[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84580-en":3,"doc-seo-84580-105":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},84580,8796095360427,"Lucas Martin","https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d",8,"Research & Report","Learning from Demonstration via Spatiotemporal Tubes for Unknown Euler-Lagrange Systems","STT-LfD presents a unified Learning from Demonstration framework that jointly learns motion and control for unknown Euler–Lagrange systems. Instead of tracking a fixed reference, demonstrations are treated as a data-driven safety specification, encoded as Spatiotemporal Tubes (STTs) learned with heteroscedastic Gaussian Processes to capture time-varying precision. A closed-form feedback controller enforces tube invariance under actuator limits without explicit system identification, preserving demonstration temporal structure. Experiments on a mobile robot and a 7-DOF manipulator show improved robustness and computational speed.","LEARNING FROM DEMONSTRATION VIA SPATIOTEMPORAL TUBES FOR UNKNOWN EULER–LAGRANGE SYSTEMS ∗  \narXiv :2607 .00534v 1 [ cs .RO] 1 Jul 2026  \nRatnangshu Das  \nRobert Bosch Centre for Cyber-Physical Systems IISc, Bengaluru, India [ratnangshud@iisc.ac.in](ratnangshud@iisc.ac.in)  \nVaruni Buereddy  \nRobert Bosch Centre for Cyber-Physical Systems IISc, Bengaluru, India [varunib@iisc.ac.in](varunib@iisc.ac.in)  \nPuneeth Shankar  \nRobert Bosch Centre for Cyber-Physical Systems IISc, Bengaluru, India [puneethz1z3z2@gmail.com](puneethz1z3z2@gmail.com)  \nRavi Prakash  \nRobert Bosch Centre for Cyber-Physical Systems IISc, Bengaluru, India [ravipr@iisc.ac.in](ravipr@iisc.ac.in)  \nPushpak Jagtap  \nRobert Bosch Centre for Cyber-Physical Systems  \nIISc, Bengaluru, India  \n[pushpak@iisc.ac.in](pushpak@iisc.ac.in)  \nJuly 2, 2026  \nABSTRACT  \nWe present STT-LfD, a unified Learning from Demonstration (LfD) framework that integrates motion learning with control for unknown Euler–Lagrange systems. Unlike traditional decoupled approaches that track a fixed reference, the proposed method treats demonstrations as a data-driven safety specification. Using heteroscedastic Gaussian Processes, STT-LfD learns Spatiotemporal Tubes (STTs) as an intent envelope that capture time-varying precision requirements of a task. A closed-form feedback controller then enforces these learned constraints while respecting actuator limits, without requiring explicit system identification. The approach preserves the temporal structure of demonstrations, remains computationally efficient, and avoids explicit system identification.  \nHardware experiments on a mobile robot and a 7-DOF manipulator show that it outperforms baselinesin robustness to disturbances and computational speed. Video Linkperturbed conditions.  \n1 Introduction  \nRobots operating in safety-critical and unstructured environments often need to perform complex skills that are easier to demonstrate than to manually program. Learning from Demonstration (LfD) offers a natural way to transfer human expertise directly into robotic policies [1, 2] . However, traditional LfD architectures typically suffer from a rigid decoupling: a high-level motion generation stage (e.g., DMP [3, 4] or KMP) produces a reference trajectory, which a separate low-level controller (e.g., LQR [5] or MPC [6]) then attempts to track. This separation is inherently fragile, as the motion generator ignores the hardware’s physical constraints, while the tracker treats all trajectory points with uniform importance. As a result, these approaches fail to capture what we call the intent envelope: a time-varying spatial tolerance implicitly expressed by the expert. For example, during precise manipulation (e.g., threading a needle), this envelope is narrow and restrictive, whereas in free-space motion, it can be much wider.  \n∗This work was supported in part by the SERB Start-Up Research Grant; in part by the ARTPARK. The work of Ratnangshu Das was supported by the Prime Minister’s Research Fellowship from the Ministry of Education, Government of India.  \nA PREPRINT-JULY 2, 2026  \nFigure 1: STT-LfD framework: Expert demonstrations are aligned using DTW and spatiotemporal tubes are obtained using HGPs. A closed-form controller then enforces tube invariance for safe and robust task execution under input constraints.  \nIn this letter, we address this limitation by introducing STT-LfD, a unified framework that bridges the gap between probabilistic motion representation and robust control for unknown Euler-Lagrange systems. We use heteroscedastic Gaussian Processes (HGPs) [7] to learn Spatiotemporal Tubes (STTs) [8, 9] from demonstrations that capture both the nominal task behavior and its time-varying precision requirements. However, previous STT formulations primarily focused on satisfying formally specified temporal logic constraints through optimization-or learning-based tube synthesis. In contrast, the proposed framework constructs STTs directly from","cbCaiaZPUFxzxY3G","https://ap.wps.com/l/cbCaiaZPUFxzxY3G","pdf",3100096,1,14,"English","en",105,"# Introduction\n## Unified task specification (STT-LfD)\n## Closed-form control under input constraints\n## Experimental validation","[{\"question\":\"What problem does STT-LfD address in learning from demonstrations?\",\"answer\":\"STT-LfD addresses the fragility of conventional LfD pipelines where motion generation and tracking are decoupled, causing failure to represent time-varying precision requirements and to respect physical constraints.\"},{\"question\":\"How does STT-LfD represent a demonstrated task as actionable constraints?\",\"answer\":\"It learns Spatiotemporal Tubes (STTs) from expert demonstrations using heteroscedastic Gaussian Processes, forming an intent envelope that specifies admissible time-varying regions rather than a single reference trajectory.\"},{\"question\":\"Does STT-LfD require explicit system identification or online optimization?\",\"answer\":\"No. The execution uses a closed-form feedback controller mathematically coupled with the learned tube, and it does not require explicit system identification or real-time optimization.\"}]",1784196916,35,{"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},"learning-from-demonstration-via-spatiotemporal-tubes-for-unknown-euler-lagrange-systems","",{"@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/learning-from-demonstration-via-spatiotemporal-tubes-for-unknown-euler-lagrange-systems/84580/",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 STT-LfD address in learning from demonstrations?","Question",{"text":75,"@type":76},"STT-LfD addresses the fragility of conventional LfD pipelines where motion generation and tracking are decoupled, causing failure to represent time-varying precision requirements and to respect physical constraints.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does STT-LfD represent a demonstrated task as actionable constraints?",{"text":80,"@type":76},"It learns Spatiotemporal Tubes (STTs) from expert demonstrations using heteroscedastic Gaussian Processes, forming an intent envelope that specifies admissible time-varying regions rather than a single reference trajectory.",{"name":82,"@type":73,"acceptedAnswer":83},"Does STT-LfD require explicit system identification or online optimization?",{"text":84,"@type":76},"No. The execution uses a closed-form feedback controller mathematically coupled with the learned tube, and it does not require explicit system identification or 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