{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:13:36Z","timestamp":1760228016862,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,5,7]],"date-time":"2022-05-07T00:00:00Z","timestamp":1651881600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Education and Training of Vietnam","award":["B2020-SKH-01"],"award-info":[{"award-number":["B2020-SKH-01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The paper focuses on faulty actuator problems in an industrial robot using servomotors, and provides an adaptive sliding mode control law to overcome this circumstance. Because of multifarious reasons, robot actuators can undergo a variety of failures, such as locked or stuck joints, free-swinging joints, and partial or total loss of actuation effectiveness. The robot behavior will become worsen if the system controller has not been designed with adequate faulty tolerance. The proportional degradation of actuator torque at unknown degrees of loss, which is one type of partial loss of actuation effectiveness, is considered in this study to design a suitable controller. The robot model is constructed with uncertain parameters and unknown friction, whereas the controller uses only the approximate parameters. Symmetry and skew-symmetry give important contributions in robot modeling and transformation, as well as in the process of proving the system stability. An adjustable coefficient vector of the proposed controller can adaptively reach the upper bounds of an uncertain parametric vector, which guarantees the criterion of Lyapunov stability. In the numerical simulation stage, the selected industrial robot is a Serpent 1 robot with three degrees of freedom. A quasi-physical model based on MATLAB\/Simscape Multibody for the robot is built and used in order to increase the reliability of the simulation performance closer to reality. Simulation results illustrate the efficiency of the proposal control methodology in the presence of the mentioned failure. The controller can still deliver satisfactory responses to the robot system under reasonable levels of actuator torque degradation.<\/jats:p>","DOI":"10.3390\/sym14050957","type":"journal-article","created":{"date-parts":[[2022,5,8]],"date-time":"2022-05-08T23:27:25Z","timestamp":1652052445000},"page":"957","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Adaptive Sliding Mode Control Anticipating Proportional Degradation of Actuator Torque in Uncertain Serial Industrial Robots"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8631-8252","authenticated-orcid":false,"given":"Le Ngoc","family":"Truc","sequence":"first","affiliation":[{"name":"Faculty of Automobile Engineering, Hung Yen University of Technology and Education, Hung Yen 17817, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3637-5536","authenticated-orcid":false,"given":"Le Anh","family":"Vu","sequence":"additional","affiliation":[{"name":"Faculty of Automobile Engineering, Hung Yen University of Technology and Education, Hung Yen 17817, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7720-9414","authenticated-orcid":false,"given":"Tran Van","family":"Thoan","sequence":"additional","affiliation":[{"name":"Faculty of Automobile Engineering, Hung Yen University of Technology and Education, Hung Yen 17817, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bui Trung","family":"Thanh","sequence":"additional","affiliation":[{"name":"Faculty of Automobile Engineering, Hung Yen University of Technology and Education, Hung Yen 17817, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4108-8275","authenticated-orcid":false,"given":"Tung Lam","family":"Nguyen","sequence":"additional","affiliation":[{"name":"School of Electrical and Electronic Engineering, Hanoi University of Science and Technology, Hanoi 11615, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bi, M. (2020). Control of Robot Arm Motion Using Trapezoid Fuzzy Two-Degree-of-Freedom PID Algorithm. Symmetry, 12.","DOI":"10.3390\/sym12040665"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Elawady, W.M., Bouteraa, Y., and Elmogy, A. (2020). An Adaptive Second Order Sliding Mode Inverse Kinematics Approach for Serial Kinematic Chain Robot Manipulators. Robotics, 9.","DOI":"10.3390\/robotics9010004"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Mourtzis, D., Angelopoulos, J., and Panopoulos, N. (2022). Closed-Loop Robotic Arm Manipulation Based on Mixed Reality. Appl. Sci., 12.","DOI":"10.3390\/app12062972"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1016\/j.ifacol.2016.03.084","article-title":"Training data selection criteria for detecting failures in industrial robots","volume":"49","author":"Sathish","year":"2016","journal-title":"IFAC-PapersOnLine"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/j.conengprac.2008.05.012","article-title":"Actuators fault diagnosis for robot manipulators with uncertain model","volume":"17","author":"Caccavale","year":"2009","journal-title":"Control Eng. Pract."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3167","DOI":"10.1109\/TIE.2011.2167110","article-title":"A PLS-based statistical approach for fault detection and isolation of robotic manipulators","volume":"59","author":"Muradore","year":"2012","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1028","DOI":"10.1109\/TRO.2005.851356","article-title":"Fault identification for robot manipulators","volume":"21","author":"McIntyre","year":"2005","journal-title":"IEEE Trans. Robot."