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Discriminant functions for isotropic configurations in robot manipulators

Published online by Cambridge University Press:  08 June 2011

Ignacy Duleba
Ignacy Duleba*
Affiliation:
Institute of Computer Engineering, Control and Robotics, Wroclaw University of Technology, Janiszewski St. 11/17, 50-372 Wroclaw, Poland
*
*Corresponding author. E-mail: ignacy.duleba@pwr.wroc.pl
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Summary

In this paper, a family of discriminant functions is defined for searching isotropic configurations in robot manipulators. A subfamily of the functions extensively exploits properties of symmetric polynomials derived from a manipulability matrix. The complexity analysis of computing the discriminant functions is provided. Possible applications of the functions are mentioned and illustrated.

Keywords

ManipulatorIsotropyDiscriminant functionComplexityRoboticsApplications
Type
Articles
Information
Robotica , Volume 30 , Issue 2 , March 2012 , pp. 221 - 227
Copyright
Copyright © Cambridge University Press 2011

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References

1.Arechavaleta, G., Laumond, J.-P. and Hicheur, H., “An optimality principle governing human walking,” IEEE Trans. Robot. 21 (1), 5–14 (2008).CrossRefGoogle Scholar
2.Klein, C. and Blaho, B., “Dexterity measures for the design and control of kinematically redundant manipulators,” Int. J. Robot. Res. 6 (2), 72–83 (1987).CrossRefGoogle Scholar
3.Bicchi, A., Prattichizzo, D. and Melchiorri, C., “Force and Dynamic Manipulability for Cooperating Robots,” Proceedings of the International Conference on Intelligent Robots and Systems, Grenoble, France, (1991) pp. 1479–1484.Google Scholar
4.Barcio, B. and Walker, I., “Impact Ellipsoids and Measures for Robot Manipulators,” Proceedings of the IEEE International Conference on Robotics and Automation, San Diego, CA, USA (1994) pp. 1588–1594.Google Scholar
5.Yoshikawa, T., “Analysis and Control of Robot Manipulators with Redundancy,” Proceedings of the First International Symposium on Robotics Research (Brady, M. and Paul, R., eds.) (MIT Press, Cambridge, MA, 1984) pp. 735–747.Google Scholar
6.Yoshikawa, T., “Manipulability of robotic mechanisms,” Int. J. Robot. Res. 4 (2), 3–9 (1985).CrossRefGoogle Scholar
7.Tchon, K. and Zadarnowska, K., “Kinematic dexterity of mobile manipulators: An endogenous configuration space approach,” Robotica 21 (5), 521–530 (2003).CrossRefGoogle Scholar
8.Alici, G. and Shirinzadeh, B., “Optimum synthesis of planar parallel menipuloators based on kinematic isotropy and force balancing,” Robotica 22 (1), 97–108 (2004).CrossRefGoogle Scholar
9.Carriacolo, M. and Parenti-Castelli, V., “Singularity-free fully isotropic translational parallel mechanisms,” Int. J. Robot. Res. 21 (2), 161–174 (2002).Google Scholar
10.Kircanski, M., “Kinematic isotropy and optimal kinematic design of planar manipulators and a 3-dof spatial manipulator,” Int. J. Robot. Res. 15 (1), 61–77 (1996).CrossRefGoogle Scholar
11.Spong, M. and Vidyasagar, M., Introduction to Robotics. Robot Dynamics and Control (MIT Press, Cambridge, 1989).Google Scholar
12.Nakamura, Y., Chung, W. and Sordalen, O.. “Design and control of the nonholonomic manipulator,” IEEE Trans. Robot. Autom. 17 (1), 48–59 (2001).CrossRefGoogle Scholar
13.Maciejewski, A. and Klein, C., “The singular value decomposition: Computation and applications to robotics,” Int. J. Robot. Res., 8 (6), 63–79 (1989).CrossRefGoogle Scholar
14.Horn, R. and Johnson, C., Matrix Analysis, (Cambridge University Press, 1986).Google Scholar
15.Niculescu, C., “A new look at Newton's inequalities,” J. Inequalities Pure Appl. Math. 1 (2), Article 17, 14 pp., http://www.emis.de/journals/JIPAM/ (2000).Google Scholar
16.Nakamura, Y., Advanced Robotics: Redundancy and Optimization (Addison Wesley, New York, 1991).Google Scholar