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A new program package for the generation of efficient manipulator kinematic and dynamic equations in symbolic form

Published online by Cambridge University Press:  09 March 2009

M. Kirćanski ,
M. Vukobratović ,
N. Kirćanski  and
A. Timčenko
M. Kirćanski
Affiliation:
Mihajlo Pupin Institute, Beograd, Yugoslavia
M. Vukobratović
Affiliation:
Mihajlo Pupin Institute, Beograd, Yugoslavia
N. Kirćanski
Affiliation:
Mihajlo Pupin Institute, Beograd, Yugoslavia
A. Timčenko
Affiliation:
Mihajlo Pupin Institute, Beograd, Yugoslavia
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Summary

This paper presents a new program package for the generation of efficient manipulator kinematic and dynamic equations in symbolic form.

The basic algorithm belongs to the class of customized algorithms that reduce the computational burden by taking into account the specific characteristics of the manipulator to be modelled. The output of the package is high-level computer program code for evaluation of various kinematic and dynamic variables: the homogeneous transformation matrix between the hand and base coordinate frame, Jacobian matrices, driving torques and the elements of dynamic model matrices. The dynamic model is based on the recursive Newton-Euler equations. The application of recursive symbolic relations yields nearly minimal numerical complexity. Further improvement of computational efficiency is achieved by introducing different computational rates for the terms depending on joint angles, velocities and accelerations. A comparative study of numerical complexity for several typical industrial robots is presented.

Keywords

EquationsSymbolic formProgram generationManipulator
Type
Research Article
Information
Robotica , Volume 6 , Issue 4 , October 1988 , pp. 311 - 318
Copyright
Copyright © Cambridge University Press 1988

