{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T14:46:28Z","timestamp":1784645188888,"version":"3.55.0"},"reference-count":27,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,6,26]],"date-time":"2025-06-26T00:00:00Z","timestamp":1750896000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Basic Science Research Program","award":["NRF-2016R1A6A1A03013567"],"award-info":[{"award-number":["NRF-2016R1A6A1A03013567"]}]},{"name":"Basic Science Research Program","award":["NRF-2021R1A2B5B01001484"],"award-info":[{"award-number":["NRF-2021R1A2B5B01001484"]}]},{"name":"Basic Science Research Program","award":["NRF-2022K2A9A2A06045121"],"award-info":[{"award-number":["NRF-2022K2A9A2A06045121"]}]},{"name":"framework of the International Cooperation Program","award":["NRF-2016R1A6A1A03013567"],"award-info":[{"award-number":["NRF-2016R1A6A1A03013567"]}]},{"name":"framework of the International Cooperation Program","award":["NRF-2021R1A2B5B01001484"],"award-info":[{"award-number":["NRF-2021R1A2B5B01001484"]}]},{"name":"framework of the International Cooperation Program","award":["NRF-2022K2A9A2A06045121"],"award-info":[{"award-number":["NRF-2022K2A9A2A06045121"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>This study aims to explore the tracking control challenge in a swarm of multiple nonholonomic wheeled mobile robots (NWMRs) by utilizing a distributed leader\u2013follower strategy grounded in the cascade system theory. Firstly, the kinematic control law is developed for the leader by constructing a sliding surface based on the error tracking model with a virtual reference trajectory. Secondly, a communication topology with the desired formation pattern is modeled for the multiple robots by using the graph theory. Further, in the leader\u2013follower NWMR system, each follower lacks direct access to the leader\u2019s information. Therefore, a novel distributed-based controller by PD-based controller for the follower is developed, enabling each follower to obtain the leader\u2019s information. Thirdly, for each case, we give a further analysis of the closed-loop system to guarantee uniform global asymptotic stability with the conditions based on the cascade system theory. Finally, the trajectory tracking performance of the proposed controllers for the NWMR system is illustrated through simulation results. The leader robot achieved a low RMSE of 1.6572 (Robot 1), indicating accurate trajectory tracking. Follower robots showed RMSEs of 2.6425 (Robot 2), 3.0132 (Robot 3), and 4.2132 (Robot 3), reflecting minor variations due to the distributed control strategy and local disturbances.<\/jats:p>","DOI":"10.3390\/robotics14070088","type":"journal-article","created":{"date-parts":[[2025,7,2]],"date-time":"2025-07-02T06:46:12Z","timestamp":1751438772000},"page":"88","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Cascade-Based Distributed Estimator Tracking Control for Swarm of Multiple Nonholonomic Wheeled Mobile Robots via Leader\u2013Follower Approach"],"prefix":"10.3390","volume":"14","author":[{"given":"Dinesh","family":"Elayaperumal","sequence":"first","affiliation":[{"name":"School of IT Information and Control Engineering, Kunsan National University, 588 Daehak-ro, Gunsan-si 54150, Jeonbuk, Republic of Korea"},{"name":"APGS Team, Division of PARCS, HUMAX Mobility, Bundang-gu, Seongnam-si 13595, Gyeonggi-do, Republic of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7919-1844","authenticated-orcid":false,"given":"Sachin Sakthi","family":"Kuppusami Sakthivel","sequence":"additional","affiliation":[{"name":"School of IT Information and Control Engineering, Kunsan National University, 588 Daehak-ro, Gunsan-si 54150, Jeonbuk, Republic of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sathishkumar","family":"Moorthy","sequence":"additional","affiliation":[{"name":"School of IT Information and Control Engineering, Kunsan National University, 588 Daehak-ro, Gunsan-si 54150, Jeonbuk, Republic of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sathiyamoorthi","family":"Arthanari","sequence":"additional","affiliation":[{"name":"School of IT Information and Control Engineering, Kunsan National University, 588 Daehak-ro, Gunsan-si 54150, Jeonbuk, Republic of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4662-1916","authenticated-orcid":false,"given":"Young Hoon","family":"Joo","sequence":"additional","affiliation":[{"name":"School of IT Information and Control Engineering, Kunsan National University, 588 Daehak-ro, Gunsan-si 54150, Jeonbuk, Republic of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6371-8007","authenticated-orcid":false,"given":"Jae Hoon","family":"Jeong","sequence":"additional","affiliation":[{"name":"College of Computer and Software, Kunsan National University, 588 Daehak-ro, Gunsan-si 54150, Jeonbuk, Republic of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1109\/TRA.2002.803463","article-title":"A vision-based formation control framework","volume":"18","author":"Das","year":"2002","journal-title":"IEEE Trans. Robot. Autom."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1343","DOI":"10.1016\/j.automatica.2007.09.019","article-title":"Leader\u2013follower formation control of nonholonomic mobile robots with input constraints","volume":"44","author":"Consolini","year":"2008","journal-title":"Automatica"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"114589","DOI":"10.1016\/j.eswa.2021.114589","article-title":"Connectivity-maintaining obstacle avoidance approach for leader-follower formation tracking of uncertain multiple nonholonomic mobile robots","volume":"171","author":"Park","year":"2021","journal-title":"Expert Syst. Appl."},{"key":"ref_4","first-page":"15","article-title":"Autonomous control of complex systems: Robotic applications","volume":"120","author":"Jamshidi","year":"2001","journal-title":"Appl. Math. Comput."},{"key":"ref_5","first-page":"126349","article-title":"Quantized feedback control strategy for tracking performance guarantee of nonholonomic mobile robots with uncertain nonlinear dynamics","volume":"407","author":"Yoo","year":"2021","journal-title":"Appl. Math. Comput."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1007\/s44430-025-00001-5","article-title":"A study of advanced mathematical modeling and adaptive control strategies for trajectory tracking in the Mitsubishi RV-2AJ 5-DOF Robotic Arm","volume":"1","author":"Guler","year":"2025","journal-title":"Discov. Robot."