Jacobs, Henry and Nair, Sujit and Marsden, Jerrold E. (2010) Multiscale Surveillance of Riemannian Manifolds. In: 2010 American Control Conference (ACC). Proceedings of the American Control Conference . IEEE , pp. 5732-5737. ISBN 978-1-4244-7426-4 http://resolver.caltech.edu/CaltechAUTHORS:20110412-133114485
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When surveying a surface, such as a spherical shell around a planet or a mine field, it is often desirable to survey a pre-chosen distribution while simultaneously respecting all its length scales. We review the Mix Norm developed by Mathew and Mezic  and their application for a multiscale coverage algorithm on the unit square and torus.We then develop tools to do multiscale surveillance on arbitrary Riemannian manifolds (M, g). Next, we study the effects of applying the mix norm algorithm to more realistic scenarios where we have vehicles with different maximum speeds and frequency responses. We demonstrate this by applying the algorithm on the unit square to the case of a slow vehicle and a fast vehicle simultaneously exploring different spatial scales; we then test how well the uniform coverage algorithm allows a vehicle to estimate a function in a least squares sense. We also study the effects of varying the parameter s in the definition of mix norm for (M, g). In future work, we plan to apply a motions primitive based approach and explore ways of working with more general surfaces using triangular meshes.
|Item Type:||Book Section|
|Additional Information:||© 2010 AACC. Issue Date: June 30 2010-July 2 2010. Date of Current Version: 29 July 2010. This research was supported by a Graduate Research Fellowship from the Rose Hills Foundation. We owe special thanks to Phillip du Toit and Marin Kobilarov for general comments and suggestions.|
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|Official Citation:||Jacobs, H.; Nair, S.; Marsden, J.; , "Multiscale surveillance of Riemannian manifolds," American Control Conference (ACC), 2010 , vol., no., pp.5732-5737, June 30 2010-July 2 2010 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5531152&isnumber=5530425|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||25 May 2011 19:52|
|Last Modified:||29 Mar 2014 02:31|
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