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On well-defined kinematic metric functions

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
Related URLs:
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https://doi.org/10.1109/ROBOT.2000.844055DOIArticle
Additional Information:© 2000 IEEE. The authors would like to thank Prof. J.E. Marsden for valuable discussions on the general principle of objectivity.
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:03 Oct 2019 21:24

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