Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-24T20:01:46.730Z Has data issue: false hasContentIssue false
  • English
  • Français

A unified approach to mathematical modelling of robotic manipulator dynamics

Published online by Cambridge University Press:  09 March 2009

M.K. Vukobratović ,
V.F. Filaretov  and
A.I. Korzun
Get access Rights & Permissions [Opens in a new window]

Summary

A new method for computer forming of dynamic equations of open-chain mechanical robot configurations is presented. The algorithm used is of a numeric-iterative type, based on mathematical apparatus of screw theory, which has enabled elimination of the unnecessary computations in the process of dynamic model derivation. In addition to conventional kinematic schemes of robotic manipulators, the branched kinematic chains which have recently found their application in the locomotion of robotic mechanisms were also treated. Both the inverse and direct problems of dynamics were addressed. A comparative analysis was carried out of the numerical complexity of various existing algorithms of numeric-iterative type dealing with the problems of spatial active mechanisms dynamics. It has been shown that the proposed method regardless of its generality, approaches by its models complexity symbolic models, which are valid for particular robotic mechanisms only where they achieve a high degree of efficiency.

Keywords

Robot dynamicsModellingScrew theoryNumeric-iterative algorithm
Type
Article
Information
Robotica , Volume 12 , Issue 5 , September 1994 , pp. 411 - 420
Copyright
Copyright © Cambridge University Press 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Popov, E.P., Vereschagin, A.F. and Zenkevich, S.L., Manipulation Robots: Dynamics and Algorithms (in Russian) (Nauka, 1978, Moscow).Google Scholar
2Vukobratovid, M. and Potkonjak, V., Scientific Fundamentals of Robotics, Vol. 1, Dynamics of Manipulation Robots (Springer-Verlag, Berlin, 1982).Google Scholar
3.Vukobratović, M. and Cvetković, V. “Computer Oriented Algorithm Modelling of Active Spatial Mechanisms for Application in Robotics” Trans, on Systems, Man and Cybernetics SMC-12, No. 6, 838–848 (1982).Google Scholar
4.Luh, J.J.S., Walker, M.W. and Paul, R.P., “On-line Computational Scheme for Mechanical Manipulator” ASME J. Dynamics Systems, Measurement and Control 102, No. 2, 69–76 (1980).CrossRefGoogle Scholar
5.Walker, M.W. and Orin, D.E., “Efficient Dynamic Computer Simulation of Robotic Mechanisms” J. Dynamic Systems, Measurement and Control 104, No. 3, 205–211 (1982).CrossRefGoogle Scholar
6.Vukobratovic, M. and Kircanski, N., Scientific Fundamenta of Robotics. Vol. 4, Real-Time Dynamics of Manipulation Robots (Springer-Verlag, Berlin, 1985).Google Scholar
7.Vukobratovic, M., Li, Shi Gang and KirCanski, N., “One Efficient Procedure for Generating Dynamic Manipulator Models” Robotica, Part 3, 147–152 (1985).CrossRefGoogle Scholar
8.Vukobratovic, M. and Kirdanski, N., “Numerical Generation of Closed Form Mathematical Models of Robotic Mechanisms” Ada Applicandea Mathematicae 3, 49–70 (1985).Google Scholar
9.Neuman, C.P. and Murray, J.J., “Computational Robot Dynamics: Foundations and Applications” J. Robotic Systems 2, No. 4, 425–452 (1985).CrossRefGoogle Scholar
10.Kircanski, N., Vukobratovid, M., Kircanski, M. and TimCenko, A., “A New Program Package for the Generation of Efficient Manipulator Kinematic and Dynamic Equations in Symbolic Form” Robotica 6, 311–318 (1988).CrossRefGoogle Scholar
11.Burdick, J., “An Algorithm for Generation of Efficient Manipulator Dynamic Equations” Proc. IEEE Int. Conf. on Robotics and Automation,San Francisco (1986) pp. 212–218.Google Scholar
12.Khalil, W., Kleinfinger, J.F. and Gautier, M., “Reducing the Computational Burden of the Dynamic Models of Robots” Proc. IEEE Int. Conf. on Robotics and Automation,San Francisco (1986) pp. 525–632.Google Scholar
13.Vukobratovic, M. et al. , “SYM-Program for Computer Aided Generation of Optimal Symbolic Models of Robot Manipulators” In: Multibody Systems Handbook (Schiehlen, W., ed.) (Springer-Verlag, Berlin, 1989).Google Scholar
14.Timcenko, A., Kircanski, N. and Vukobratovid, M., “A Two-Step Algorithm for Generating Efficient Manipulator Models in Symbolic Form”, Proc. IEEE Conf. on Robotics and Automation,Sacramento (1991) pp. 1887–1893.Google Scholar
15.Vukobratović, M. and Stokić, D., Scientific Fundamentals of Robotics, Vol. 2., Control of Manipulation Robots (Springer-Verlag, Berlin, 1982).Google Scholar
16.Wang, L.T. and Ravani, B., “Recursive Computations of Kinematic and Dynamic Equations for Mechanical Manipulators” IEEE J. Robotics and Automation, Vol. 1, No. 3, 98–104 (1985).CrossRefGoogle Scholar
17.Akselrod, B.V., “Description of Manipulator Dynamics by Using Screw Theory” (in Russian) Solid Body Mechanics (Moscow) No. 2, 79–84 (1985).Google Scholar
18.Auzinish, Y.P. and Sliede, P.B., “Computer-Aided Modelling of Manipulation Dynamics Based on Implicit Method” (in Russian), Technical Cybernetics AN USSR (Moscow), No. 6, 18–26 (1984).Google Scholar
19.Vereshchagin, A.F., “Dynamics Modelling of Complex Mechanisms of Robot Manipulators” (In Russian) Technical Cybernetics (Moscow) No. 6, 14–21 (1974).Google Scholar
20.Featherstone, R. “The Calculation of Robots Dynamics Using Articulated-Body Inertias”, Int. J. Robotics Research 2, 13–30 (1983).CrossRefGoogle Scholar
21.Filaretov, V.F. and Korzun, A.I., “Modelling of Manipulators Dynamics by Using Screw-Coordinates and Dynamic Programming” (in Russian), Solid-Body Dynamics (Moscow) No. 3, 29–36 (1988).Google Scholar
22.Samson, C., Leborgne, M. and Espiau, B., Robot Control: The Task-Function Approach, Oxford Engineering Science Series No. 22 (Oxford University Press, Oxford, 1991).Google Scholar
23.Denavit, J. and Hartenberg, R.S., “A Kinematic Notation for Lower-Pair Mechanisms Based on Matrices” Trans. ASME, J. Applied Mechanics 22, 215–221 (06, 1955).CrossRefGoogle Scholar
24.Lawson, C.L. and Hanson, R., Solving Least Squares Problems (Prentice Hall, Inc., Englewood Cliffs, New Jersey, 1974).Google Scholar
25.Bryson, A.E. and Yy-Shi-Ho, Applied Optimal Control, Revised Printing (John Wiley and Sons, New York, 1975).Google Scholar
26.Wittenburg, J., Dynamics of Systems of Rigid Bodies (B.G. Teubner, Stuttgart, 1977).CrossRefGoogle Scholar