O. and Roth, B., Theoretical Kinematics (North Holland, Amsterdam, 1979).Google Scholar
5.Gupta, K.C., “Kinematic Analysis of Manipulators Using the Zero Reference Position Description” Intl. J. Robotic Research 5(2) 5–13.CrossRefGoogle Scholar
6.Gupta, K.C. and Carlson, G.J., “On Certain Aspects of the Zero Reference Position Method and its Applications on Industrial Robots.” J. Robotic systems 3(1), 41–57 (1986).CrossRefGoogle Scholar
7.Vukobratovic, M. and Stockic, D., Control of Manipulation Robots (Springer-Verlag, Berlin, 1982); also see Proc. IEEE Intl. Conf. Robotics. Atlanta, 519–528 (1983) (with N. Kircanski).CrossRefGoogle Scholar
8.Stepanenko, Y. and Vukobratovic, M., “Dynamics of Articulated Open Chain Active Mechanisms” Math Biosciences 28, 137–170 (1976); also see ASME CIME 3(6); 61–68 (1985) (with T. S. Sanker), and Proc. ASME Computers in Eng. Conf, l, 107–111 (1986) (with R.L. Huston).CrossRefGoogle Scholar
9.Whittaker, E.T.Analytical Dynamics Of Particles and Rigid Bodies, 4th ed. (Cambridge University Press, London, 1937).Google Scholar
10.Beggs, J.S., Advanced Mechanisms (Macmillan, New York, 1966); also see Kinematics (Hemisphere, Washington, 1983).Google Scholar
11.Wittenberg, J., Dynamics of System of Rigid Bodies (B.G. Teubner, Stuttgart, 1977).CrossRefGoogle Scholar
12.Goldstein, H., Classical Mechanics (Addison-Wesley, Reading, 1980).Google Scholar
13.Kane, T.R., Likins, P.W. and Levinson, D.A., Spacecraft Dynamics (McGraw-Hill, New York, 1983).CrossRefGoogle Scholar
14.Gibbs, J.W. and Wilson, E.B., Vector Analysis 2nd ed (C. Scribner's Sons, 1909) (Dover, New York, 1960).Google Scholar
15.Hamilton, W.R., Elements of Quaternions, Vols. 1 & 2, 2nd ed, (1901); also (Chesla, New York, 1969).Google Scholar
16.Gupta, K.C. and Kazerounian, K. “An Investigation of Time Efficiency and Near Singular Behavior of Numerical Robot Kinematics” Mech. Mach. Theory, 22, No. 4, 371–381 (1987).CrossRefGoogle Scholar
17.Gupta, K.C. and Singh, V.K., “A Numerical Algorithm For Solving Robot Inverse Kinematics” presented at the 7th IFToMM World Congress. Spain (09 17–22, 1987).Google Scholar