Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-28T21:55:02.809Z Has data issue: false hasContentIssue false
  • English
  • Français

Exact solution of inverse kinematic problem of 6R serial manipulators using Clifford Algebra

Published online by Cambridge University Press:  09 August 2012

Eriny W. Azmy
Eriny W. Azmy*
Affiliation:
School of Mathematical Sciences, Faculty of Science, Monash University, Melbourne, Australia
*
*Corresponding author. E-mail: eriny.azmy@monash.edu
Get access Rights & Permissions [Opens in a new window]

Summary

In this paper, Clifford Algebra is used to model and facilitate solving the inverse kinematic problem for robots with only two consecutive parallel axes. It is shown that when a solution exists, it is usually the case that one of the angles of rotation can be arbitrarily chosen from a union of intervals. The remaining angles are then uniquely determined. Of course, there are cases when no solution exists, such as when the object is out of reach. But typically, when solutions exist, there are infinitely many sets of solutions.

Keywords

Clifford AlgebraInverse kinematic problem6R serial robot
Type
Articles
Information
Robotica , Volume 31 , Issue 3 , May 2013 , pp. 417 - 422
Copyright
Copyright © Cambridge University Press 2012

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.Pieper, D., “The Kinematics of Manipulators Under Computer Control,” Ph.D. thesis (Stanford University, Stanford, CA, 1968).Google Scholar
2.Selig, J. M., “Clifford Algebra of points, lines and planes,” Robotica 18, 545–556 (2000).CrossRefGoogle Scholar
3.Selig, J. M., Geometric Fundamentals of Robotics (Springer, New York, 2005).Google Scholar
4.Bayro-Corrochano, E. and Sobczyk, G., Geometric Algebra with Applications in Science and Engineering (Birkhauser, New York, 2001).CrossRefGoogle Scholar
5.Bayro-Corrochano, E. and Kahler, D., “Motor algebra approach for computing the kinematics of robot manipulators,” J. Robot. Syst. 17 (9), 495–516 (2000).3.0.CO;2-S>CrossRefGoogle Scholar
6.Bayro-Corrochano, E. and Falcon, L. Eduardo, “Geometric algebra of points, lines, planes and spheres for computer vision and robotics,” Robotica 23, 755–770 (2005).CrossRefGoogle Scholar
7.Sariyildiz, E. and Temeltas, H., “Solution of Inverse Kinematic Problem for Serial Robot using Quaternions,” In: Proceedings of IEEE, International Conference of Mechatronics and Automation, Changchun (2009) pp. 26–31.Google Scholar
8.Payandeh, S. and Goldenberg, A. A., “Formulation of the kinematic model of a general (6 DOF) robot manipulator using a screw operator,” J. Robot. Syst. 4 (6), 771–797 (1987).CrossRefGoogle Scholar
9.Vasilyev, I. A. and Lyashin, A. M., “Analytical solution of inverse kinematic problem for 6-DOF robot-manipulator,” Autom. Remote Control 71 (10), 2195–2199 (2010).CrossRefGoogle Scholar
10.Pfurner, M. and Husty, M. L., “A method to determine the motion of over constrained 6R-Mechanisms,” Proceedings of the 12th IFToMM World Congress, Besançon, France (Jun. 18–21, 2007).Google Scholar
11.Manfred, L. Husty, Pfurner, M. and Schrocker, Hans-Peter, “A new and efficient algorithm for inverse kinematics of a general serial 6R manipulator,” Mech. Mach. Theory 42, 66–81 (2006).Google Scholar
12.Joubert, N., Numerical Methods for Inverse Kinematics (UC, Berkeley, CA, 2008).Google Scholar
13.Duffy, J. and Crane, C., Kinematic Analysis of Robot Manipulators (Cambridge University Press, Cambridge, UK, 1998).Google Scholar
14.Selig, J. M., Introductory Robotics (Prentice Hall, Upper Saddle River, NJ, 1992).Google Scholar