[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83726-en":3,"doc-seo-83726-105":30,"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},83726,549758252649,"Ivy","https://ap-avatar.wpscdn.com/avatar/8000253669c5317157?_k=1778319167496531819",8,"Research & Report","Interception-Driven Inverse Reachability for Engagement Zone Construction","In contested environments, autonomous vehicles must plan around adversarial pursuers whose launch locations are unknown. This paper introduces an interception-driven inverse-reachability framework that infers a feasible pursuer launch region directly from observed interception events for a single pursuer. Each interception yields a geometric constraint, whose intersection provides a bounded set guaranteed to contain the true origin under bounded-capability assumptions. Propagating this set produces deterministic engagement zones with an explicit worst-case safety meaning, and a probabilistic extension yields graded engagement-risk fields. An information-driven planner for sacrificial agents contracts the feasible region efficiently, reducing launch uncertainty and enabling substantially shorter safe trajectories after few deployments.","arXiv :2607 .03554v1 [ ee ss . SY] 3 Jul 2026  \nInterception-Driven Inverse Reachability for Engagement Zone  \nConstruction  \nGrant Stagg∗ and Cameron K. Peterson†  \nBrigham Young University, Provo, Utah, 84602, USA  \nAlexander Von Moll‡ and Isaac Weintraub§  \nAir Force Research Laboratory, WPAFB, Ohio, 45433, USA  \nIn contested environments, autonomous vehicles may need to plan around adversarial pursuers whose launch locations are unknown. This paper presents an interception-driven inverse-reachability framework for inferring a feasible pursuer launch region directly from observed interception events for a single pursuer. Each interception induces a geometric constraint on the unknown launch location, and intersecting these constraints yields a bounded set guaranteed to contain the true origin under maximum-capability assumptions. Mapping this inferred set through the pursuer reachable region produces deterministic engagement zones with an explicit worst-case safety interpretation. A probabilistic extension models uncertainty in the pursuer launch location and yields graded engagement-risk fields for risk-aware planning. To accelerate localization, we introduce an information-driven planner for sacrificial agents that selects trajectories to maximize expected contraction of the feasible launch region. Monte Carlo simulations show that the proposed framework rapidly reduces launch-location uncertainty and enables substantially shorter safe trajectories after only a small number of sacrificial deployments.  \nI. Introduction  \nAutonomous vehicles operating in contested environments must reason about adversarial threats whose launch locations are often unknown [1] . Traditional engagement analysis typically assumes that pursuer parameters—such as launch position, range, and maneuverability—are available a priori or described by a known probability distribution [2, 3] . In many operational settings, however, threat locations must instead be inferred from indirect, sparse, or event-driven observations, motivating active localization methods that infer hidden sources from sparse binary contacts or geometrydependent measurements [4, 5] . This creates a coupled estimation–planning problem in which agents must gather  \n∗PhD Candidate, Electrical and Computer Engineering, Brigham Young University.  \n†Associate Professor, Electrical and Computer Engineering, Brigham Young University, and AIAA Senior Member.‡Aerospace Engineer, Control Science Center, Air Force Research Laboratory, AIAA Member.  \n§ Electronics Engineer, Control Science Center, Air Force Research Laboratory, AIAA Associate Fellow.  \nDistribution Statement A. Approved for public release: distribution is unlimited. AFRL-2026-1807 . Cleared 13 Apr 2026 .  \ninformative data about a threat while simultaneously generating trajectories that remain safe during information acquisition [6] .  \nInterception events provide direct geometric information about the pursuer origin. If a pursuer successfully interceptsan agent, it must have launched from a location capable of reaching the interception location within its travel budget. Each interception therefore imposes a spatial constraint on the unknown launch location. Intersecting these constraints yields a feasible launch region that is guaranteed to contain the true origin under bounded-capability assumptions. As additional interceptions are observed, this region contracts, progressively reducing uncertainty about the threat location.  \nCrucially, a bounded launch region induces a bounded reachable region (RR), the set of positions that a pursuer originating anywhere within the feasible launch region could attain. Expressed in the evader frame, this RR defines a corresponding engagement zone (EZ) that contains all evader positions from which interception could occur by a pursuer launched from any admissible location. Any trajectory whose position remains outside the EZ corresponding to the evader’s instantaneous heading is safe agai","cbCaibOMbcFw6o2l","https://ap.wps.com/l/cbCaibOMbcFw6o2l","pdf",1034722,3,1,32,"English","en",105,"# Introduction\n## Problem motivation: unknown adversary launch locations\n## Interception events as geometric constraints\n## From launch-region inference to deterministic engagement zones\n## Probabilistic engagement-risk fields\n## Information gathering with sacrificial agents","[{\"question\":\"How does the framework infer an unknown pursuer launch location from interception events?\",\"answer\":\"Each successful interception imposes a geometric spatial constraint on the pursuer origin. Intersecting the constraints from multiple interceptions yields a feasible launch region that is guaranteed to contain the true origin under bounded-capability assumptions.\"},{\"question\":\"What safety interpretation do the deterministic engagement zones provide?\",\"answer\":\"The inferred feasible launch region induces a bounded reachable region, which defines an engagement zone containing all evader positions from which interception could occur. Any trajectory that stays outside the engagement zone corresponding to the evader heading is safe against all admissible pursuers.\"},{\"question\":\"How do sacrificial agents help reduce uncertainty and improve trajectory efficiency?\",\"answer\":\"Sacrificial agents deliberately create informative interceptions at selected locations. An information-driven planner chooses their trajectories to maximize expected contraction of the feasible launch region, enabling faster uncertainty reduction and shorter safe trajectories after a small number of deployments.\"}]",1784190008,81,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"interception-driven-inverse-reachability-for-engagement-zone-construction","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/interception-driven-inverse-reachability-for-engagement-zone-construction/83726/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-26","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},"How does the framework infer an unknown pursuer launch location from interception events?","Question",{"text":75,"@type":76},"Each successful interception imposes a geometric spatial constraint on the pursuer origin. Intersecting the constraints from multiple interceptions yields a feasible launch region that is guaranteed to contain the true origin under bounded-capability assumptions.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What safety interpretation do the deterministic engagement zones provide?",{"text":80,"@type":76},"The inferred feasible launch region induces a bounded reachable region, which defines an engagement zone containing all evader positions from which interception could occur. Any trajectory that stays outside the engagement zone corresponding to the evader heading is safe against all admissible pursuers.",{"name":82,"@type":73,"acceptedAnswer":83},"How do sacrificial agents help reduce uncertainty and improve trajectory efficiency?",{"text":84,"@type":76},"Sacrificial agents deliberately create informative interceptions at selected locations. An information-driven planner chooses their trajectories to maximize expected contraction of the feasible launch region, enabling faster uncertainty reduction and shorter safe trajectories after a small number of deployments.","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":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]