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Steven R. Hall and David Benson. Saunders, Benjamin R. (Benjamin Robert) Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics. Massachusetts Institute of Technology. Department of Aeronautics and Astronautics 2013-02-14T15:15:38Z 2013-02-14T15:15:38Z 2012 2012 http://hdl.handle.net/1721.1/76902 824132162 Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2012. Cataloged from PDF version of thesis. Includes bibliographical references (p. 121-123). Reference trajectory design for atmospheric reentry vehicles can be accomplished through trajectory optimization using optimal control techniques. However, this method generally focuses on nominal vehicle performance and does not include robustness considerations during trajectory design. This thesis explores the use of linear covariance analysis to directly include trajectory robustness in the design process. The covariance matrix can be propagated along a trajectory to provide the expected errors about the nominal trajectory in the presence of uncertainties. During the optimization process, the covariance matrix is used as a performance metric to be minimized, directly penalizing expected errors so that the trajectory is shaped to reduce its sensitivity to uncertainties. This technique can penalize the open-loop covariance of the trajectory or the closed-loop covariance with the inclusion of a feedback guidance law. This covariance shaping technique is applied to reference trajectory design for a generic small reentry vehicle. A baseline trajectory is generated without any robustness considerations, along with an open-loop covariance shaped trajectory and a closed-loop covariance shaped trajectory, which uses a feedback guidance law based on a linear quadratic regulator scheme. Uncertainties in initial conditions, atmospheric density, aerodynamic coefficients, and unmodeled dynamics are applied to each trajectory and performance is analyzed using linear covariance analysis and Monte Carlo simulations. The results show that when the vehicle is flown closed-loop with feedback, shaping using the open-loop covariance produces a trajectory that is less robust than the baseline trajectory, while shaping using the closed-loop covariance generates a trajectory with reduced sensitivity to uncertainty for more robust performance. by Benjamin R. Saunders. S.M. 123 p. eng Massachusetts Institute of Technology M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 Aeronautics and Astronautics. Optimal trajectory design under uncertainty Thesis application/pdf false Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="aa35802e-e261-41f4-bf96-d2cd337b6b72"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>Optimal trajectory design under uncertainty</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2012</PublicationDate> <Authors> <Author> <DisplayName>Saunders, Benjamin R. (Benjamin Robert)</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Aeronautics and Astronautics.</Keyword> <Abstract>Reference trajectory design for atmospheric reentry vehicles can be accomplished through trajectory optimization using optimal control techniques. However, this method generally focuses on nominal vehicle performance and does not include robustness considerations during trajectory design. This thesis explores the use of linear covariance analysis to directly include trajectory robustness in the design process. The covariance matrix can be propagated along a trajectory to provide the expected errors about the nominal trajectory in the presence of uncertainties. During the optimization process, the covariance matrix is used as a performance metric to be minimized, directly penalizing expected errors so that the trajectory is shaped to reduce its sensitivity to uncertainties. This technique can penalize the open-loop covariance of the trajectory or the closed-loop covariance with the inclusion of a feedback guidance law. This covariance shaping technique is applied to reference trajectory design for a generic small reentry vehicle. A baseline trajectory is generated without any robustness considerations, along with an open-loop covariance shaped trajectory and a closed-loop covariance shaped trajectory, which uses a feedback guidance law based on a linear quadratic regulator scheme. Uncertainties in initial conditions, atmospheric density, aerodynamic coefficients, and unmodeled dynamics are applied to each trajectory and performance is analyzed using linear covariance analysis and Monte Carlo simulations. The results show that when the vehicle is flown closed-loop with feedback, shaping using the open-loop covariance produces a trajectory that is less robust than the baseline trajectory, while shaping using the closed-loop covariance generates a trajectory with reduced sensitivity to uncertainty for more robust performance.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>