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"De Luca, A., and Mattone, R. (2005, January 2\u20136). An identification scheme for robot actuator faults. Proceedings of the 2005 IEEE\/RSJ International Conference on Intelligent Robots and Systems, IROS, Edmonton, AB, Canada.","DOI":"10.1109\/IROS.2005.1545370"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1858","DOI":"10.1109\/TCST.2012.2212196","article-title":"Discrete-time framework for fault diagnosis in robotic manipulators","volume":"21","author":"Caccavale","year":"2013","journal-title":"IEEE Trans. Control. Syst. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zeng, Y., Xing, Y.R., Ma, H.J., and Yang, G.H. (2015, January 23\u201325). Adaptive fault diagnosis for robot manipulators with multiple actuator and sensor faults. Proceedings of the 27th Chinese Control and Decision Conference (CCDC), Qingdao, China.","DOI":"10.1109\/CCDC.2015.7162006"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Domski, W., and Mazur, A. (2017, January 28\u201331). Emergency control of a space 3R manipulator in case of one joint failure. Proceedings of the 22nd International Conference on Methods and Models in Automation and Robotics (MMAR), Miedzyzdroje, Poland.","DOI":"10.1109\/MMAR.2017.8046858"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1186\/s40638-016-0048-9","article-title":"Kinematic analysis and fault-tolerant trajectory planning of space manipulator under a single joint failure","volume":"3","author":"Mu","year":"2016","journal-title":"Robot. Biomimetics"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"114","DOI":"10.13189\/ujme.2020.080206","article-title":"Effect of Actuator Torque Degradation on Behavior of a 6-DOF Industrial Robot","volume":"8","author":"Truc","year":"2020","journal-title":"Univers. J. Mech. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4850","DOI":"10.11591\/ijece.v11i6.pp4850-4864","article-title":"Impact Analysis of Actuator Torque Degradation on the IRB 120 Robot Performance using Simscape-Based Model","volume":"11","author":"Truc","year":"2021","journal-title":"Int. J. Electr. Comput. Eng. (IJECE)"},{"key":"ref_15","unstructured":"Liu, G. (2001, January 21\u201326). Control of robot manipulators with consideration of actuator performance degradation and failures. Proceedings of the 2001 IEEE International Conference on Robotics & Automation, Seoul, Korea."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"964","DOI":"10.1016\/j.dt.2019.07.010","article-title":"Adaptive fault-tolerant control based on boundary estimation for space robot under joint actuator faults and uncertain parameters","volume":"15","author":"Lei","year":"2019","journal-title":"Def. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Jin, X. (2016, January 6\u20138). Adaptive finite-time tracking control for joint position constrained robot manipulators with actuator faults. Proceedings of the 2016 American Control Conference (ACC), Boston, MA, USA.","DOI":"10.1109\/ACC.2016.7526614"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Lopac, N., Bulic, N., and Vrkic, N. (2019). Sliding Mode Observer-Based Load Angle Estimation for Salient-Pole Wound Rotor Synchronous Generators. Energies, 12.","DOI":"10.3390\/en12091609"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Aljarbouh, A., Fayaz, M., Qureshi, M.S., and Boujoudar, Y. (2021). Hybrid Sliding Mode Control of Full-Car Semi-Active Suspension Systems. Symmetry, 13.","DOI":"10.3390\/sym13122442"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Vu, M.T., Le, T.H., Thanh, H.L.N.N., Huynh, T.T., Van, M., Hoang, Q.D., and Do, T.D. (2021). Robust Position Control of an Over-actuated Underwater Vehicle under Model Uncertainties and Ocean Current Effects Using Dynamic Sliding Mode Surface and Optimal Allocation Control. Sensors, 21.","DOI":"10.3390\/s21030747"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Nguyen, N., and Hong, S. (2019). Fault Diagnosis and Fault-Tolerant Control Scheme for Quadcopter UAVs with a Total Loss of Actuator. Energies, 12.","DOI":"10.3390\/en12061139"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Zheng, B., Wu, Y., Li, H., and Chen, Z. (2022). Adaptive Sliding Mode Attitude Control of Quadrotor UAVs Based on the Delta Operator Framework. Symmetry, 14.","DOI":"10.3390\/sym14030498"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2669","DOI":"10.1177\/1077546320964287","article-title":"Adaptive nonsingular proportional\u2013integral\u2013derivative-type terminal sliding mode tracker based on rapid reaching law for nonlinear systems","volume":"27","author":"Goel","year":"2021","journal-title":"J. Vib. Control"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Alattas, K.A., Mostafaee, J., Sambas, A., Alanazi, A.K., Mobayen, S., Vu, M.T., and Zhilenkov, A. (2021). Nonsingular Integral-Type Dynamic Finite-Time Synchronization for Hyper-Chaotic Systems. Mathematics, 10.","DOI":"10.3390\/math10010115"},{"key":"ref_25","unstructured":"Nasiri, M., Mobayen, S., Member, S., and Arzani, A. (2021). PID-type terminal sliding mode control for permanent magnet synchronous generator based enhanced wind energy conversion systems. CSEE J. Power Energy Syst., 1\u201310."