[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84649-en":3,"doc-seo-84649-105":29,"detail-sidebar-cat-0-en-105":90},{"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":11,"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},84649,3848291630094,"Emma Wilson","https://eur-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45",8,"Research & Report","Nonholonomic Source Seeking by Torque Tuning: Local and Semi-Global Feedbacks","This paper studies source seeking for a torque-controlled nonholonomic vehicle equipped with a laterally displaced scalar sensor. The vehicle maintains constant forward speed, while yaw motion is driven by torque despite unknown inertia and damping. Control steers the vehicle into a source-centered circular orbit so the sensor converges toward an unknown source without using position, heading, gradient, or source-value information. A torque law combines fast oscillatory excitation for averaged steering with a slowly tuned bias for orbit selection, yielding local practical and semi-global practical stability, supported by simulations.","arXiv :2607 .02458v1 [ ee ss . SY] 2 Jul 2026  \nNonholonomic Source Seeking by Torque Tuning: Local and Semi-Global Feedbacks  \nBo Wanga,∗  \na Department of Mechanical Engineering, The City College of New York, The City University of New York, New York, NY 10031, USA  \nARTICLE INFO  \nKeywords:  \nSource seeking Averaging Nonholonomic vehicles Practical stability  \nAB STRACT  \nThis paper studies source seeking for a torque-controlled nonholonomic vehicle with a laterally displaced scalar sensor. The vehicle has constant forward speed, while its yaw motion is controlled by torque input with unknown inertia and damping. The objective is to steer the vehicle to a sourcecentered circular motion so that the lateral sensor approaches the unknown source, without using position, heading, source-location, gradient, or source-value information. The proposed torque law combines a fast oscillatory component, which generates averaged steering through symmetric-product approximation, with a slowly tuned bias component, which selects the desired orbit. Two bias-tuning designs are developed. The first is an output-feedback design using only the scalar measurement; it applies a Lie-bracket extremum-seeking update and yields local practical stability. The second is a velocity-assisted design using forward-speed and yaw-rate measurements; it tunes the bias through the yaw-rate tracking error and yields a globally asymptotically stable averaged system, implying semi-global practical stability of the original system. Simulations illustrate the proposed designs.  \n1. Introduction  \nSource seeking concerns the problem of steering a dynamical system toward the extremum of an unknown spatial signal using real-time measurements of the signal value [1, 2, 3] . This problem arises in applications such as locating chemical, thermal, electromagnetic, or acoustic sources, where the source position, signal gradient, and extremal value are not available a priori. Source-seeking techniques have been used in diverse engineering systems, including autonomous vehicles [4, 5], marine vessels [6], satellites [7], and particle accelerators [8], among others. In this paper, we consider source seeking for a torque-controlled nonholonomic vehicle moving in an unknown static scalar field. The vehicle is equipped with a suitable sensor that measures the signal value at the sensor location. The objective is to drive the vehicle toward the source, or equivalently to steer the vehicle toward a source-centered circular motion. Following the standard convention in extremum seeking, the source is treated as the unique minimum of the signal.  \nVelocity-level nonholonomic source seeking has been studied extensively for kinematic unicycle models, where the forward and angular velocities are treated as directly assignable control inputs. One line of work tuned the forward velocity while maintaining a constant angular velocity, using extremum-seeking dithers to recover gradient information without position measurements [4, 9, 10]. A complementary line of work keeps the forward speed constant and tunes the angular velocity to steer the vehicle toward a source-centered orbit [11, 12, 13] . Source-seeking schemes that combine forward-speed regulation with steering control have also been developed [14]. Related velocity-regulation ideas have also been developed for three-dimensional nonholonomic vehicles by tuning forward, pitch, and yaw velocities [15] .  \n∗Corresponding author. [E-mail addresses:](E-mail addresses: bwang1@ccny.cuny.edu)[ bwang1@ccny.cuny.edu](E-mail addresses: bwang1@ccny.cuny.edu) (B. Wang).  \nThese results provide a mature velocity-level theory for nonholonomic source seeking, but they do not address source seeking under the force-or torque-actuated dynamics.  \nMore recently, source seeking has been extended from velocity-level kinematic models to second-order dynamic models, where the inputs are forces or torques rather than velocities. This shift is natural for rob","cbCairiSmRQHFYt4","https://ap.wps.com/l/cbCairiSmRQHFYt4","pdf",1135974,3,1,"English","en",105,"# Introduction\n## Background on extremum and source seeking\n## Velocity-level vs force/torque actuation\n## Related work in nonholonomic dynamic models\n## Contributions of the proposed approach","[{\"question\":\"What sensing setup and control goal are used for the nonholonomic vehicle?\",\"answer\":\"The vehicle carries a scalar sensor laterally displaced from its center, measuring the field value at the sensor location. The goal is to steer toward a source-centered circular motion so the sensor approaches the unknown source without relying on position or gradient information.\"},{\"question\":\"How does the proposed torque law generate steering toward the source?\",\"answer\":\"It combines a fast oscillatory torque component that produces averaged steering via a symmetric-product approximation, with a slowly tuned bias component that selects the desired orbit.\"},{\"question\":\"What stability results are obtained and how do the two tuning designs differ?\",\"answer\":\"An output-feedback bias tuning using only the scalar measurement yields local practical stability. A velocity-assisted bias tuning using forward-speed and yaw-rate measurements tunes bias via yaw-rate tracking error and yields a globally asymptotically stable averaged system, implying semi-global practical stability of the original dynamics.\"}]",1784197473,20,{"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":85,"head_meta":87,"extra_data":89,"updated_unix":27},"nonholonomic-source-seeking-by-torque-tuning-local-and-semi-global-feedbacks","",{"@graph":35,"@context":84},[36,52,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,49],{"item":40,"name":41,"@type":42,"position":21},"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":20},"https://docshare.wps.com/document/research-report/",{"item":50,"name":13,"@type":42,"position":51},"https://docshare.wps.com/document/nonholonomic-source-seeking-by-torque-tuning-local-and-semi-global-feedbacks/84649/",4,{"url":50,"name":13,"@type":53,"author":54,"headline":13,"publisher":56,"fileFormat":59,"inLanguage":23,"description":14,"dateModified":60,"datePublished":61,"encodingFormat":59,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":55},"Person",{"url":40,"name":57,"@type":58},"DocShare","Organization","application/pdf","2026-07-22","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":20},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What sensing setup and control goal are used for the nonholonomic vehicle?","Question",{"text":74,"@type":75},"The vehicle carries a scalar sensor laterally displaced from its center, measuring the field value at the sensor location. The goal is to steer toward a source-centered circular motion so the sensor approaches the unknown source without relying on position or gradient information.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How does the proposed torque law generate steering toward the source?",{"text":79,"@type":75},"It combines a fast oscillatory torque component that produces averaged steering via a symmetric-product approximation, with a slowly tuned bias component that selects the desired orbit.",{"name":81,"@type":72,"acceptedAnswer":82},"What stability results are obtained and how do the two tuning designs differ?",{"text":83,"@type":75},"An output-feedback bias tuning using only the scalar measurement yields local practical stability. A velocity-assisted bias tuning using forward-speed and yaw-rate measurements tunes bias via yaw-rate tracking error and yields a globally asymptotically stable averaged system, implying semi-global practical stability of the original dynamics.","https://schema.org",{"og:url":50,"og:type":86,"og:title":13,"og:site_name":57,"og:description":14},"article",{"robots":88,"canonical":50},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":91},[92,96,100,104,109,114,119,122,126,129,133],{"id":21,"doc_module":4,"doc_module_name":45,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":51,"doc_module":4,"doc_module_name":45,"category_name":101,"show_sort_weight":102,"slug":103},"Exam",70,"exam",{"id":105,"doc_module":4,"doc_module_name":45,"category_name":106,"show_sort_weight":107,"slug":108},5,"Comic",60,"comic",{"id":110,"doc_module":4,"doc_module_name":45,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":45,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":45,"category_name":124,"show_sort_weight":28,"slug":125},9,"Religion & Spirituality","religion-spirituality",{"id":28,"doc_module":4,"doc_module_name":45,"category_name":127,"show_sort_weight":28,"slug":128},"World Cup","world-cup",{"id":130,"doc_module":4,"doc_module_name":45,"category_name":131,"show_sort_weight":130,"slug":132},10,"Lifestyle","lifestyle",{"id":134,"doc_module":4,"doc_module_name":45,"category_name":135,"show_sort_weight":105,"slug":136},19,"General","general"]