{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T06:10:53Z","timestamp":1772777453484,"version":"3.50.1"},"reference-count":41,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T00:00:00Z","timestamp":1772409600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Shandong Province Key R&amp;D Program (Competitive Innovation Platform) Project","award":["2024CXPT001"],"award-info":[{"award-number":["2024CXPT001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This study introduces a novel robust finite-time adaptive sliding mode control (FTSMC) strategy, emphasizing its contributions to the synchronized deployment of hydraulically actuated multi-arm systems in confined environments, such as coal bunker cleaning. Key innovations include the integration of adaptive sliding mode control with guaranteed finite-time convergence, a distributed leader\u2013follower framework, and a graph-theoretical communication topology for localized interactions. Specifically, we developed a dynamic model for a multi-agent system comprising one leader and multiple followers, incorporating nonlinear dynamics and unknown external disturbances. The proposed controller ensures rapid finite-time convergence of tracking errors while maintaining robustness against parameter uncertainties, frictional forces, and external perturbations. The theoretical analysis, based on Lyapunov stability, rigorously proves the boundedness and convergence of all system states. Simulation results on a three-arm robotic platform validate the method\u2019s superiority, demonstrating higher tracking accuracy, faster convergence, and stronger disturbance rejection compared with baseline controllers, including SMC, ETASMC, PID, Fixed-Time Consensus Control (FTCC), Disturbance Observer-Based Control (DOBC), and Adaptive Sliding Mode Control (ASMC). This research provides a practical and scalable solution for multi-arm coordination in unstructured environments, significantly advancing the autonomy and reliability of industrial robotic systems.<\/jats:p>","DOI":"10.3390\/s26051567","type":"journal-article","created":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T14:55:01Z","timestamp":1772463301000},"page":"1567","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Adaptive Sliding Mode with Finite-Time Convergence for Synchronized Hydraulic Multi-Arm Systems"],"prefix":"10.3390","volume":"26","author":[{"given":"Bo","family":"Gao","sequence":"first","affiliation":[{"name":"Robot Research Center, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fuqiang","family":"Yang","sequence":"additional","affiliation":[{"name":"Robot Research Center, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guangwei","family":"Ji","sequence":"additional","affiliation":[{"name":"Robot Research Center, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guanghai","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Electrical and Electronic Engineering, Changchun University of Technology, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuliang","family":"Lin","sequence":"additional","affiliation":[{"name":"Robot Research Center, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liangsong","family":"Huang","sequence":"additional","affiliation":[{"name":"Robot Research Center, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1605","DOI":"10.1109\/TCYB.2018.2805167","article-title":"Adaptive Sliding Mode Consensus Tracking for Second-Order Nonlinear Multiagent Systems With Actuator Faults","volume":"49","author":"Qin","year":"2019","journal-title":"IEEE Trans. Cybern."},{"key":"ref_2","first-page":"104535","article-title":"Advanced control strategies for hydraulic manipulators in industrial applications","volume":"126","author":"Zhao","year":"2023","journal-title":"Control Eng. Pract."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/s10846-021-01360-y","article-title":"Kinematic Cooperative Optimization Control Algorithm for Underground Heavy-Load Robot","volume":"102","author":"Fang","year":"2021","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_4","first-page":"121013","article-title":"Fault-tolerant control for multi-arm hydraulic systems in dynamic environments","volume":"144","author":"Zhang","year":"2022","journal-title":"J. Dyn. Syst. Meas. Control"},{"key":"ref_5","first-page":"503","article-title":"Optimal control design for hydraulic multi-arm robots","volume":"35","author":"Hu","year":"2021","journal-title":"Adv. Robot."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1137\/S0363012997321358","article-title":"Finite-time stability of continuous autonomous systems","volume":"38","author":"Bhat","year":"2000","journal-title":"SIAM J. Control Optim."