Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-27T10:50:19.429Z Has data issue: false hasContentIssue false
  • English
  • Français

An efficient numerical approach for calculating the inverse kinematics for robot manipulators

Published online by Cambridge University Press:  09 March 2009

Jadran Lenarčič
Jadran Lenarčič
Affiliation:
Department of Automatics, Biocybernetics and Robotics, University of “Edvard Kardell”, Institut “Jožef Stefan”, Ljubljana (Yugoslavia)
Get access Rights & Permissions [Opens in a new window]

Summary

This paper compares three numerical methods for obtaining the joint trajectory of a robot manipulator, which causes movement along the desired Cartesian path. The first solves the kinematic equations, which are given in the Jacobian form, while the other two solve the nonlinear kinematic equations directly by using an iterative computational procedure based on the conjugate gradient technique. The computational efficiency of the proposed methods is estimated in terms of the execution time on a VAX 11/750 minicomputer. It is shown that by using the capacity of microcomputers, these methods could be well used in real-time computation.

Type
Article
Information
Robotica , Volume 3 , Issue 1 , January 1985 , pp. 21 - 26
Copyright
Copyright © Cambridge University Press 1985

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.Whitney, D.E., “The Mathematics of Coordinated Control of Prosthetic Arms and Manipulators” ASME Trans. J. of Dynamic Systems, Measurement, and Control 303–309 (1972).CrossRefGoogle Scholar
2.Paul, R.P., Robot Manipulators: Mathematics, Programming and Control (The MIT Press, Massachusetts and London, UK, 1981).Google Scholar
3.Paul, R.P., “Manipulator Cartesian Path Control” IEEE Trans. Syst., Man, Cybern., SMC-9, No. 11, 702–711 (1979).Google Scholar
4.Luh, J.Y.S., “Approximate Joint Trajectories for Control of Industrial Robots Along Cartesian Paths” IEEE Trans. Syst., Man, Cyben., SMC-14, No. 3, 444–450 (1984).Google Scholar
5.Lin, C.S. and Chang, P.R., “Joint Trajectories of Mechanical Manipulators for Cartesian Path Approximation” IEEE Trans. Syst., Man, Cybern. SMC-13, No. 6, 1094–1102 (1983).Google Scholar
6.Featherstone, R., “Position and Velocity Transformations Between Robot End-Effector Coordinates and Joint Angles” Int. J. of Robotics Research 2, No. 2, 35–45 (1983).Google Scholar
7.Lenarčič, J., “A New Method for Calculating the Jacobian for a Robot Manipulator” Robotica 1, No. 4, 205–209 (1983).Google Scholar
8.Lenarčič, J., Oblak, P. and Stanič, U., “Methods for Computing Functional Trajectories of an Industrial Robot” Proc. of the 3rd Yugoslav Symposium on Applied Robotics, Vmjačka Banja, Yugoslavia (1983),Google Scholar
9.Takano, M., Yashima, K. and Yada, S., “Development of Computer Simulation System of Kinematics and Dynamics of Robot” J. Faculty of Eng. The University of Tokyo XXXVI, No. 4, 677–711 (1982).Google Scholar
10.Milenkovic, V. and Huang, B., “Kinematics of Major Robot Linkage” Proc. of 13th ISIR, Chicago, USA (1983).Google Scholar
11.Lumelsky, V.J., “Iterative Coordinate Transformation Procedure for One Class of Robots” IEEE Trans. Syst., Man, Cybern. SMC-14, No. 3 (1984).Google Scholar
12.Takano, M., “A New Method of Solution of Synthesis Problem of a Robot and its Application to Computer Simulation System” Proc. of 14th ISIR, Gothenburg, Sweden (1984).Google Scholar
13.Fletcher, R. and Reeves, C.M., “Function Minimization by Conjugate Gradients” Brit. Computer J. 7, 149–154 (1964).Google Scholar