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On numerical techniques for kinematics problems of general serial-link robot manipulators

Published online by Cambridge University Press:  09 March 2009

Shinobu Sasaki
Shinobu Sasaki
Affiliation:
Reactor Engineering, Japan Atomic Energy Research Institute, Tokai-mura, Naka-gum, lbaraki-ken, 319–11 (Japan) (Received in Final Form; September 21, 1993)
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Summary

This paper addresses widely applicable methods for solving the kinematics problem of any class of serial-link robot manipulators. First, the position and orientation of the manipulator hand, the Jacobian matrix and their symbolic generation are clearly presented using recursive relations. Second, the inverse problem to such formulations is posed as an unconstrained non-linear optimization one, where numerical techniques for the overdetermined and underdetermined kinematic problems are considered separately to derive consistent arm solutions. On the basis of several proposals on step lengths involved to maintain good numerical stability, the results of computer simulation show that performance is sufficiently reliable.

Keywords

Serial manipulatorsKinematicsRecursive relationsOptimization.
Type
Article
Information
Robotica , Volume 12 , Issue 4 , July 1994 , pp. 309 - 322
Copyright
Copyright © Cambridge University Press 1994

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References

1.Coiffet, P., Robot Technology-Modelling and Control, Vol. 1 (Prentice-Hall Inc., Englewood Cliffs, 1983).CrossRefGoogle Scholar
2.Paul, R.P., Robot Manipulators; Mathematics, Programming and Control (The MIT Press, Cambridge, MASS, 1981).Google Scholar
3.Pieper, D.L., “The Kinematics of Manipulators under Computer Control” (Stanford Artificial Intelligence Lab. Stanford CA) Memo AIM 72 (1968).Google Scholar
4.Paul, R.P., Shimano, B. and Mayer, G.E., “Kinematic Control Equations for Simple Manipulators” IEEE Trans. Syst. Man Cybern. SMC-11(6), 449–455 (1981).Google Scholar
5.Duffy, J., Analysis of Mechanismss and Robot Manipulators (Edward Arnold, London, 1980).Google Scholar
6.Young, A.T. and Freudenstein, R., “Application of Dual Number Quaternion Algebra to the Analysis of Spacial Mechanisms” J. Appl. Mech., Trans. ASME 31, 300–308 (1964).CrossRefGoogle Scholar
7.Featherstone, R., “Position and Velocity Transformations between Robot End-Effector Co-ordinates and Joint Angles” Int. J. Robotics Res. 2(2), 35–45 (1983).CrossRefGoogle Scholar
8.Hollerbach, J.M. and Sahar, G., “Wrist-Partitioned, Inverse Kinematic Accelerations and Manipulator Dynamics” It. J. Robotics Res. 2(4), 61–76 (1983).CrossRefGoogle Scholar
9.Lee, C.S.G. and Ziegler, M., “A Geometric Approach in Solving the Inverse Kinematics of PUMA Robots” 13th ISIR. Chicago (1983) pp. 16–1/16–18.Google Scholar
10.Sasaki, S., “Feasibility Study of Manipulator Inverse Kinematics Problems with Applications of Optimization Principles” Mechanism and Machine Theory 28(5), 685–697 (1993).CrossRefGoogle Scholar
11.Uicker, J.J., Denavit, J. and Hartenberg, R.S., “An Iterative Method for the Displacement Analysis of Spatial Mechanisms” J. Appl. Mech., Trans. ASME 31, 309–314 (1964).CrossRefGoogle Scholar
12.Ortega, J.M. and Rheinboldt, W.C., Iterative Solution of Nonlinear Equations in Several Variables (Academic Press, New York, 1970).Google Scholar
13.Orin, D.E. and Schrader, W.W., “Efficient Computation of the Jacobian for Robot manipulators” Int. J. Robotics Res. 3(4), 66–75 (1984).CrossRefGoogle Scholar
14.Klein, C.A. and Huang, C.H., “Review of Pseudo-Inverse Control for Use with Kinematically Redundant Manipulators” IEEE Trans. Syst. Man Cybern. SMC-13(3), 245–250 (1983).CrossRefGoogle Scholar
15.Vukobratović, M. and Kirćanski, M., “Kinematics and Trajectory Synthesis of Manipulation Robots” In: Scientific Fundamentals of Robotics 3 (Springer Verlag, Berlin, 1986).Google Scholar
16.Wampler, C.W. II, “Manipulator Inverse Kinematic Solutions Based on Vector Formulations and Damped Least-Squares Methods” IEEE Trans. Syst. Man Cybern. SMC-16(1), 93–101 (1986).CrossRefGoogle Scholar
17.Wang, Z. and Kazerounian, K., “An Efficient Algorithm for Global Optimization in Redundant Manipulations” J. Mech. Trans. Automation in Design, Trans. of ASME 111, 488–493 (1989).CrossRefGoogle Scholar
18.Won, J.H., Choi, B.W. and Chung, M.J., “A Unified Approach to the Inverse Kinematic Solution for a Redundant Manipulator” Robotica 11, part 2, 159–165 (1993).CrossRefGoogle Scholar
19.Zomaya, A.Y., “On the Fast Simulation of Direct and Inverse Jacobian for Robot Manipulators” Robotics and Autonoumous Systems 10, 43–61 (1992).CrossRefGoogle Scholar
20.Denavit, J. and Hartenberg, R.S., “A Kinematic Notation for Low-Pair Mechanisms Based on Matrices” J. Appl. Mech., Trans. ASME 22, 215–221 (1955).CrossRefGoogle Scholar
21.Hearn, A.C., REDUCE User's Manual (version 3.1) (The Rand Corporation, oSanta Monica 1984).Google Scholar
22.Sasaki, S., “Expressions of Manipulator Kinematic Equations via Symbolic Computation” Japan Atomic Energy Research Institute Report JAER1-M 93–168, 1–17 (1993). (in Japanese).Google Scholar
23.Kowalik, J. and Osborne, M.R., Methods for Unconstrained Optimization Problems (American Elsevier Publishing Company, Inc., New York, 1968).Google Scholar
24.Fletcher, R., “A Modified Marquardt Subroutine for Nonlinear Least Squares” UKAEA Harwell Report, AERE-R, 6799 (1971).Google Scholar
25.Davidon, W.C., “Variable Metric Method for Minimization” AEC Research and Development Report, ANL-5990 (REV.), (1959).CrossRefGoogle Scholar
26.Huang, H.Y., “Unified Approach to Quadratically Convergent Algorithms for Function Minimization” J. Optimization Theory & Appl. 5, 405–423 (1970).CrossRefGoogle Scholar
27.Broyden, C.G., “Quasi-Newton Methods and Theis Application to Function Minimization” Math. Comp. 21, 368–381 (1967).CrossRefGoogle Scholar
28.Golub, G.H. and Reinsch, C., “Singular Value Decomposition and Least Squares Solutions” Numer. Math. 14, 403–420 (1970).CrossRefGoogle Scholar
29.Neider, J.A. and Mead, R., “A Simplex Method for Function Minimization” Computer J. 7, 308–313 (1965).Google Scholar