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1016\/j.matcom.2021.12.017","article-title":"Disturbance observer-based sliding mode control for consensus tracking","volume":"194","author":"Derakhshannia","year":"2022","journal-title":"Math. Comput. Simul."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1595","DOI":"10.1007\/s11424-025-4355-5","article-title":"Observer-Based Prescribed-Time Leader-Follower Consensus for MAS under Directed Topologies","volume":"38","author":"Cheng","year":"2025","journal-title":"J. Syst. Sci. Complex."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Hua, L.-G., Ali, A., Ullah, S., Hafeez, G., Zaidi, M.M., and Jun, L. (2023). Robust finite-time integral terminal sliding mode control design for maximum power extraction of standalone wind energy system based on permanent magnet synchronous generator. Front. Energy Res., 11.","DOI":"10.3389\/fenrg.2023.1293267"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1007\/s11370-025-00590-5","article-title":"Finite-time sliding mode control strategy for two-way teleoperation systems with uncertain inputs","volume":"18","author":"Dao","year":"2025","journal-title":"Intell. Serv. Robot."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/j.automatica.2016.01.004","article-title":"Fully distributed flocking with a moving leader for Lagrange networks with parametric uncertainties","volume":"63","author":"Ghapani","year":"2016","journal-title":"Automatica"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"7167","DOI":"10.1007\/s00034-023-02464-6","article-title":"Finite-time and fixed-time consensus tracking of multiple Euler\u2013Lagrange systems via hierarchical control approach","volume":"42","author":"Pan","year":"2023","journal-title":"Circuits Syst. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1016\/j.jfranklin.2022.11.043","article-title":"Finite-time event-triggered containment control of multiple Euler\u2013Lagrange systems with unknown control coefficients","volume":"360","author":"Zhang","year":"2023","journal-title":"J. Frankl. Inst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4140","DOI":"10.1109\/TAC.2018.2798805","article-title":"Affine Formation Maneuver Control of Multiagent Systems","volume":"63","author":"Zhao","year":"2018","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_15","first-page":"101160","article-title":"A robust distributed model predictive control strategy for Leader\u2013Follower formation control of multiple perturbed wheeled mobile robotics","volume":"75","author":"Nguyen","year":"2024","journal-title":"Eur. J. Control"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Li, M., Liu, H., Xie, F., and Huang, H. (2024). Adaptive distributed control for leader\u2013follower formation based on a recurrent SAC algorithm. Electronics, 13.","DOI":"10.3390\/electronics13173513"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2993","DOI":"10.1007\/s12555-021-0393-5","article-title":"Finite-time consensus of networked Euler\u2013Lagrange systems via STA-based Output Feedback","volume":"20","author":"Li","year":"2022","journal-title":"Int. J. Control Autom. Syst."},{"key":"ref_18","first-page":"2123","article-title":"Formation control and tracking of mobile robots using distributed estimators and a biologically inspired approach","volume":"17","author":"Moorthy","year":"2022","journal-title":"J. Electr. Eng. Technol."},{"key":"ref_19","first-page":"450","article-title":"Leader-follower formation control with prescribed performance guarantees","volume":"8","author":"Chen","year":"2021","journal-title":"IEEE Trans."},{"key":"ref_20","first-page":"1529","article-title":"Distributed finite-time attitude consensus control for multiple rigid bodies","volume":"46","author":"Xu","year":"2010","journal-title":"Automatica"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2188","DOI":"10.1109\/TNNLS.2018.2878463","article-title":"Adaptive leader-following consensus for multiple Euler\u2013Lagrange systems with an uncertain leader system","volume":"30","author":"Wang","year":"2019","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Wu, X., Wu, R., Zhang, Y., and Peng, J. (2023). Distributed formation control of multi-robot systems with path navigation via complex Laplacian. Entropy, 25.","DOI":"10.3390\/e25111536"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2170","DOI":"10.1007\/s12555-019-0817-7","article-title":"Sliding mode control for robust consensus of general linear multi-agent systems with disturbance","volume":"18","author":"Zhao","year":"2020","journal-title":"Int. J. Control Autom. Syst."},{"key":"ref_24","unstructured":"Everett, M., Chen, Y.F., Liu, M., and How, J.P. (2017). Decentralized non-communicating multiagent collision avoidance with deep reinforcement learning. Proceedings of the 2017 IEEE International Conference on Robotics and Automation (ICRA), Singapore, 29 May\u20133 June 2017, IEEE."