Lin, Qiao and Burdick, Joel W. (2000) On well-defined kinematic metric functions. In: Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings. Vol.1. IEEE , Piscataway, NJ, pp. 170-177. ISBN 0-7803-5886-4. https://resolver.caltech.edu/CaltechAUTHORS:20190624-104335160
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Abstract
This paper presents both formal as well as practical well-definedness conditions for kinematic metric functions. To formulate these conditions, we introduce an intrinsic definition of a rigid body's configuration space. Based on this definition, the principle of objectivity is introduced to derive a formal condition for well-definedness of kinematic metric functions, as well as to gain physical insight into left, right and bi-invariances on the Lie group SE(3). We then relate the abstract notion of objectivity to the more intuitive notion of frame-invariance, and show that frame-invariance can be used as a practical condition for determining objective functions. Examples demonstrate the utility of objectivity and frame-invariance.
| Item Type: | Book Section | ||||||
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| Additional Information: | © 2000 IEEE. The authors would like to thank Prof. J.E. Marsden for valuable discussions on the general principle of objectivity. | ||||||
| DOI: | 10.1109/ROBOT.2000.844055 | ||||||
| Record Number: | CaltechAUTHORS:20190624-104335160 | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20190624-104335160 | ||||||
| Official Citation: | Qiao Lin and J. W. Burdick, "On well-defined kinematic metric functions," Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065), San Francisco, CA, USA, 2000, pp. 170-177 vol.1. doi: 10.1109/ROBOT.2000.844055 | ||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
| ID Code: | 96663 | ||||||
| Collection: | CaltechAUTHORS | ||||||
| Deposited By: | Tony Diaz | ||||||
| Deposited On: | 24 Jun 2019 18:22 | ||||||
| Last Modified: | 16 Nov 2021 17:22 |
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