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Optimal navigation functions for nonlinear stochastic systems

Horowitz, Matanya B. and Burdick, Joel W. (2014) Optimal navigation functions for nonlinear stochastic systems. In: 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems. IEEE , Piscataway, NJ, pp. 224-231. ISBN 978-1-4799-6934-0. https://resolver.caltech.edu/CaltechAUTHORS:20150402-131605354

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Abstract

This paper presents a new methodology to craft navigation functions for nonlinear systems with stochastic uncertainty. The method relies on the transformation of the Hamilton-Jacobi-Bellman (HJB) equation into a linear partial differential equation. This approach allows for optimality criteria to be incorporated into the navigation function, and generalizes several existing results in navigation functions. It is shown that the HJB and that existing navigation functions in the literature sit on ends of a spectrum of optimization problems, upon which tradeoffs may be made in problem complexity. In particular, it is shown that under certain criteria the optimal navigation function is related to Laplace's equation, previously used in the literature, through an exponential transform. Further, analytical solutions to the HJB are available in simplified domains, yielding guidance towards optimality for approximation schemes. Examples are used to illustrate the role that noise, and optimality can potentially play in navigation system design.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/IROS.2014.6942565 DOIArticle
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6942565PublisherArticle
https://arxiv.org/abs/1409.5993arXivDiscussion Paper
Additional Information:© 2014 IEEE. Matanya Horowitz is supported by a NSF Graduate Research Fellowship.
Funders:
Funding AgencyGrant Number
NSF Graduate Research FellowshipUNSPECIFIED
Record Number:CaltechAUTHORS:20150402-131605354
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20150402-131605354
Official Citation:Horowitz, M.B.; Burdick, J.W., "Optimal navigation functions for nonlinear stochastic systems," Intelligent Robots and Systems (IROS 2014), 2014 IEEE/RSJ International Conference on , vol., no., pp.224,231, 14-18 Sept. 2014 doi: 10.1109/IROS.2014.6942565 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6942565&isnumber=6942370
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:56310
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:02 Apr 2015 20:44
Last Modified:03 Oct 2019 08:13

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