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Wei, H., Lv, Q., Duo, N., Wang, G., and Liang, B. (2019). Consensus algorithms based multi-robot formation control under noise and time delay conditions. Appl. Sci., 9.","DOI":"10.3390\/app9051004"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1721","DOI":"10.1177\/10775463231170032","article-title":"H\u221e performance tracking and group consensus of delayed multiagent systems under attack","volume":"30","author":"Nasir","year":"2023","journal-title":"J. Vib. Control."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"7567","DOI":"10.1109\/LRA.2023.3316889","article-title":"Combined leaderless control of translational, shape-preserving and affine multirobot formations","volume":"8","author":"Aranda","year":"2023","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1109\/TCST.2022.3211130","article-title":"Distributed nonlinear trajectory optimization for multi-robot motion planning","volume":"31","author":"Ferranti","year":"2022","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1109\/TSMC.2018.2884491","article-title":"Robust H\u221e. sliding mode controller design of a class of time-delayed discrete conic-type nonlinear systems","volume":"51","author":"He","year":"2018","journal-title":"IEEE Trans. Syst. Man. Cybern. Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"4153","DOI":"10.1109\/TMECH.2022.3148541","article-title":"Periodic event-triggered terminal sliding mode speed control for networked PMSM system: A GA-optimized extended state observer approach","volume":"27","author":"Song","year":"2022","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1007\/s10846-022-01759-1","article-title":"A Fast and Robust Solution for Common Knowledge Formation in Decentralized Swarm Robots","volume":"106","author":"Luo","year":"2022","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2460440","DOI":"10.1080\/21642583.2025.2460440","article-title":"Higher-Order Sliding Mode Observer and Fractional-Order Sliding Mode Control for Precise Wildfire Tracking in Heterogeneous Multi-Agent Systems","volume":"13","author":"Alsinaia","year":"2025","journal-title":"Syst. Sci. Control. Eng."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1109\/TAC.1977.1101446","article-title":"Variable Structure Systems with Sliding Modes","volume":"22","author":"Utkin","year":"1977","journal-title":"IEEE Trans. Automat. Contr."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2818","DOI":"10.1109\/TFUZZ.2018.2802458","article-title":"Observer-Based Fuzzy Integral Sliding Mode Control for Nonlinear Descriptor Systems","volume":"26","author":"Li","year":"2018","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1109\/TCST.2005.847331","article-title":"PID Control System Analysis, Design, and Technology","volume":"13","author":"Ang","year":"2005","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.cja.2021.04.022","article-title":"A review on fault-tolerant cooperative control of multiple unmanned aerial vehicles","volume":"35","author":"Yu","year":"2022","journal-title":"Chin. J. Aeronaut."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"3628","DOI":"10.1109\/TIE.2016.2522386","article-title":"A New Adaptive Sliding-Mode Control Scheme for Application to Robot Manipulators","volume":"63","author":"Baek","year":"2016","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1109\/TIE.2015.2478397","article-title":"Disturbance-Observer-Based Control and Related Methods\u2014An Overview","volume":"63","author":"Chen","year":"2016","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2106","DOI":"10.1109\/TAC.2011.2179869","article-title":"Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems","volume":"57","author":"Polyakov","year":"2012","journal-title":"IEEE Trans. Automat. Contr."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1049\/iet-cta.2014.0202","article-title":"Non-singular fixed-time terminal sliding mode control of non-linear systems","volume":"9","author":"Zuo","year":"2014","journal-title":"IET Control Theory Appl."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"17473","DOI":"10.1038\/s41598-022-21704-4","article-title":"Event-triggered adaptive sliding mode control for consensus of multiagent systems with unknown disturbances","volume":"12","author":"Chen","year":"2022","journal-title":"Sci. Rep."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/5\/1567\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T05:10:55Z","timestamp":1772773855000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/5\/1567"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,2]]},"references-count":41,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2026,3]]}},"alternative-id":["s26051567"],"URL":"https:\/\/doi.org\/10.3390\/s26051567","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,2]]}}}