Variational Principles for the Trajectory Tracking Control of Underactuated Mechanical Systems

https://m2.mtmt.hu/ eng 2026-04-16 13:35 JournalArticle 33563467 VALIDATED true Funding Agency and Grant Number: National Research, Development and Innovation Fund; [BME-NVA-02]; [TKP2021-EGA-02] Funding text: National Research, Development and Innovation Fund(Grant Nos. BME-NVA-02 and TKP2021-EGA-02; FunderID: 10.13039/100009567). 0 false 2026-01-01T12:22:35.627+0000 2024-01-28T08:39:23.607+0000 2023-01-14T21:00:29.811+0000 true 10063324 Bodor Bálint /api/author/10063324 Author Bálint Bodor (műszaki mechanika) true 10063324 2024-05-08T14:41:41.413+0000 2024-05-08T14:41:41.413+0000 2023-07-13T13:07:38.401+0000 true 10087553 Heincz Orsolya /api/admin/10087553 Admin Orsolya Heincz (BME admin 5) true true false true 24 24 /api/publicationtype/24 PublicationType Journal Article 1 true 24 JournalArticle true 10000059 Article true 24 24 /api/publicationtype/24 PublicationType Journal Article 1 true 24 JournalArticle /api/subtype/10000059 Szakcikk SubType Article (Journal Article) 101 true 10000059 true 1 /api/category/1 Category Scientific true 1 Bodor, Bálint Variational Principles for the Trajectory Tracking Control of Underactuated Mechanical Systems true true /api/journal/10006367 REVIEWED JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS 1555-1415 1555-1423 true false 10006367 false 10006367 true 1555-1415 1555-1423 Journal FOREIGN 18 6 061002, CND-22-1183 061002, CND-22-1183 10 2023 Robotics is undergoing dynamic progression with the spread of soft robots and compliant mechanisms. The mechanical models describing these systems are underactuated, having more degrees-of-freedom than inputs. The trajectory tracking control of underactuated systems is not straightforward. The solution of the inverse dynamics is not stable in all cases, as it only considers the actual state of the system. Therefore employing the advances of optimal control theory is a reasonable choice. However, the real-time application of these is challenging as the solution to the discretized optimization problems is numerically expensive. This paper presents a novel iterative approach to solving nonlinear optimal control problems. The authors first define the iteration formula after which the obtained equations are discretized to prepare the numerical solution, contrarily to the accessible works in the literature having reverse order. The main idea is to approximate the cost functional with a second-order expansion in each iteration step, which is then extremized to get the subsequent approximation of the optimum. In the case of nonlinear optimal control problems, the process leads to a sequence of time-variant linear-quadratic regulator (LQR) problems. The proposed technique was effectively applied to the trajectory tracking control of a flexible rotational-rotational joint (RR) manipulator. The case study showed that the initialization of the iteration is simple, and the convergence is rapid. true 2023 true true true false true false NONE 2026-01-01 false 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 2 2 Folyóiratcikk Journal Article 24 1 Könyvrészlet Chapter in Book 25 0 Könyv Book 23 0 Egyéb konferenciaközlemény Conference paper 31 0 Egyéb konferenciakötet Conference proceedings 32 0 Oltalmi formák Protection forms 26 0 Disszertáció Thesis 28 0 Egyéb Miscellaneous 29 0 Alkotás Achievement 22 0 Kutatási adat Research data 33 0 Folyóiratcikk Journal Article 24 0 0 0 Könyvrészlet Chapter in Book 25 0 0 0 Könyv Book 23 0 0 0 Egyéb konferenciaközlemény Conference paper 31 0 0 0 Egyéb konferenciakötet Conference proceedings 32 0 0 0 Oltalmi formák Protection forms 26 0 0 0 Disszertáció Thesis 28 0 0 0 Egyéb Miscellaneous 29 0 0 0 Alkotás Achievement 22 0 0 0 Kutatási adat Research data 33 0 0 0 2025 0 1 1 1 1 Q2 false false false false 2023-04-06T08:49:37.515+0000 ELKH-BME Gépek Dinamikája Kutatócsoport (BME / GPK / MM); Műszaki Mechanikai Tanszék (BME / GPK) 2 8 2 2 0 true Language 10002 /api/language/10002 English Angol English true 2 true PersonAuthorship 106305696 /api/authorship/106305696 Bodor, Bálint [Bodor, Bálint (műszaki mechanika), author] Department of Applied Mechanics (BUTE / FME); ELKH-BME Gépek Dinamikája Kutatócsoport (BUTE / FME / DAM) 1 1.0 true false Author 10063324 /api/author/10063324 Bálint Bodor (műszaki mechanika) Bodor Bálint true 10063324 true Bodor Bálint true false false AuthorshipType 1 /api/authorshiptype/1 Author 0 true 0 true false true PersonAuthorship 106305701 /api/authorship/106305701 Bencsik, László [Bencsik, László (műszaki mechanika), author] Department of Applied Mechanics (BUTE / FME) 2 0.0 false true Author 10042439 /api/author/10042439 László Bencsik (műszaki mechanika) Bencsik László true 10042439 true Bencsik László true false false AuthorshipType 1 /api/authorshiptype/1 Author 0 true 0 true false true PublicationIdentifier 22843752 /api/publicationidentifier/22843752 DOI: 10.1115/1.4056593 PlainSource 6 /api/publicationsource/6 DOI PublicationSourceType 10001 /api/publicationsourcetype/10001 DOI true true true DOI DOI https://doi.org/@@@ true true 6 true IDENTICAL 10.1115/1.4056593 https://doi.org/10.1115/1.4056593 false true PublicationIdentifier 24155157 /api/publicationidentifier/24155157 WoS: 001009961300005 PlainSource 1 /api/publicationsource/1 WoS PublicationSourceType 10003 /api/publicationsourcetype/10003 Indexelő adatbázis false true true WoS WoS https://www.webofscience.com/wos/woscc/full-record/@@@ true true 1 true IDENTICAL 001009961300005 https://www.webofscience.com/wos/woscc/full-record/001009961300005 false true PublicationIdentifier 23718659 /api/publicationidentifier/23718659 Scopus: 85157981223 PlainSource 3 /api/publicationsource/3 Scopus PublicationSourceType 10003 /api/publicationsourcetype/10003 Indexelő adatbázis false true true Scopus Scopus http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-@@@ true true 3 true IDENTICAL 85157981223 http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85157981223 false true PublicationIdentifier 25375411 /api/publicationidentifier/25375411 Other URL: https://phd.gpk.bme.hu/pub/s/j/l9/t3?3001773 PlainSource 40 /api/publicationsource/40 Other URL PublicationSourceType 10006 /api/publicationsourcetype/10006 Link true true true Egyéb URL Other URL @@@ true true 40 true https://phd.gpk.bme.hu/pub/s/j/l9/t3?3001773 https://phd.gpk.bme.hu/pub/s/j/l9/t3?3001773 true true Classification 10807 /api/classification/10807 ENGINEERING AND TECHNOLOGY true true Keyword 1518634 /api/keyword/1518634 Engineering, Mechanical true true SjrRating 11395960 /api/sjrrating/11395960 sjr:Q2 (2023) Scopus - Mechanical Engineering JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS 1555-1415 1555-1423 277 0.49 journal RatingType 10002 /api/ratingtype/10002 sjr sjr true true ClassificationExternal 2210 /api/classificationexternal/2210 Scopus - Mechanical Engineering true 2210 true Q2 DIRECT true true /api/publication/33563467 Bodor Bálint et al. Variational Principles for the Trajectory Tracking Control of Underactuated Mechanical Systems. (2023) JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS 1555-1415 1555-1423 18 6<div class="JournalArticle Publication long-list"> <div class="authors"> <img title="Forrásközlemény" style="float: left" src="/frontend/resources/grid/publication-core-icon.png"> <img title="Idézőközlemény" style="float: left" src="/frontend/resources/grid/publication-citation-icon.png"> <div class="autype autype0"> <span class="author-name" mtid="10063324"><a href="/gui2/?type=authors&mode=browse&sel=10063324" target="_blank">Bodor Bálint (<span class="authorship-author-name">Bodor Bálint</span> <span class="authorAux-mtmt"> műszaki mechanika</span>) </a> </span> <span class="author-affil"><span title="Budapest University of Technology and Economics">BUTE</span>/<span title="Faculty of Mechanical Engineering">FME</span>/Department of Applied Mechanics; <span