[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83339-en":3,"doc-seo-83339-105":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},83339,687197207919,"Theodora","https://ap-avatar.wpscdn.com/avatar/a000253d6f5f7c60be?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779446848396160552",8,"Research & Report","Input-Constrained Spatiotemporal Tubes for Safe Navigation of Unknown Euler-Lagrange Systems in Dynamic Environments","Safe navigation in dynamic environments becomes difficult when system dynamics are unknown and actuator inputs are limited. This paper introduces a real-time control framework for unknown Euler–Lagrange systems that enforces finite-time reach-avoid-stay (FTRAS) specifications while honoring actuator limits. The spatiotemporal tube (STT) framework is extended by embedding input constraints in controller design, and offline-verifiable feasibility conditions link available control authority, tube design, and uncertainty bounds. The method is approximation-free and computationally efficient, and is validated via simulations and hardware experiments.","INPUT-CONSTRAINED SPATIOTEMPORAL TUBES FOR SAFE NAVIGATION OF UNKNOWN EULER–LAGRANGE SYSTEMS IN  \nDYNAMIC ENVIRONMENTS  \nSiddhartha Upadhyay  \nDepartment of Cyber-Physical Systems Indian Institute of Science, Bengaluru, India [siddharthau@iisc.ac.in](siddharthau@iisc.ac.in)  \nRatnangshu Das  \nDepartment of Cyber-Physical Systems Indian Institute of Science„ Bengaluru, India [ratnangshud@iisc.ac.in](ratnangshud@iisc.ac.in)  \narXiv :2607 .08189v1 [ ee ss . SY] 9 Jul 2026  \nPushpak Jagtap  \nDepartment of Cyber-Physical Systems  \nIndian Institute of Science„ Bengaluru, India  \n[pushpak@iisc.ac.in](pushpak@iisc.ac.in)  \nJuly 10, 2026  \nABSTRACT  \nSafe navigation in dynamic environments is challenging when system dynamics are unknown and actuator inputs are limited. Existing methods either rely on accurate models, require online optimization, or do not explicitly account for input constraints. This paper presents a real-time control framework for unknown Euler–Lagrange systems that guarantees finite-time reach-avoid-stay (FTRAS) specifications while respecting actuator limits. We extend the spatiotemporal tube (STT) framework by incorporating input constraints into the controller design and derive offline-verifiable feasibility conditions that relate the available control authority to the tube design and uncertainty bounds. The resulting framework is approximation-free and computationally efficient, making it suitable for real-time implementation. The proposed approach is validated through simulations on a mobile robot, a quadrotor, and a spacecraft, together with hardware experiments on a mobile robot, demonstrating safe navigation while satisfying actuator constraints.  \nKeywords Input Constraint, Safety Guarantees, Spatiotemporal Tube, Unknown Euler-Lagrange  \n1 Introduction  \nAutonomous systems are increasingly being deployed in safety-critical applications [1] such as autonomous driving, aerial robotics, industrial automation, and medical robotics. The deployment of autonomous robotic systems in realworld environments presents several challenges [2], [3] . In practice, system dynamics are often partially known or unknown, the operating environment is dynamic and uncertain, and external disturbances can significantly affect system performance. Moreover, all robotic platforms are subject to actuator input constraints arising from physical limitations on force, torque, velocity, and acceleration [4] . These constraints are particularly important in practice, as neglecting them may lead to infeasible control inputs, actuator saturation, degraded performance, and even safety violations. Therefore, developing real-time control frameworks that explicitly account for input constraints while providing formal safety guarantees remain a challenging problem.  \nThe problem of navigation in dynamic environments has been extensively studied in the literature, with planning-based approaches emerging as one of the most prominent solution paradigms. Classical planning approaches, such as A* and RRT [5], and reactive methods such as Artificial Potential Fields (APF) [6], have been widely adopted for autonomous navigation. However, these methods primarily focus on generating collision-free paths without explicitly considering the system dynamics. Consequently, the resulting trajectories may not be dynamically feasible or trackable under  \nA PREPRINT-JULY 10, 2026  \nthe available actuator input constraints. Moreover, APF-based methods are susceptible to local minima, and both approaches generally lack formal guarantees on safety and task completion while providing limited support for explicitly handling actuator input constraints. Model-based optimization approaches like MPC [7, 8] have also been proposed to bridge planning and control. For instance, an event-triggered MPC [9] integrated with an adaptive APF achieves simultaneous trajectory tracking and obstacle avoidance while explicitly accounting for input and state constraints. However, such ap","cbCaieH3YlWCnbjn","https://ap.wps.com/l/cbCaieH3YlWCnbjn","pdf",5122194,4,1,20,"English","en",105,"# Abstract\n# Introduction\n## Motivation and challenges in dynamic navigation\n## Related work: planning, MPC, and barrier methods\n## Symbolic control and problem setup (partial)","[{\"question\":\"What safety objective does the proposed framework guarantee for unknown Euler–Lagrange systems?\",\"answer\":\"It guarantees finite-time reach-avoid-stay (FTRAS) specifications, ensuring the system reaches desired states, avoids unsafe sets, and stays safe over a finite horizon while navigating dynamically.\"},{\"question\":\"How does the paper handle limited actuator inputs in the controller design?\",\"answer\":\"It extends the spatiotemporal tube (STT) framework by incorporating input constraints directly into the controller design, and derives offline-verifiable feasibility conditions that relate control authority to tube design and uncertainty bounds.\"},{\"question\":\"How is the feasibility of the approach checked without online optimization?\",\"answer\":\"The framework uses offline-verifiable feasibility conditions that connect the available control authority, the tube design parameters, and uncertainty bounds, enabling computationally efficient real-time implementation.\"}]",1784186849,50,{"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},"input-constrained-spatiotemporal-tubes-for-safe-navigation-of-unknown-euler-lagrange-systems-in-dynamic-environments","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"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":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":20},"https://docshare.wps.com/document/input-constrained-spatiotemporal-tubes-for-safe-navigation-of-unknown-euler-lagrange-systems-in-dynamic-environments/83339/",{"url":52,"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","2026-07-23","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 safety objective does the proposed framework guarantee for unknown Euler–Lagrange systems?","Question",{"text":75,"@type":76},"It guarantees finite-time reach-avoid-stay (FTRAS) specifications, ensuring the system reaches desired states, avoids unsafe sets, and stays safe over a finite horizon while navigating dynamically.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the paper handle limited actuator inputs in the controller design?",{"text":80,"@type":76},"It extends the spatiotemporal tube (STT) framework by incorporating input constraints directly into the controller design, and derives offline-verifiable feasibility conditions that relate control authority to tube design and uncertainty bounds.",{"name":82,"@type":73,"acceptedAnswer":83},"How is the feasibility of the approach checked without online optimization?",{"text":84,"@type":76},"The framework uses offline-verifiable feasibility conditions that connect the available control authority, the tube design 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