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Trajectory Optimization for Chance-Constrained Nonlinear Stochastic Systems

Nakka, Yashwanth Kumar and Chung, Soon-Jo (2019) Trajectory Optimization for Chance-Constrained Nonlinear Stochastic Systems. In: 2019 IEEE Conference on Decision and Control (CDC). IEEE , Piscataway, NJ, pp. 3811-3818. ISBN 978-1-7281-1398-2. https://resolver.caltech.edu/CaltechAUTHORS:20190918-132943526

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Abstract

This paper presents a new method of computing a sub-optimal solution of a continuous-time continuous-space chance-constrained stochastic nonlinear optimal control problem (SNOC) problem. The proposed method involves two steps. The first step is to derive a deterministic nonlinear optimal control problem (DNOC) with convex constraints that are surrogate to the SNOC by using generalized polynomial chaos (gPC) expansion and tools taken from chance-constrained programming. The second step is to solve the DNOC problem using sequential convex programming (SCP) for trajectory generation. We prove that in the unconstrained case, the optimal value of the DNOC converges to that of SNOC asymptotically and that any feasible solution of the constrained DNOC is a feasible solution of the chance-constrained SNOC because the gPC approximation of the random variables converges to the true distribution. The effectiveness of the gPC-SCP method is demonstrated by computing safe trajectories for a second-order planar robot model with multiplicative stochastic uncertainty entering at the input while avoiding collisions with a specified probability.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/CDC40024.2019.9028893DOIArticle
ORCID:
AuthorORCID
Nakka, Yashwanth Kumar0000-0001-7897-3644
Chung, Soon-Jo0000-0002-6657-3907
Additional Information:© 2019 IEEE. This work was in part funded by the Jet Propulsion Laboratory, California Institute of Technology and the Raytheon Company.
Group:GALCIT, Center for Autonomous Systems and Technologies (CAST)
Funders:
Funding AgencyGrant Number
JPL/CaltechUNSPECIFIED
Raytheon CompanyUNSPECIFIED
Record Number:CaltechAUTHORS:20190918-132943526
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190918-132943526
Official Citation:Y. K. Nakka and S. Chung, "Trajectory Optimization for Chance-Constrained Nonlinear Stochastic Systems," 2019 IEEE 58th Conference on Decision and Control (CDC), Nice, France, 2019, pp. 3811-3818, doi: 10.1109/CDC40024.2019.9028893
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:98729
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:18 Sep 2019 20:44
Last Modified:10 Sep 2020 18:04

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