title="Budapest University of Technology and Economics">BUTE</span>/<span title="Faculty of Mechanical Engineering">FME</span>/<span title="Department of Applied Mechanics">DAM</span>/ELKH-BME Gépek Dinamikája Kutatócsoport</span> ;    <span class="author-name" mtid="10042439"><a href="/gui2/?type=authors&mode=browse&sel=10042439" target="_blank">Bencsik László (<span class="authorship-author-name">Bencsik László</span> <span class="authorAux-mtmt"> műszaki mechanika</span>) </a> </span> <span class="author-affil"><span title="Budapest University of Technology and Economics">BUTE</span>/<span title="Faculty of Mechanical Engineering">FME</span>/Department of Applied Mechanics</span> </div> </div> <div class="title"><a href="/gui2/?mode=browse&params=publication;33563467" target="_blank">Variational Principles for the Trajectory Tracking Control of Underactuated Mechanical Systems</a></div> <div> <span class="journal-title">JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS</span> <span class="journal-issn">(<a target="_blank" href="https://portal.issn.org/resource/ISSN/1555-1415">1555-1415</a> <a target="_blank" href="https://portal.issn.org/resource/ISSN/1555-1423">1555-1423</a>)</span>: <span class="journal-volume">18</span> <span class="journal-issue">6</span> <span class="page"> Paper 061002, CND-22-1183. 10 p. </span> <span class="year">(2023)</span> </div> <div class="pub-footer"> <span class="language" xmlns="http://www.w3.org/1999/html">Language: English | </span> <span class="identifiers"> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="10.1115/1.4056593" target="_blank" href="https://doi.org/10.1115/1.4056593"> DOI </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="001009961300005" target="_blank" href="https://www.webofscience.com/wos/woscc/full-record/001009961300005"> WoS </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="85157981223" target="_blank" href="http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85157981223"> Scopus </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="https://phd.gpk.bme.hu/pub/s/j/l9/t3?3001773" target="_blank" href="https://phd.gpk.bme.hu/pub/s/j/l9/t3?3001773"> Other URL </a> </span> </span> <OnlyViewableByAuthor><div class="ratings"> <div class="journal-subject">Journal subject: Scopus - Mechanical Engineering   Rank: Q2</div> <div class="journal-subject">Journal subject: Scopus - Applied Mathematics   Rank: Q3</div> <div class="journal-subject">Journal subject: Scopus - Control and Systems Engineering   Rank: Q3</div> </div></OnlyViewableByAuthor> <div class="publication-citation" style="margin-left: 0.5cm;"> <span title="" class="citingPub-count">Citing papers: 1</span> | Independent citation: 1 | Self citation: 0 | Unknown citation: 0 | Number of citations in WoS: 1 | Number of citations in Scopus: 1 | WoS/Scopus assigned: 1 | Number of citations with DOI: 1 </div> <div class="publication-citation"> <a target="_blank" href="/api/publication?cond=citations.related;eq;33563467&sort=publishedYear,desc&sort=title"> Number of cited publications: 2 </a> </div> <div class="mtid"><span class="long-pub-mtid">Publication: 33563467</span> | <span class="status-data status-VALIDATED"> Validated </span> Core Citing | <span class="type-subtype">Journal Article ( Article ) </span> | <span class="pub-category">Scientific</span> | <span class="publication-sourceOfData">kézi felvitel</span> </div> <div class="notDuplums"><a target="_blank" href="/api/publication/33563467/notduplums">350 marked as not duplum</a> </div> <div class="lastModified">Last Modified: 2024.01.28. 09:39 Bálint Bodor (műszaki mechanika) </div> <pre class="comment" style="margin-top: 0; margin-bottom: 0;"><u>Comments</u>: Funding Agency and Grant Number: National Research, Development and Innovation Fund; [BME-NVA-02]; [TKP2021-EGA-02] Funding text: National Research, Development and Innovation Fund(Grant Nos. BME-NVA-02 and TKP2021-EGA-02; FunderID: 10.13039/100009567).</pre> </div></div>