[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82655-en":3,"doc-seo-82655-105":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},82655,1649267921044,"Ava Thompson","https://us-avatar.wpscdn.com/avatar/1800007509477c92dfb?_k=1782875107921204101",8,"Research & Report","Reachability-Based Safe-Start Regions for Approach to a Tumbling Target with Rotating LOS Constraints","Reachability-aware guidance enables autonomous approach to a tumbling, uncooperative target through a rotating line-of-sight (LOS) docking corridor. The LOS admissible set rotates with the target body frame, yielding time-varying polyhedral constraints in the chaser’s relative coordinates. A safe-start region is built using directional per-constraint erosion and a synchronization range bound to ensure thruster arrest without overshoot. Receding-horizon MPC with CWH prediction and embedded LOS constraints maintains feasibility with exact discrete state-transition sub-stepping. Analytical criteria benchmarked against BRS/BRT, Hamilton–Jacobi, and Monte Carlo show ~250× faster synchronization certification with high predictive quality and onboard go/no-go suitability.","arXiv :2607 .02128v1 [ ee ss . SY] 2 Jul 2026  \nReachability-Based Safe-Start Regions for Approach to a Tumbling Target with Rotating LOS  \nConstraints  \nOmer Burak Iskendera,b,* , Keck Voon Linga , Wee Seng Limb , Erick Lansardb  \na Nanyang Technological University, Singapore. E-mail: [iske0001@e.ntu.edu.sg](iske0001@e.ntu.edu.sg), [ekvling@ntu.edu.sg](ekvling@ntu.edu.sg)b Satellite Research Center, Nanyang Technological University (NTU), Singapore. E-mail: [limWS@ntu.edu.sg](limWS@ntu.edu.sg),  \n[erick.lansard@ntu.edu.sg](erick.lansard@ntu.edu.sg)  \n* Corresponding author  \nPreprint of a paper submitted to the 77th International Astronautical Congress (IAC 2026), Antalya, Türkiye, 5 –9 October 2026.  \nAbstract  \nThis paper presents a reachability-aware guidance architecture for autonomous approach to a tumbling, uncooperative target under a rotating line-of-sight (LOS) docking corridor. The LOS admissible set rotates with the target body frame, producing time-varying polyhedral constraints in the chaser’s relative coordinates. A safe-start region is constructed via two conservative criteria: (i) directional per-constraint erosion, quantifying the margin consumed by rotation-induced drift before the thruster can arrest it, and (ii) a synchronization range bound 􀁁 \u003C 2􀀰max /􀁬2􀁃 ensuring the chaser can cancel the apparent rotational velocity without overshooting the hold point. Closed-loop guidance uses a receding-horizon MPC controller with Clohessy-Wiltshire-Hill (CWH) prediction dynamics and explicit LOS corridor constraints embedded in the quadratic program. Truth propagation uses the exact discrete CWH state-transition matrix with sub-stepping, ensuring physically honest feasibility claims: no reference blending or state projection is applied. A three-regime tracking law (far LVLH approach, close body-frame tracking, synchronized hold) manages the transition from long-range inertial approach to body-frame co-rotation. The analytical safe-start region is benchmarked against four standard reachability engines (backward and forward polytopic reachable sets, Hamilton–Jacobi level sets, and closed-loop Monte Carlo), revealing that the closed-form synchronization criteria are ∼250× faster than Hamilton–Jacobi reachability while predicting closed-loop feasibility with precision 0 . 80 and recall 0 .91 (overall accuracy 0 .92, Matthews correlation 0 . 80) on a 500-case closed-loop sweep. The residual 6% false-positive rate (concentrated at high tumble rate) and the IoU gap against Hamilton–Jacobi (0.008–0.375 across 􀁬 􀁃 = 1–5 deg/s) quantify a structural property rather than a method error: the synchronization set (reach and co-rotate) is a strict subset of the positional reachable set, the gap widening with 􀁬 􀁃 . The analytical bound is therefore a sound inner certificate for onboard go/no-go decisions where Hamilton–Jacobi is prohibitively expensive. The framework is reproducible from a single command.  \nKeywords: proximity operations, uncooperative target, time-varying LOS corridor, safe-start region, synchronization bound, Hamilton-Jacobi reachability, MPC  \nNomenclature  \n􀀽 target orbit mean motion (rad/s)  \nx = [􀁇, 􀁈, 􀁉, 􀁇¤ , 􀁈¤ , ¤􀁉] ⊤ 3D LVLH relative state u = [􀀰 􀁇, 􀀰 􀁈, 􀀰 􀁉] ⊤ LVLH control acceleration  \n􀀰max maximum thrust-to-mass ratio  \n􀁬 􀁃 target tumble rate about LVLH 􀁉  \n􀀧􀁉 (􀁜) rotation matrix about 􀁉 by angle 􀁜  \n􀀲 􀁇, 􀀲 􀁉 LOS cone half-angle slopes  \n􀁇0, 􀁉 0 docking port lateral half-widths  \n􀁁 ℎ hold stand-off radius  \n􀁁sync synchronization range limit Φ (􀁧) CWH state-transition matrix  \n􀀗 􀀳 (􀁧) CWH zero-order-hold input matrix  \nAcronyms/Abbreviations  \nBRS: Backward Reachable Set  \nBRT: Backward Reachable Tube  \nCWH: Clohessy-Wiltshire-Hill  \nFRS: Forward Reachable Set  \nHCW: Hill-Clohessy-Wiltshire  \nHJ: Hamilton-Jacobi  \nHJI: Hamilton-Jacobi-Isaacs  \nIoU: Intersection over Union  \nLOS: line of sight  \nLVLH: local vertical local horizontal  \nMC: Monte Carlo  \nMPC: model predictive control  \nQP: quadratic progra","cbCaivmdmAYjKgSG","https://ap.wps.com/l/cbCaivmdmAYjKgSG","pdf",936133,1,10,"English","en",105,"# Abstract\n# Keywords\n# Introduction\n# Dynamics Model","[{\"question\":\"What problem does the paper address for autonomous docking?\",\"answer\":\"It addresses which initial relative states allow a chaser to safely approach and synchronize with a tumbling, uncooperative target when the LOS docking corridor rotates over time.\"},{\"question\":\"How is the safe-start region constructed?\",\"answer\":\"It uses two conservative criteria: directional per-constraint erosion to account for rotation-induced drift before thruster arrest, and a synchronization range bound that limits rotational-velocity cancellation without overshooting the hold point.\"},{\"question\":\"What guidance and prediction method is used in closed-loop operation?\",\"answer\":\"A receding-horizon MPC controller uses Clohessy-Wiltshire-Hill (CWH) prediction dynamics and includes explicit LOS corridor constraints inside the quadratic program, with exact discrete state-transition propagation and sub-stepping.\"}]",1784182100,25,{"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},"reachability-based-safe-start-regions-for-approach-to-a-tumbling-target-with-rotating-los-constraints","",{"@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/reachability-based-safe-start-regions-for-approach-to-a-tumbling-target-with-rotating-los-constraints/82655/",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 problem does the paper address for autonomous docking?","Question",{"text":75,"@type":76},"It addresses which initial relative states allow a chaser to safely approach and synchronize with a tumbling, uncooperative target when the LOS docking corridor rotates over time.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is the safe-start region constructed?",{"text":80,"@type":76},"It uses two conservative criteria: directional per-constraint erosion to account for rotation-induced drift before thruster arrest, and a synchronization range bound that limits rotational-velocity cancellation without overshooting the hold point.",{"name":82,"@type":73,"acceptedAnswer":83},"What guidance and prediction method is used in closed-loop operation?",{"text":84,"@type":76},"A receding-horizon MPC controller uses Clohessy-Wiltshire-Hill (CWH) prediction dynamics and includes explicit LOS corridor constraints inside the quadratic program, with exact discrete state-transition propagation and 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