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References

1.Luh, J.Y.S., Walker, M.W. & Paul, R.P.C., “On-Line Computational Scheme for Mechanical Manipulators”, ASME J. of Dyn. Sys. Meas, and Cont. 102, 69–76 (06, 1980).CrossRefGoogle Scholar
2.Vukobratović, M. & Stepanenko, Y., “Mathematical Models of General Anthropomorphic Systems” Math. Biosci. 17, 191–242 (1973).CrossRefGoogle Scholar
3.Paul, P.R., Robot Manipulators: Mathematics, Programming, and Control (MIT Press, Cambridge Mass., 1981).Google Scholar
4.Hollerbach, M.J., “A Recursive Lagrangian Formulation of Manipulator Dynamics and a Comparative Study of Dynamics Formulation Complexity” IEEE Trans. on SMC SMC-10, No. 11, 730–740 (11, 1980).Google Scholar
5.Vukobratović, M. & Potkonjak, V., “Contribution to Automatic Forming of Active Chain Models via Lagrangian Form” ASME J. Appl. Mech. No. 1, 76–85 (1979).Google Scholar
6.Kane, T.R. & Levinson, D.L., “The Use of Kane's Dynamical Equations in Robotics” Int. J. Robotics Research 2, No. 3, 3–21 (1983).Google Scholar
7.Kirćanski, N. & Vukobratović, M., “Computer Aided Procedure of Forming Robot Motion Equations in Analytical Forms” Proc. VI IFToMM Congress, New Delhi (1983).Google Scholar
8.Aldon, M.J. & Legois, A., “Computational Aspects in Robot Dynamics Modeling” Proc. of Advanced Software in Robotics (Elsvier Science Publishers B.V., Liege, Belgium, 05 4–6, 1983) pp. 3–14.Google Scholar
9.Neuman, P.Ch. & Murray, J.J., “Computational Robot Dynamics: Foundations and Applications”, J. Robotic Systems 2, No. 4, 425–452 (1985).Google Scholar
10.Cesareo, G., Nicolo, F. & Nicosia, S., “DYMIR: A Code for Generating Dynamic Model of Robots” Proc. 1st Int. IEEE Conf, on Robotics, Atlanta, GA (03, 1984) pp. 115–120.Google Scholar
11.Murray, J.J. & Neuman, P.Ch., “Computational Dynamic Robot Modeling” Proc. 27th Midwest Symp., on Circuits and Systems, Morgantown, WV (1984) pp. 479–481.Google Scholar
12.Renaud, M., “An Efficient Iterative Analytical Procedure for Obtaining a Robot Manipulator Dynamic Model” Proc. 1st Inter. Symp. of Robotics Research, Bretton Woods, New Hampshire, USA (1983).Google Scholar
13.Horak, D.T., “A Fast Computational Scheme for Dynamic Control of Manipulators Proc. 1984. American Control Conference,San Francisco, CA (06, 1984).CrossRefGoogle Scholar
14.Kanade, T., Khosla, P. & Tanaka, N., “Real-Time Control of CMU Direct-Drive Arm II Using Customized Inverse Dynamics” Proc. 23rd CDC, Las Vegas (1984).CrossRefGoogle Scholar
15. M. Vukobratović & N. Kirćanski, Real-Time Dynamics of Manipulation Robots, Series: Scientific Fundamentals of Robotics, 4 (Springer-Verlag, Berlin, 1985).CrossRefGoogle Scholar
16.Khosla, P.K. & Neuman, P.Ch., “Computational Requirements of Customized Newton-Euler Algorithms” J. Robotic Syst. 2(3), 309–327 (Fall, 1985).CrossRefGoogle Scholar
17.Khalil, W. & Kleinfinger, J.F., “Une modelisation performante pour la commande dynamique de robots” RAIRO, APII 6, 561–574 (1985).Google Scholar
18.Vukobratović, M. & Kirćanski, N., “Computer Assisted Generation of Robot Dynamic Models in Analytical Form” Acta Applicandea Mathematicae, Inter. J. of Applying mathematics and Mathematical Applications 2, No. 2 (1984).Google Scholar
19.Li, C.J., “A New Method for Dynamic Analysis of Robot” Proc. IEEE Int. Conf. on Robotics and Automation,San Francisco, 227–233 (1986).Google Scholar
20.Izaguirre, A. & Paul, R., “Automatic Generation of the Dynamic Equations of the Robot Manipulators Using a LISP Program” Proc IEEE Int. Conf. on Robotics and Automation,San Francisco, 220–227 (1986).Google Scholar
[21]Burdick, J., “An Algorithm for Generation of Efficient Manipulator Dynamic Equations” Proc. IEEE Int. Conf. on Robotics and Automation, San Francisco 212–218 (1986).Google Scholar
22.Khalil, W., Kleinfinger, J.F. & Gautier, M., “Reducing the Computational Burden of the Dynamic Models of Robots” Proc. IEEE Int. Conf. on Robotics and Automation, San Francisco, 525–532 (1986).Google Scholar
23. M. Kirćanski & M. Vukobratović, “Computer-Aided Generation of Manipulator Kinematic Models in Symbolic Form” Proc. of 15th ISIR, Tokyo (1985).Google Scholar
24. M. Kirćanski & M. Vukobratović, “A New Program Package for Generating Symbolic Kinematic Models of Arbitrary Serial-Link Manipulators” 16th ISIR, Proceedings, 249–259 (1986).Google Scholar
25.Vukobratović, M. & Kirćanski, M., Kinematics and Trajectory Synthesis of Manipulation Robots Series: Scientific Fundamentals of Robotics 3 (Springer-Verlag, Berlin, 1985).Google Scholar
26.Armstrong, B., Khatib, O. & Burdick, J., “The explicit Dynamic Model and Inertial Parameters of the PUMA 560 Arm”Proc. IEEE Int. Conf. on Robotics and Automation,San Francisco, 510–519 (1986).Google Scholar
27.Kirćanski, N., Kirćanski, M., Vukobratović, M. & Timčenko, O., “An Approach to Development of Real-Time Robot Models” VI IFToMM Symp. on Theory and Practice of Robots and Manipulators, Krakov (1986).Google Scholar
28.Kirćanski, N., Vukobratović, M. & Kirćanski, M., “General-purpose software system for computer-aided generator of real-time robot dynamic models” Proc. 7th World IFToMM Congress, Sevilla (1987).Google Scholar