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"926","DOI":"10.1109\/70.736776","article-title":"Behavior-based formation control for multirobot teams","volume":"14","author":"Balch","year":"1998","journal-title":"IEEE Trans. Robot. Autom."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1023\/A:1008814708459","article-title":"High precision formation control of mobile robots using virtual structures","volume":"4","author":"Lewis","year":"1997","journal-title":"Auton. Robot."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1109\/TCST.2007.908214","article-title":"Formation tracking control of unicycle-type mobile robots with limited sensing ranges","volume":"16","author":"Do","year":"2008","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"998","DOI":"10.1016\/j.procs.2018.07.076","article-title":"Obstacle avoidance and navigation planning of a wheeled mobile robot using amended artificial potential field method","volume":"133","author":"Sudhakara","year":"2018","journal-title":"Procedia Comput. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"988","DOI":"10.1016\/j.robot.2013.05.004","article-title":"Leader\u2013follower formation control of nonholonomic mobile robots based on a bioinspired neurodynamic based approach","volume":"61","author":"Peng","year":"2013","journal-title":"Robot. Auton. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"592","DOI":"10.1016\/j.automatica.2012.11.031","article-title":"Distributed formation control of nonholonomic mobile robots without global position measurements","volume":"49","author":"Liu","year":"2013","journal-title":"Automatica"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1109\/TIE.2015.2504042","article-title":"Distributed formation control of nonholonomic vehicles subject to velocity constraints","volume":"63","author":"Yu","year":"2015","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1485","DOI":"10.1016\/j.neucom.2015.09.022","article-title":"Adaptive distributed formation control for multiple nonholonomic wheeled mobile robots","volume":"173","author":"Peng","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_15","first-page":"3162","article-title":"Formation control of nonholonomic mobile robots using distributed estimators","volume":"67","author":"Lu","year":"2020","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"ref_16","first-page":"125829","article-title":"Distributed formation control for multiple non-holonomic wheeled mobile robots with velocity constraint by using improved data-driven iterative learning","volume":"395","author":"Hou","year":"2021","journal-title":"Appl. Math. Comput."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1109\/JAS.2021.1004329","article-title":"Distributed Control of Nonholonomic Robots Without Global Position Measurements Subject to Unknown Slippage Constraints","volume":"9","author":"Zhang","year":"2021","journal-title":"IEEE\/CAA J. Autom. Sin."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1016\/j.neucom.2022.04.001","article-title":"Distributed Leader-Following Formation Control for Multiple Nonholonomic Mobile Robots via Bioinspired Neurodynamic Approach","volume":"492","author":"Moorthy","year":"2022","journal-title":"Neurocomputing"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Moorthy, S., Kuppusami Sakthivel, S.S., Joo, Y.H., and Jeong, J.H. (2025). Distributed Observer-Based Adaptive Trajectory Tracking and Formation Control for the Swarm of Nonholonomic Mobile Robots with Unknown Wheel Slippage. Mathematics, 13.","DOI":"10.3390\/math13101628"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.ins.2014.06.037","article-title":"Finite-time cascaded tracking control approach for mobile robots","volume":"284","author":"Zhang","year":"2014","journal-title":"Inf. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"107579","DOI":"10.1016\/j.compeleceng.2021.107579","article-title":"Cascaded continuous sliding mode control for tracked mobile robot via nonlinear disturbance observer","volume":"97","author":"Wang","year":"2022","journal-title":"Comput. Electr. Eng."},{"key":"ref_22","unstructured":"Khalil, H. (2002). Nonlinear Systems, Prentice Hall. Pearson Education."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Liu, W., Wang, X., and Liang, S. (2020, January 18\u201321). Trajectory tracking control for wheeled mobile robots based on a cascaded system control method. Proceedings of the IECON 2020 The 46th Annual Conference of the IEEE Industrial Electronics Society, Singapore.","DOI":"10.1109\/IECON43393.2020.9255003"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Lewis, F., Zhang, H., Hengster-Movric, K., and Das, A. (2014). Cooperative Control of Multi-Agent Systems: Optimal and Adaptive Design Approaches, Springer. Communications and Control Engineering.","DOI":"10.1007\/978-1-4471-5574-4"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1080\/00207170601148291","article-title":"Finite-time stability of cascaded time-varying systems","volume":"80","author":"Li","year":"2007","journal-title":"Int. J. Control"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1002\/asjc.773","article-title":"Finite-time tracking control for nonholonomic mobile robots based on visual servoing","volume":"16","author":"Ou","year":"2014","journal-title":"Asian J. Control."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2293","DOI":"10.1109\/TSMC.2018.2803147","article-title":"Pinning a complex network to follow a target system with predesigned control inputs","volume":"50","author":"Wen","year":"2018","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."}],"container-title":["Robotics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2218-6581\/14\/7\/88\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:59:03Z","timestamp":1760032743000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2218-6581\/14\/7\/88"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,26]]},"references-count":27,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2025,7]]}},"alternative-id":["robotics14070088"],"URL":"https:\/\/doi.org\/10.3390\/robotics14070088","relation":{},"ISSN":["2218-6581"],"issn-type":[{"value":"2218-6581","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,26]]}}}