[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85689-en":3,"doc-seo-85689-105":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},85689,137441390410,"Hazel","https://ap-avatar.wpscdn.com/avatar/2000252f4ab5702993?_k=1776741390130283984",8,"Research & Report","Saturation-Aware Robust Trajectory Optimization for Reusable Launch Vehicles via Differentiable Physics","High-angle-of-attack flip maneuvers in reusable launch vehicles create major difficulty for robust trajectory optimization because nonlinear dynamics, aerodynamic uncertainties, and actuator saturation act together. The work introduces a differentiable physics framework for saturation-aware robust optimization, centered on a Differentiable Particle Tube Control (DPTC) method. State uncertainty is modeled with a Lagrangian particle ensemble, while hard actuator projection operators are embedded in the computation graph for end-to-end gradient backpropagation of nominal and time-varying feedback. Monte Carlo results show improved closed-loop robustness and constraint satisfaction.","arXiv :2607 .09736v 1 [ cs .RO] 2 Jul 2026  \nSaturation-Aware Robust Trajectory Optimization for Reusable Launch Vehicles via Differentiable Physics  \nLiwei Chena,∗, Tong Qina  \na Beijing Institute of Aeronautical Systems Engineering, Beijing 100076, China  \nAbstract  \nThe high-angle-of-attack flip maneuver of reusable launch vehicles presents significant challenges for robust trajectory optimization due to the combined effects of highly nonlinear dynamics, aerodynamic uncertainties, and actuator saturation. This paper presents a differentiable physics framework for saturationaware robust trajectory optimization. At its core, a Differentiable Particle Tube Control (DPTC) scheme is developed to optimize uncertainty evolution through an ensemble-based distribution shaping strategy. State uncertainty is represented by a Lagrangian particle ensemble, while hard actuator projection operators are embedded directly into the computational graph, enabling the joint optimization of the nominal feedforward trajectory and a time-varying feedback policy via end-to-end backpropagation. The proposed framework is evaluated against an automatic differentiation-based Successive Convexification (AD-SCvx) baseline combined with a conventional covariance steering feedback strategy. Six-degree-of-freedom Monte Carlo simulations demonstrate that, although the baseline achieves nominal fuel-optimal solutions, its unconstrained feedback formulation becomes susceptible to actuator saturation under aerodynamic disturbances, leading to degraded closed-loop robustness. In contrast, the proposed DPTC framework proactively performs a constraint-aware performance trade-off by relaxing spatial tracking to preserve critical control authority. Consequently, it prevents actuator saturation-induced performance degradation,  \n∗ Corresponding author  \nEmail address: [liwei.chen.aero@gmail.com](liwei.chen.aero@gmail.com) (Liwei Chen)  \nreduces the 50% Circular Error Probable (CEP50 ) by 87%, and significantly improves terminal landing precision while maintaining strict physical constraint satisfaction. These results demonstrate that integrating differentiable physics with ensemble-based optimization provides an effective and practical framework for robust guidance in highly constrained aerospace flight systems.  \nKeywords: Differentiable physics, Robust trajectory optimization, Reusable launch vehicle, Actuator saturation, Guidance and control,  \n1. Introduction  \nThe advent of reusable launch vehicles (RLVs) has fundamentally transformed the aerospace industry, driving a paradigm shift toward economical and sustainable space access. For next-generation super-heavy reusable launch vehicles (RLVs)—exemplified by the Starship architecture—the vertical powered landing (VPL) phase represents one of the most critical and dynamically challenging segments of the flight profile [1, 2] . Unlike traditional slender rockets, these vehicles perform a high-angle-of-attack “belly-flop” atmospheric entry to dissipate kinetic energy, followed by an aggressive and highly nonlinear “flip maneuver” to achieve a vertical orientation prior to touchdown. During this transient phase, the vehicle is subjected to intense aerodynamic coupling, large structural loads, and rapid variations in dynamic pressure [3] . Thus, the trajectory becomes highly sensitive to environmental perturbations, including unsteady aerodynamic coefficients, wind shear, and mass-property uncertainties. Ensuring extreme landing precision and vehicle survivability under such severe multi-source uncertainties remains an open challenge in modern aerospace guidance, navigation, and control (GNC) [4] .  \nTo address the stringent requirements of VPL, Successive Convexification (SCvx) has emerged as a cornerstone methodology, demonstrating remarkable success by iteratively approximating non-convex dynamics into tractable convex subproblems [5–7] . To account for exogenous disturbances, robust variants such as Tube-based Mod","cbCaisdkulPzuqsG","https://ap.wps.com/l/cbCaisdkulPzuqsG","pdf",12299354,1,36,"English","en",105,"# Abstract\n# 1. Introduction\n## Problem context: RLV VPL and flip maneuver\n## Existing robust SCvx approaches and limitations\n## Differentiable predictive control and related gaps\n## Proposed motivation: uncertainty distribution shaping under actuator limits","[{\"question\":\"What challenge motivates saturation-aware robust trajectory optimization for reusable launch vehicles?\",\"answer\":\"The high-angle-of-attack flip maneuver combines highly nonlinear dynamics with aerodynamic uncertainties and actuator saturation, making robust optimization difficult and breaking traditional guarantees when commands exceed actuator limits.\"},{\"question\":\"How does the proposed differentiable physics framework represent and optimize uncertainty?\",\"answer\":\"It uses a Lagrangian particle ensemble to represent state uncertainty and applies an ensemble-based distribution shaping strategy, embedding hard actuator projection operators directly into the computational graph for end-to-end backpropagation.\"},{\"question\":\"How does the method compare with an AD-SCvx baseline in simulations?\",\"answer\":\"The AD-SCvx baseline achieves nominal fuel-optimal solutions but becomes sensitive to actuator saturation under aerodynamic disturbances, while the proposed DPTC framework relaxes spatial tracking to preserve control authority and maintain terminal landing precision with strict physical constraint satisfaction.\"}]",1784205615,91,{"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},"saturation-aware-robust-trajectory-optimization-for-reusable-launch-vehicles-via-differentiable-physics","",{"@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/saturation-aware-robust-trajectory-optimization-for-reusable-launch-vehicles-via-differentiable-physics/85689/",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},"What challenge motivates saturation-aware robust trajectory optimization for reusable launch vehicles?","Question",{"text":75,"@type":76},"The high-angle-of-attack flip maneuver combines highly nonlinear dynamics with aerodynamic uncertainties and actuator saturation, making robust optimization difficult and breaking traditional guarantees when commands exceed actuator limits.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed differentiable physics framework represent and optimize uncertainty?",{"text":80,"@type":76},"It uses a Lagrangian particle ensemble to represent state uncertainty and applies an ensemble-based distribution shaping strategy, embedding hard actuator projection operators directly into the computational graph for end-to-end backpropagation.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the method compare with an AD-SCvx baseline in simulations?",{"text":84,"@type":76},"The AD-SCvx baseline achieves nominal fuel-optimal solutions but becomes sensitive to actuator saturation under aerodynamic disturbances, while the proposed DPTC framework relaxes spatial tracking to preserve control authority and maintain terminal landing precision with strict physical constraint satisfaction.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Story & 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