[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84563-en":3,"doc-seo-84563-105":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},84563,8796095360427,"Lucas Martin","https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d",8,"Research & Report","Robust Operational Space Control with Conformal Disturbance Bounds for Safe Redundant Manipulation","Redundant robotic manipulators operating in constrained, human-interactive environments demand accurate task-space tracking and rigorous safety under dynamic uncertainties. The paper develops a robust operational space computed torque controller by combining an extended state observer with conformal prediction and a robust control barrier function. The ESO estimates lumped operational-space disturbances without full-state residual learning. To avoid conservatism from fixed disturbance bounds, a sliding-window conformal predictor updates the bound online, yielding distribution-free probabilistic safety. Experiments on a 7-DoF Franka arm achieve millimeter-level tracking and 1 kHz real-time safe control.","Robust Operational Space Control with Conformal Disturbance Bounds  \nfor Safe Redundant Manipulation  \nWenhua Liu 1 , Fan Zhang 1 , Qin Lin 1  \narXiv :2607 .00424v 1 [ cs .RO] 1 Jul 2026  \nAbstract—Redundant robotic manipulators operating in constrained and human-interactive environments require accurate task-space tracking together with rigorous safety guarantees under dynamic uncertainties. Classical operational space computed torque controller (OSCTC) relies on accurate dynamic models and degrades in the presence of disturbances. In contrast, the data-driven paradigm of residual learning approximates disturbances as functions learned from full-state measurements, which are often noisy in practice, lack rigorous theoretical guarantees, and introduce additional design complexity. This paper proposes a robust OSCTC framework that integrates an extended state observer (ESO) with conformal prediction to combine model-based robustness and data-driven adaptability. The ESO estimates lumped disturbances directly in operational space without requiring full-state measurements as in residual learning, and a robust control barrier function (CBF) is constructed to enforce safety under uncertainty. However, robust CBFs require a known disturbance-variation bound to guarantee absolute safety, which often leads to conservatism in practice. To address this limitation, we further employ a sliding-window conformal prediction mechanism to estimate the bound online in a distribution-free manner, thereby achieving practical probabilistic safety guarantees. Experiments on a 7-DoF Franka Research 3 manipulator demonstrate millimeterlevel tracking accuracy and real-time safe control at 1 kHz under various disturbances. Video: [https://www.youtube](https://www.youtube) . com/watch?v=KHs64uKjZ1w.  \nI. INTRODUCTION  \nRedundant robotic manipulators, equipped with additional degrees of freedom, are increasingly deployed in constrained and human-interactive environments due to their enhanced dexterity and flexibility. By exploiting kinematic redundancy, they can simultaneously achieve obstacle avoidance, posture optimization, and safe human-robot collaboration.  \nFor robotic manipulators, control strategies are typically formulated either in joint space or directly in operational (task) space. Joint-space control requires mapping desired task-space trajectories to joint motions through inverse kinematics (IK) . For redundant manipulators, this mapping is not unique and requires additional redundancy resolution, which complicates the coordination of task-space objectives and constraints. In contrast, operational space computed torque controller (OSCTC) [1] enables direct regulation of endeffector motion in task space without solving IK, while preserving null-space freedom for secondary objectives such as posture optimization.  \n1These authors are with the Department of Engineering Technology and the Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77004, USA. {wliu40, [fzhang28](fzhang28}@cougarnet.uh.edu)[}](fzhang28}@cougarnet.uh.edu)[@cougarnet.uh.edu](fzhang28}@cougarnet.uh.edu); [qlin12@uh.edu](qlin12@uh.edu)  \nThis material is based upon work supported by the National Science Foundation under Grants No. 2301543.  \nFig. 1. Task-space trajectory forming the letters “AIR” under model uncertainty. Yellow: reference trajectory. Blue: conventional OSCTC without disturbance compensation [1] . Green: Residual learning. Red: proposed method, which has the minimum deviations caused by model mismatch in the hardware.  \nHowever, classical OSCTC is essentially based on feedback linearization [2] . As such, it requires accurate knowledge of the system dynamics to achieve precise cancellation of nonlinear terms. When model uncertainties or disturbances are present, this assumption is violated, resulting in performance degradation and reduced robustness. This phenomenon is partially illustrated in Fig. 1, where conventional OSCT","cbCaicOTb1vFGfu3","https://ap.wps.com/l/cbCaicOTb1vFGfu3","pdf",3738435,1,7,"English","en",105,"# Introduction\n## Task-space vs joint-space control for redundant manipulators\n## Disturbance challenges and limitations of classical OSCTC\n## Robust OSCTC framework with ESO and conformal prediction","[{\"question\":\"What problem does the paper address for redundant robotic manipulators?\",\"answer\":\"It targets accurate task-space tracking together with rigorous safety guarantees in constrained and human-interactive settings under dynamic uncertainties and disturbances.\"},{\"question\":\"How does the proposed method improve robustness compared with classical operational space computed torque control?\",\"answer\":\"It integrates an extended state observer to estimate lumped disturbances in operational space and uses a robust control barrier function to enforce safety under uncertainty.\"},{\"question\":\"Why is conformal prediction used in the safety barrier function design?\",\"answer\":\"Robust control barrier functions typically need a known disturbance-variation bound, which can be conservative; the sliding-window conformal prediction estimates this bound online in a distribution-free way to provide practical probabilistic safety.\"}]",1784196827,18,{"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},"robust-operational-space-control-with-conformal-disturbance-bounds-for-safe-redundant-manipulation","",{"@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/robust-operational-space-control-with-conformal-disturbance-bounds-for-safe-redundant-manipulation/84563/",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 redundant robotic manipulators?","Question",{"text":75,"@type":76},"It targets accurate task-space tracking together with rigorous safety guarantees in constrained and human-interactive settings under dynamic uncertainties and disturbances.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed method improve robustness compared with classical operational space computed torque control?",{"text":80,"@type":76},"It integrates an extended state observer to estimate lumped disturbances in operational space and uses a robust control barrier function to enforce safety under uncertainty.",{"name":82,"@type":73,"acceptedAnswer":83},"Why is conformal prediction used in the safety barrier function design?",{"text":84,"@type":76},"Robust control barrier functions typically need a known disturbance-variation bound, which can be conservative; 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