Hostname: page-component-76dd75c94c-h9cmj Total loading time: 0 Render date: 2024-04-30T09:35:06.155Z Has data issue: false hasContentIssue false
  • English
  • Français

On the sensitivity analysis of the computational kinematics of the robotic manipulators

Published online by Cambridge University Press:  09 March 2009

Siamak Vahidi  and
Kazem Kazerounian
Siamak Vahidi
Affiliation:
191 Auditorium Road, Department of Mechanical Engineering, The University of Connecticut, Storrs, CT06269-3139 (USA)
Kazem Kazerounian
Affiliation:
191 Auditorium Road, Department of Mechanical Engineering, The University of Connecticut, Storrs, CT06269-3139 (USA)
Get access Rights & Permissions [Opens in a new window]

Summary

In the computational kinematics of robotic manipulators, accuracy and sensitivity of the results are highly dependent on the choice of the coordinate system, the metric system, and the appropriateness of performance evaluation measure. In this paper, these undesired sensitivities are examined and suitable performance criteria are developed to eliminate the coordinate system and metric system dependencies, and adverse numerical effects associated with them. Also a new formulation for the Jacobian matrix, joint velocities, and hand velocities, based on the Euler angles, is developed. This formulation, further improves numerical accuracy of the computations. Numerical experiments are included.

Keywords

Sensitivity analysisComputational kinematicsRobots
Type
Articles
Information
Robotica , Volume 13 , Issue 6 , November 1995 , pp. 575 - 581
Copyright
Copyright © Cambridge University Press 1995

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” Trans. ASME J. of Dynamic Systems, Measurement, and Control 94, 303–309 (1972).CrossRefGoogle Scholar
2.Hall, A.S., Root, R.R. and Sandgren, E., “A Dependable Method for Solving Matrix Loop Equations for the General Tree-Dimensional Mechanisms” Trans. ASME J. of Engineering for Industry 99(3), 547–550 (1977).CrossRefGoogle Scholar
3.Gupta, K.C., “A Note on the Position Analysis of Manipulators” Proc. of the Seventh Applied Mechanism Conference, Kansas City,Missoury(1981)pp.3.1–3.33; also Mechanisms and Machine Theory 19(1), 5–8 (1984).Google Scholar
4.Goldernberg, A.A. and Lawrence, D.L., “A Generalized Solution to the Inverse Kinematics of Robotic Manipulators” Trans. ASME J. of Dynamic Systems, Measurement, and Control 107, 102–106 (1985).Google Scholar
5.Pennock, G.R. and Stevenson, C.N., “Application of Dual- Number Matrices to the Inverse Kinematics Problem of Robot Manipulators” Trans ASME J. of Mechanisms, Transmissions, and Automation in Design 107, 201–208 (1985).CrossRefGoogle Scholar
6.Angeles, J., “Iterative Kinematic Inversion of General Five-Axis Robot Manipulators” Int. J. Robotics Research 4(4), 59–70 (1986).CrossRefGoogle Scholar
7.Kazerounian, K., “On the Numerical Inverse Kinematic of Robot Manipulators” Trans. ASME J. of Mechanisms, Transmissions, and Automation in Design 109, 8–13 (1987).CrossRefGoogle Scholar
8.Rastegar, J. and Singh, R. J., “Determination of Manipulator Kinematic Characteristics: A Probabilistic Approach” Int. J. Robotics and Automation 7(4), 161–170 (1992).Google Scholar
9.McCarthy, L.M., An Introduction to Theoretical Kinematics (The MIT Press, Cambridge, MA, 1990).Google Scholar
10.Gupta, K.C. and Kazerounian, K., “An Investigation of Time Efficiency and Near Singular Behavior of Numerical Robot Kinematics” Mechanisms and Machine Theory 22(4), 371–381 (1987).CrossRefGoogle Scholar
11.Suh, H.H. and Radcliffe, C.W., Kinematics and Mechanism Design (Robert E. Krieger Publishing Company, Malabar: FL, 1983).Google Scholar
12.Kazerounian, K., “Manipulation and Simulation of General Robots Using Zero-Position Description” Ph.D Dissertation (University of Illinois at Chicago, 1984).Google Scholar
13.Burden, R.L. and Faires, J.D., Numerical Analysis, Third Edition (PWS Publications, Boston, 1985).Google Scholar
14.Torby, B.J., Advanced Dynamics for Engineers (Holt. Rinehart and Winston, New York, 1984).Google Scholar
15.Kraus, A.D., Matrices for Engineers (Hemisphere Publishing Corporation, New York, 1987).Google Scholar
16.Vahidi, S.. “Computational Kinematics of Multi-Arm Manipulators” Ph.D. Dissertation (University of Connec-ticut. Storrs: CT. 1992).Google Scholar
17.Craig, J.J., Introduction to Robotic Mechanisms and Control (Addison-Wesley Publishing Company, Reading: MA. 1986).Google Scholar