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Shao, K., Zheng, J., Tang, R., Li, X., Man, Z., and Liang, B. (2022). Barrier Function Based Adaptive Sliding Mode Control for Uncertain Systems With Input Saturation. IEEE\/ASME Trans. Mechatronics, 1\u201311.","DOI":"10.1109\/TMECH.2022.3153670"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"8356","DOI":"10.1016\/j.jfranklin.2021.08.027","article-title":"Adaptive sliding mode control for uncertain Euler\u2013Lagrange systems with input saturation","volume":"358","author":"Shao","year":"2021","journal-title":"J. Frankl. Inst."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Sami, I., Ullah, S., Ali, Z., Ullah, N., and Ro, J.S. (2020). A Super Twisting Fractional Order Terminal Sliding Mode Control for DFIG-Based Wind Energy Conversion System. Energies, 13.","DOI":"10.3390\/en13092158"},{"key":"ref_29","unstructured":"Bing, X., and Yin, S. (2016, January 1\u20134). An fast reconstruction approach for actuator fault in robot manipulators. Proceedings of the 14th International Workshop on Variable Structure Systems (VSS), Nanjing, China."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"886","DOI":"10.1016\/j.ifacol.2018.09.680","article-title":"Fault Tolerant Control Scheme for Robotic Manipulators Affected by Torque Faults","volume":"51","author":"Freddi","year":"2018","journal-title":"IFAC-PapersOnLine"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1497","DOI":"10.1049\/iet-cta.2011.0508","article-title":"Actuator fault detection and adaptive accommodation control of flexible-joint robots","volume":"6","author":"Yoo","year":"2012","journal-title":"IET Control. Theory Appl."},{"key":"ref_32","unstructured":"Shin, J.H., and Lee, J.J. (1999, January 10\u201315). Fault detection and robust fault recovery control for robot manipulators with actuator failures. Proceedings of the 1999 IEEE International Conference on Robotics and Automation, Detroit, MI, USA."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1016\/j.actaastro.2015.12.012","article-title":"Fault-tolerant analysis and control of SSRMS-type manipulators with single-joint failure","volume":"120","author":"She","year":"2016","journal-title":"Acta Astronaut."},{"key":"ref_34","first-page":"13","article-title":"Robust adaptive fault tolerant control for a class of Lipschitz nonlinear systems with actuator failure and disturbances","volume":"230","author":"Azmi","year":"2015","journal-title":"Proc. Inst. Mech. Eng. Part I J. Syst. Control. Eng."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Mirkin, B., Gutman, P.O., and Shtessel, Y. (2010, January 26\u201328). Adaptive continuous control with sliding mode for plants under nonlinear perturbations, external disturbances and actuator failures. Proceedings of the 11th International Workshop on Variable Structure Systems, Mexico City, Mexico.","DOI":"10.1109\/VSS.2010.5544645"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1080\/23307706.2014.885292","article-title":"Direct adaptive actuator failure compensation control: A tutorial","volume":"1","author":"Tao","year":"2014","journal-title":"J. Control. Decis."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1109\/TIE.2016.2595481","article-title":"Robust Adaptive Fault-Tolerant Control for a Class of Unknown Nonlinear Systems","volume":"64","author":"Zhang","year":"2017","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2082","DOI":"10.1016\/j.automatica.2010.09.006","article-title":"Adaptive actuator failure compensation control of uncertain nonlinear systems with guaranteed transient performance","volume":"46","author":"Wang","year":"2010","journal-title":"Automatica"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.automatica.2015.07.006","article-title":"Adaptive actuator fault tolerant control for uncertain nonlinear systems with multiple actuators","volume":"60","author":"Yang","year":"2015","journal-title":"Automatica"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.automatica.2017.07.061","article-title":"Adaptive compensation for actuator failures with event-triggered input","volume":"85","author":"Xing","year":"2017","journal-title":"Automatica"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"89","DOI":"10.15625\/1813-9663\/36\/1\/14557","article-title":"Dynamic model with a new formulation of Coriolis\/centrifugal matrix for robot manipulators","volume":"36","author":"Truc","year":"2020","journal-title":"J. Comput. Sci. Cybern."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1949","DOI":"10.3906\/elk-1909-131","article-title":"Quasi-physical modeling of robot IRB 120 using Simscape Multibody for dynamic and control simulation","volume":"28","author":"Truc","year":"2020","journal-title":"Turk. J. Electr. Eng. Comput. Sci."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/5\/957\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:07:35Z","timestamp":1760137655000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/5\/957"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,7]]},"references-count":42,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["sym14050957"],"URL":"https:\/\/doi.org\/10.3390\/sym14050957","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,5,7]]}}}