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Symbolically Automated Direct Kinematic Equations Solver for Robotic Manipulators

Published online by Cambridge University Press:  09 March 2009

C.Y. Ho  and
Jen Sriwattanathamma
C.Y. Ho
Affiliation:
Department of Computer Science, University of Missouri–Rolla, Rolla, Missouri 65401 (USA)
Jen Sriwattanathamma
Affiliation:
Department of Computer Science, University of Missouri–Rolla, Rolla, Missouri 65401 (USA)
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Summary

Solving the direct kinematic problem in a symbolic form requires a laborious process of successive multiplications of the link homogeneous transformation matrices and involves a series of algebraic and trigonometric simplifications. The manual production of such solutions is tedious and error-prone. Due to the efficiency of the Prolog language in symbolic processing, a rule–based Prolog program is developed to automate the creation of the following processes: Link transformation matrices; forward kinematic solutions; and the Jacobian matrix. This paper presents the backward recursive formulation techniques, the trigonometric identity rules, and some heuristic rules for implementing the System. A verification of the System has been demonstrated in case of several industrial robots.

Keywords

PrologAutomated solverRobotsKinematic equations
Type
Article
Information
Robotica , Volume 7 , Issue 3 , July 1989 , pp. 243 - 254
Copyright
Copyright © Cambridge University Press 1989

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References

1.Paul, R.P., Robot Manipulators: Mathematics, Programming and Control (The MIT Press, Massachusetts, 1981).Google Scholar
2.Vukobratovic, M., & Kircanski, M., Scientific Fundamentals of Robotics 3: Kinematics and Trajectory Synthesis of Manipulation Robots (Springer–Verlag, Berlin, 1986).CrossRefGoogle Scholar
3.Fu, K.S., Gonzalez, R.C. and Lee, C.S.G., Robotics: Control, Sensing, Vision, and Intelligence (McGraw–Hill Book Company, New York, 1987).Google Scholar
4.Ranky, P. and Ho, C.Y., Robot Modelling (Springer–Verlag, Berlin, 1985).Google Scholar
5.Denavit, J. and Hartenberg, R.S., “A Kinematic Notation for Lower–Pair Mechanism” J. Applied Mechantes 215–221 (06, 1955)CrossRefGoogle Scholar
6.Malm, J.F., “Symbolic Matrix Multiplication with Lisp programming” Proceedings of 1984 Robots 8 20.1–20.19 (06, 1984)Google Scholar
7.Zewari, S.W., and Zugel, J.M., “Prolog Implementation in Robot Kinematics” Computers in Engineering 133–136 (1986).Google Scholar
8.Clocksin, W.F., and Mellish, C.S., Programming in Prolog Second edition (Springer–Verlag, Berlin, 1984).Google Scholar
9.Turbo Prolog: Owner's Handbook, (Borland International Inc., California, 1986).Google Scholar
10.Klahr, P., and Waterman, D.A., Expert Systems (Addison–Wesley Publishing Company, Massachusetts, 1986).Google Scholar
11.Ho, C.Y., and Sriwattanathamma, J., “Differential relationship of kinematic model and speed control strategies for a computer–controlled robot manipulator” Robotica 4, No. 3, 155–161 (1986).CrossRefGoogle Scholar