[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83356-en":3,"doc-seo-83356-105":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},83356,687197207919,"Theodora","https://ap-avatar.wpscdn.com/avatar/a000253d6f5f7c60be?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779446848396160552",8,"Research & Report","X-ACTA eXtended Analytic Center Tension distribution Algorithm for Fixed and Mobile Cable-Driven Parallel Robot","Steering Cable-Driven Parallel Robots (CDPRs) require cable tensions beyond their Wrench-Feasible Workspace (WFW) for aggressive maneuvers and after cable failures. While tension determination has been extensively studied, few methods address these out-of-WFW conditions with smooth, real-time behavior. This work extends the Analytic Center method to select differentiable tension sets using barrier-based optimization with nonlinear constraints. Results provide continuous tension profiles, fast convergence to a unique solution, and negligible wrench errors within the WFW, validated by Pareto dominance and numerical experiments.","X-ACTA: eXtended Analytic Center Tension distribution Algorithm for fixed and mobile cable-driven-parallel-robot  \nDomenico Dona’, Vincenzo Di Paola, Alberto Trevisani and Matteo Zoppi  \narXiv :2607 .08265v 1 [ cs .RO] 9 Jul 2026  \nAbstract—Steering Cable-Driven Parallel Robots (CDPRs) beyond their Wrench-Feasible Workspace (WFW) augments their capabilities in challenging scenarios such as during aggressive maneuvers or following a cable failure. In this context, although the determination of cable tensions is a well-studied topic, only a few approaches address these scenarios. Therefore, this paper introduces an extended version of the Analytic Center method as a criterion for selecting cable tensions outside the WFW while maintaining differentiability and including non-linear constraints. Notably, the proposed method maintains continuous and differentiable tension profiles, ensures fast real-time convergence to a unique solution, and, in contrast to other slack-based formulations, relegates wrench errors to a negligible area of the WFW. Its superiority in terms of smoothness and wrench error is confirmed via Pareto dominance with respect to the leading state-of-the-art method. Lastly, the effectiveness of the method is demonstrated through numerical experiments.  \nIndex Terms—Parallel, Cable Robots, Wrench Feasible Workspace, Tension Distribution Algorithm, Analytic Center, Continuous, Differentiable, Non-linear Constraints.  \nI. INTRODUCTION  \nCable-Driven Parallel Robots (CDPRs) are typically composed of a moving platform, namely a rigid body, actuated by cables exerting forces on it. The selection of cable tensions in CDPRs has been a core research topic since their birth [1] .  \nIn particular, overconstrained CDPRs, where the number of cables exceeds the payload’s Degrees of Freedom (DoFs), require the selection of a tension set among infinitely many feasible ones. This choice is typically made by solving an optimization problem known as the Tension Distribution Algorithm (TDA) . The existing approaches differ in the choice of optimization objective, constraints, and solution method, typically tailored to the task requirements [2] .  \nGenerally, p-norm-based metrics have been widely adopted as objectives for TDAs [3] . The 1-norm, for example, is key to several studies [4]–[6] . Such problems are typically solved using Linear Programming (LP) approaches due to fast convergence; however, the jump between the vertices of the feasible polyhedron, resulting from the 1−norm minimization, often results in discontinuous tension profiles. Similarly, discontinuities can occur when using the ∞-norm [3] . Because  \nDomenico Dona’ is with the Faculty of Engineering, Free University of Bozen-Bolzano, Via Bruno Buozzi 1, Bozen 39100, Italy (e-mail: [domenico.dona@unibz.it](domenico.dona@unibz.it)) .  \nVincenzo Di Paola and Matteo Zoppi are with Department of Mechanical, Energy, Management and Transportation Engineering (DIME), University of Genova, Via alla Opera Pia 15, Genova 16143, Italy (e-mail: vin[cenzo.dipaola@edu.unige.it](cenzo.dipaola@edu.unige.it); [matteo.zoppi@unige.it](matteo.zoppi@unige.it)).  \nAlberto Trevisani is with the Department of Management and Engineering (DTG), University of Padua, Stradella San Nicola 3, Vicenza 36100, Italy (e-mail: [alberto.trevisani@unipd.it](alberto.trevisani@unipd.it)).  \nCorresponding author: Domenico Dona’  \nFig. 1. Scheme of a generic cable-driven parallel robot.  \ncontinuity is a must to ensure precision while executing tasks, the criteria have been reformulated employing p-norms where 1 \u003C p \u003C ∞ [7] .  \nConsequently, a widely adopted objective is the 2-norm of the tension vector [8]–[10] or its distance with respect toa reference tension, usually taken as the mean between the minimum and maximum ones [3], [11], [12] . The popularity of these methods relies on the possibility of efficiently solving the associated optimization problem, using either closed-form solutions [9], [11] or speciali","cbCaipjP8COc66t4","https://ap.wps.com/l/cbCaipjP8COc66t4","pdf",708293,1,10,"English","en",105,"# Introduction\n## Cable-Driven Parallel Robots and Tension Distribution Algorithms\n## Limitations of p-norm and slack-based methods\n## Motivation and contributions of the proposed approach","[{\"question\":\"What problem does the extended Analytic Center method address?\",\"answer\":\"It selects cable tensions for steering CDPRs beyond the Wrench-Feasible Workspace while keeping differentiability and supporting nonlinear constraints.\"},{\"question\":\"How does the proposed method improve tension profile smoothness compared with common p-norm objectives?\",\"answer\":\"It maintains continuous and differentiable tension profiles, avoiding discontinuities that can arise from 1-norm or ∞-norm minimization over feasible polyhedra.\"},{\"question\":\"What accuracy behavior does the method achieve inside the WFW?\",\"answer\":\"Unlike slack-based formulations that can introduce wrench errors, the method relegates wrench errors to a negligible area within the WFW while operating beyond it.\"}]",1784186971,25,{"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},"x-acta-extended-analytic-center-tension-distribution-algorithm-for-fixed-and-mobile-cable-driven-parallel-robot","",{"@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/x-acta-extended-analytic-center-tension-distribution-algorithm-for-fixed-and-mobile-cable-driven-parallel-robot/83356/",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 extended Analytic Center method address?","Question",{"text":75,"@type":76},"It selects cable tensions for steering CDPRs beyond the Wrench-Feasible Workspace while keeping differentiability and supporting nonlinear constraints.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed method improve tension profile smoothness compared with common p-norm objectives?",{"text":80,"@type":76},"It maintains continuous and differentiable tension profiles, avoiding discontinuities that can arise from 1-norm or ∞-norm minimization over feasible polyhedra.",{"name":82,"@type":73,"acceptedAnswer":83},"What accuracy behavior does the method achieve inside the WFW?",{"text":84,"@type":76},"Unlike slack-based formulations that can introduce wrench errors, the method relegates wrench errors to a negligible area within the WFW while operating beyond it.","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},[93,97,101,105,110,115,120,123,128,131,134],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":45,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":45,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":45,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":21,"doc_module":4,"doc_module_name":45,"category_name":132,"show_sort_weight":21,"slug":133},"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":45,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]