[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84690-en":3,"doc-seo-84690-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},84690,4398048949847,"Eliana","https://ap-avatar.wpscdn.com/avatar/400002536579ef2da7f?_k=1778318612642679267",8,"Research & Report","An Efficient Non-Gaussian Chance Constraint Method for Stochastic Nonlinear Problems in Spaceflight","Non-Gaussian uncertainty in spacecraft guidance arises when nonlinear dynamics bend confidence regions over long measurement gaps, producing distributions such as “banana-shaped” forms that invalidate Gaussian-based chance constraints. The paper presents a non-Gaussian confidence boundary technique that treats the true contour as a perturbation of the Gaussian covariance-predicted contour and reconstructs boundary geometry using higher-order statistical moments. By parameterizing the contour with skew and kurtosis tensors, the method is applied to a stochastic nonlinear impulsive maneuver, including handling a related non-convex constraint efficiently.","arXiv :2607 .03424v1 [ ee ss . SY] 3 Jul 2026  \n(Preprint) AAS 26-899  \nAN EFFICIENT NON-GAUSSIAN CHANCE CONSTRAINT METHOD FOR STOCHASTIC NONLINEAR PROBLEMS IN SPACEFLIGHT  \nEthan R. Burnett*, Spencer Boone†, and Niccol Michelotti‡  \nStandard chance-constrained spacecraft guidance typically relies on the assumption that uncertainties in vehicle states obey Gaussian statistics. In frontier applications such as the cislunar environment or deep space flybys, the dynamics can be particularly nonlinear, and time between measurements can be long, leading to the need to make decisions whose outcomes produce non-Gaussian distributions. This paper demonstrates a non-Gaussian confidence boundary technique for stochastic guidance in such applications. Our approach is to consider the true confidence contour as a perturbation of the one predicted from covariance, then to derive perturbed boundary geometry from computed higher-order statistical moments. Applying this technique to so-called “banana-shaped distributions”, found in orbital mechanics problems, enables a simple parameterization of the confidence contour using the skew and kurtosis tensors. This parameterization is then applied to a stochastic and nonlinear impulsive spacecraft maneuver targeting problem, with special treatment of a relevant non-convex constraint.  \nINTRODUCTION  \nState-of-the-art techniques of guidance and control are often stochastic in nature, whereby control of a nominal trajectory and expected statistical dispersions is jointly enforced. In contrast with many terrestrial robotics applications, spaceflight is often plagued by comparatively large state uncertainties and, sometimes, non-Gaussian statistics. These arise due to operation in dynamic regimes that are nonlinear and chaotic, and long periods without measurements or corrective control maneuvers.  \nThe assumption of Gaussian statistics can be reasonable for some stochastic control problems in spaceflight. Spacecraft rendezvous problems can exploit the nearly linear dynamics of closeproximity relative motion, for which statistical distributions remain very nearly Gaussian. Ref. 1 leverages this property for passively safe spacecraft rendezvous with a linear covariance (“LinCov”) treatment of uncertainty evolution. This enables a “chance-constrained” approach, whereby satisfaction of the path constraint can be certified to a certain probability level. Chance-constrained approaches have become popular for safety-critical problems in spaceflight with sufficiently small and Gaussian dispersions.2 The prospect of increasingly autonomous operation in space foresees more frequent measurements and more active maneuvering, thus such approaches may often be satisfactory. However, in long time-horizon maneuver planning, or in cases where accurate measurements are not available for long periods, the specter of non-Gaussian statistics cannot be ignored.  \nIn spaceflight, a commonly observed manifestation of non-Gaussian statistics is with the so-called“banana-shaped” distributions. These emerge because the nonlinear dynamics of orbital mechanics  \n*Assistant Professor, Department of Aerospace Engineering and Engineering Mechanics, University of Texas at Austin, 2617 Wichita St, Austin TX, 78712, USA.  \n†Unaffiliated, Toulouse, FR.  \n‡PhD Student, Dept. of Aerospace Science and Technology, Politecnico di Milano, Via La Masa 34, 20156 Milano IT.  \ntend to first stretch and then bend the ellipsoidal confidence region corresponding to an initially compact (and perhaps also Gaussian) distribution. For Keplerian problems, this problem can be partially avoided via use of “less nonlinear” coordinates such as polar coordinates or orbit elements (see e.g. Ref. 3) . However, practical path constraints may not be convenient to express in such coordinates, and also non-Keplerian contexts such as cislunar astrodynamics challenge this solution strategy, as superior native coordinates are typically not available nor easy to identif","cbCaipru0jwXAjGR","https://ap.wps.com/l/cbCaipru0jwXAjGR","pdf",3145431,1,26,"English","en",105,"# Introduction\n## Motivation for non-Gaussian statistics in spaceflight\n## Banana-shaped distributions from orbital nonlinearity\n## Existing approaches: Monte Carlo and moment-based methods\n## Proposed non-Gaussian confidence boundary technique","[{\"question\":\"Why do non-Gaussian chance constraints matter in spaceflight guidance?\",\"answer\":\"Because nonlinear, long time-horizon dynamics and infrequent measurements can produce non-Gaussian state dispersions, making Gaussian-based confidence certificates unreliable.\"},{\"question\":\"How does the proposed method build a non-Gaussian confidence boundary?\",\"answer\":\"It models the true confidence contour as a perturbation of the Gaussian contour and derives corrected boundary geometry from higher-order moments.\"},{\"question\":\"How are “banana-shaped” distributions parameterized in this work?\",\"answer\":\"The confidence contour is parameterized using skew and kurtosis tensors, capturing the distribution’s geometric distortion beyond covariance.\"}]",1784197675,66,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"an-efficient-non-gaussian-chance-constraint-method-for-stochastic-nonlinear-problems-in-spaceflight","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/an-efficient-non-gaussian-chance-constraint-method-for-stochastic-nonlinear-problems-in-spaceflight/84690/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why do non-Gaussian chance constraints matter in spaceflight guidance?","Question",{"text":75,"@type":76},"Because nonlinear, long time-horizon dynamics and infrequent measurements can produce non-Gaussian state dispersions, making Gaussian-based confidence certificates unreliable.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed method build a non-Gaussian confidence boundary?",{"text":80,"@type":76},"It models the true confidence contour as a perturbation of the Gaussian contour and derives corrected boundary geometry from higher-order moments.",{"name":82,"@type":73,"acceptedAnswer":83},"How are “banana-shaped” distributions parameterized in this work?",{"text":84,"@type":76},"The confidence contour is parameterized using skew and kurtosis tensors, capturing the distribution’s geometric distortion beyond 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