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A new geometric approach to characterize the singularity of wheeled mobile robots

Published online by Cambridge University Press:  01 September 2007

Luis Gracia  and
Josep Tornero
Luis Gracia*
Affiliation:
Department of Systems Engineering and Control, Technical University of Valencia, PO Box 22012 E-46071 Valencia, Spain.
Josep Tornero
Affiliation:
Department of Systems Engineering and Control, Technical University of Valencia, PO Box 22012 E-46071 Valencia, Spain.
*
*Corresponding author. E-mail: luigraca@isa.upv.es
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Summary

This research presents a new and generic geometric approach that characterizes the kinematic singularity of wheeled mobile robots. First, the kinematic models of all the common wheels are obtained: fixed, centered orientable, castor, and Swedish. Then, a procedure for generating robot kinematic models is presented based on the set of wheel equations and the null space concept. Next, two examples are developed to illustrate the nongeneric singularity characterization. In order to improve that approach, a generic and practical geometric approach is established to characterize the singularity of any kinematic model of a wheeled mobile robot (WMR). Finally, the singular configurations for many types of mobile robots are depicted employing the proposed approach.

Keywords

Model singularitySingular configurationsKinematic modelingWheeled mobile robots (WMR)
Type
Article
Information
Robotica , Volume 25 , Issue 5 , September 2007 , pp. 627 - 638
Copyright
Copyright © Cambridge University Press 2007

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References

1.Murray, R. M. and Sastry, S. S., “Nonholonomic motion planning: Steering using sinusoids,” IEEE Trans. Autom. Control 38, 700–716 (1993).CrossRefGoogle Scholar
2.Canudasde Wit, C. and Sordalen, O. J., “Exponential Stabilization of Mobile Robots With Nonholonomic Constraints,” Proceedings of the IEEE Conference on Decision and Control, Brighton, England (1991), pp. 692–697.Google Scholar
3.Badreddin, E. and Mansour, M., “Fuzzy-Tuned State-Feedback Control of a Nonholonomic Mobile Robot,” Proceedings of the 12th World Congress of the International Federation of Automatic Control, Sidney, Australia 6, (1993), pp. 577–580.Google Scholar
4.Campion, G., Bastin, G. and D'Andrea-Novel, B., “Structural properties and classification of kinematic and dynamic models of wheeled mobile robots,” IEEE Trans. Robot. Autom. 12 (1), 47–61 (1996).Google Scholar
5.Muir, P. F. and Neuman, C. P., “Kinematic modeling of wheeled mobile robots,” J. Robot. Syst. 4 (2), 281–329 (1987).CrossRefGoogle Scholar
6.Shin, D. H. and Park, K. H., “Velocity Kinematic Modeling for Wheeled Mobile Robots,” Proceeding of the International Conference on Robotics and Automation, Seul, Korea (2001), pp. 3516–3522.Google Scholar
7.Rajagopalan, R., “A generic kinematic formulation for wheeled mobile robots,” J. Robot. Syst. 14, 77–91 (1997).Google Scholar
8.Alexander, J. C. and Maddocks, J. H., “On the kinematics of wheeled mobile robots,” Int. J. Robot. Res. 8 (5), 15–27 (1989).CrossRefGoogle Scholar
9.Kim, W., Yi, B.-J. and Lim, D. J., “Kinematic modeling of mobile robots by transfer method of augmented generalized coordinates,” J. Robot. Syst. 21 (6), 301–322 (2004).Google Scholar
10.Low, K. H. and Leow, Y. P., “Kinematic modeling, mobility analysis and design of wheeled mobile robots,” Adv. Robot. 19, 73–99 (2005).CrossRefGoogle Scholar
11.Fu, K. S., Gonzalez, R. C. and Lee, C. S. G., Robotics: Control, Sensing and Intelligence (McGraw-Hill, New York, 1987) ch. 3.Google Scholar
12.Denavit, J. and Hartenberg, R. S., “A kinematic notation for lower-pair mechanism based on matrices,” J. Appl. Mech. 77 (2), 215–221 (1955).Google Scholar
13.Sheth, P. N. and Uicker, J. J. Jr., “A generalized symbolic notation for mechanisms,” J. Eng. Ind. 93 (70), 102–112 (1971).CrossRefGoogle Scholar
14.Murray, R. M., Li, Z. and Sastry, S. S., A Mathematical Introduction to Robotic Manipulation (CRC Press. Boca Raton, FL, 1994).Google Scholar
15.Tourassis, V. D. and Ang, H. Jr., “Identification and analysis of robot manipulator singularities,” Int. J. Robot. Res. 11 (3), 248–259 (1992).CrossRefGoogle Scholar
16.Dinesh, K. and Leu, M. C., “Genericity and singularities of robot manipulators,” IEEE Trans. Robot. Autom. 8 (5), 545–559 (1992).Google Scholar
17.Liu, G., Lou, Y. and Li, Z., “Singularities of parallel manipulators: A geometric treatment,” IEEE Trans. Robot. Autom. 19 (4), 579–594 (2003).Google Scholar
18.Lipkin, H. and Pohl, E., “Enumeration of singular configurations for robotic manipulators,” ASME J. Mech. Design 113 272–279 (1991).CrossRefGoogle Scholar
19.Yi, B.-J. and Kim, W. K., “The kinematics for redundantly actuated omnidirectional mobile robots,” J. Robot. Syst. 19 (6), 255–267 (2002).Google Scholar
20.Loh, W. K., Low, K. H. and Leow, Y. P., “Mechatronics Design and Kinematic Modeling of a Singularityless Omnidirectional Wheeled Mobile Robot,” Proceedings of the International Conference on Robotics and Automation, Taiwan (2003) pp. 3237–3242.Google Scholar
21.Nenchev, D. N. and Uchiyama, M., “Singularity-consistent path planning and motion control through instantaneous self-motion singularities of parallel-link manipulators,” J. Robot. Syst. 14 (1), 27–36 (1997).Google Scholar
22.Lloyd, J. E. and Hayward, V., “Singularity-robust trajectory generation,” Int. J. Robot. Res. 20 (1), 38–56 (2001).CrossRefGoogle Scholar
23.Stanisic, M. M and Duta, O., “Symmetrically actuated double pointing systems: The basis of singularity-free robot wrists,” IEEE Trans. Robot. Autom. 6 (5), 562–569 (1990).Google Scholar
24.Lai, J. Z. C. and Yang, D., “Efficient motion control algorithm for robots with wrist singularities,” IEEE Trans. Robot. Autom. 6 (1), 113–117 (1990).CrossRefGoogle Scholar