{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T19:58:14Z","timestamp":1771703894841,"version":"3.50.1"},"reference-count":37,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2018,6,7]],"date-time":"2018-06-07T00:00:00Z","timestamp":1528329600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Foundation for Innovative Research Groups of the National Natural Science Foundation of China","award":["51521003"],"award-info":[{"award-number":["51521003"]}]},{"name":"the Major Research Plan of the National Natural Science Foundation of China","award":["61690210"],"award-info":[{"award-number":["61690210"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, a novel mechatronic design philosophy is introduced to develop a compact modular rotary elastic joint for a humanoid manipulator. The designed elastic joint is mainly composed of a brushless direct current (DC) motor, harmonic reducer, customized torsional spring, and fail-safe brake. The customized spring considerably reduces the volume of the elastic joint and facilitates the construction of a humanoid manipulator which employs this joint. The large central hole along the joint axis brings convenience for cabling and the fail-safe brake can guarantee safety when the power is off. In order to reduce the computational burden on the central controller and simplify system maintenance, an expandable electrical system, which has a double-layer control structure, is introduced. Furthermore, a robust position controller for the elastic joint is proposed and interpreted in detail. Vibration of the elastic joint is suppressed by means of resonance ratio control (RRC). In this method, the ratio between the resonant and anti-resonant frequency can be arbitrarily designated according to the feedback of the nominal spring torsion. Instead of using an expensive torque sensor, the spring torque can be obtained by calculating the product of spring stiffness and deformation, due to the high linearity of the customized spring. In addition, to improve the system robustness, a motor-side disturbance observer (DOb) and an arm-side DOb are employed to estimate and compensate for external disturbances and system uncertainties, such as model variation, friction, and unknown external load. Validity of the DOb-based RRC is demonstrated in the simulation results. Experimental results show the performance of the modular elastic joint and the viability of the proposed controller further.<\/jats:p>","DOI":"10.3390\/s18061869","type":"journal-article","created":{"date-parts":[[2018,6,8]],"date-time":"2018-06-08T03:13:18Z","timestamp":1528427598000},"page":"1869","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Design and Vibration Suppression Control of a Modular Elastic Joint"],"prefix":"10.3390","volume":"18","author":[{"given":"Hong","family":"Liu","sequence":"first","affiliation":[{"name":"State Key Laboratory of Robotics and System, Harbin Institute of Technology, West Dazhi Street, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shipeng","family":"Cui","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Robotics and System, Harbin Institute of Technology, West Dazhi Street, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yiwei","family":"Liu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Robotics and System, Harbin Institute of Technology, West Dazhi Street, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yi","family":"Ren","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Robotics and System, Harbin Institute of Technology, West Dazhi Street, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongjun","family":"Sun","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Robotics and System, Harbin Institute of Technology, West Dazhi Street, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,6,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"7767","DOI":"10.1016\/j.jfranklin.2017.09.015","article-title":"Adaptive hybrid position\/force control of dual-arm cooperative manipulators with uncertain dynamics and closed-chain kinematics","volume":"354","author":"Ren","year":"2017","journal-title":"J. Frankl. Inst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1115\/1.3140702","article-title":"Impedance control\u2014An approach to manipulation. I\u2014Theory. II\u2014Implementation. III\u2014Applications","volume":"107","author":"Hogan","year":"1985","journal-title":"J. Dyn. Syst. Meas. Control"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Ott, C., Mukherjee, R., and Nakamura, Y. (2010, January 3\u20137). Unified impedance and admittance control. Proceedings of the IEEE International Conference on Robotics and Automation, Anchorage, AK, USA.","DOI":"10.1109\/ROBOT.2010.5509861"},{"key":"ref_4","unstructured":"Pratt, G.A., and Williamson, M.M. (1995, January 5\u20139). Series elastic actuators. Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems, Pittsburgh, PA, USA."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1080","DOI":"10.1109\/TMECH.2013.2270435","article-title":"Design and Control Considerations for High-Performance Series Elastic Actuators","volume":"19","author":"Paine","year":"2014","journal-title":"IEEE\/ASME Transact. Mechatron."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Tsagarakis, N.G., Laffranchi, M., Vanderborght, B., and Caldwell, D.G. (2009, January 12\u201317). A compact soft actuator unit for small scale human friendly robots. Proceedings of the IEEE International Conference on Robotics and Automation, Kobe, Japan.","DOI":"10.1109\/ROBOT.2009.5152496"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Cummings, J.P., Ruiken, D., Wilkinson, E.L., Lanighan, M.W., Grupen, R.A., and Sup, F.C. (2016). A Compact, Modular Series Elastic Actuator. J. Mech. Robot., 8.","DOI":"10.1115\/1.4032975"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.robot.2016.01.013","article-title":"Level-ground walking for a bipedal robot with a torso via hip series elastic actuators and its gait bifurcation control","volume":"79","author":"Deng","year":"2016","journal-title":"Robot. Autonom. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Sergi, F., Lee, M.M., and Malley, M.K.O. (2013, January 24\u201326). Design of a series elastic actuator for a compliant parallel wrist rehabilitation robot. Proceedings of the 13th IEEE International Conference on Rehabilitation Robotics, Seattle, WA, USA.","DOI":"10.1109\/ICORR.2013.6650481"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Lagoda, C., Schouten, A.C., Stienen, A.H.A., Hekman, E.E.G., and van der Kooij, H. (2010, January 26\u201329). Design of an electric series elastic actuated joint for robotic gait rehabilitation training. Proceedings of the International Conference on Biomedical Robotics and Biomechatronics, Tokyo, Japan.","DOI":"10.1109\/BIOROB.2010.5626010"},{"key":"ref_11","unstructured":"Kong, K., Bae, J., and Tomizuka, M. (2010, January 3\u20137). A compact rotary series elastic actuator for knee joint assistive system. Proceedings of the IEEE International Conference on Robotics and Automation, Anchorage, AK, USA."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Tsagarakis, N.G., Sardellitti, I., and Caldwell, D.G. (2011, January 25\u201330). A new variable stiffness actuator (CompAct-VSA): Design and modelling. Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems, San Francisco, CA, USA.","DOI":"10.1109\/IROS.2011.6095006"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Cui, S., Liu, Y., Sun, Y., and Liu, H. (2017, January 16\u201318). Design of a Series Variable Stiffness Joint Based on Antagonistic Principle. Proceedings of the International Conference on Intelligent Robotics and Applications, Wuhan, China.","DOI":"10.1007\/978-3-319-65292-4_21"},{"key":"ref_14","unstructured":"Robinson, D.W. (2000). Design and Analysis of Series Elasticity in Closed-Loop Actuator Force Control. [Ph.D. Thesis, Massachusetts Institute of Technology]."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1109\/MRA.2008.927689","article-title":"Compliant Actuation of Rehabilitation Robots\u2014Benefits and Limitations of Series Elastic Actuators","volume":"15","author":"Vallery","year":"2008","journal-title":"IEEE Robot. Autom. Mag."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1208","DOI":"10.1109\/9.90238","article-title":"A simple PD controller for robots with elastic joints","volume":"36","author":"Tomei","year":"1991","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1508","DOI":"10.1109\/TRO.2015.2477957","article-title":"Disturbance-Observer-Based PD Control of Flexible Joint Robots for Asymptotic Convergence","volume":"31","author":"Kim","year":"2015","journal-title":"IEEE Trans. Robot."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1706","DOI":"10.1109\/TIE.2016.2588461","article-title":"Model-Free Robust Adaptive Control of Humanoid Robots With Flexible Joints","volume":"64","author":"Jin","year":"2017","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Palli, G., Melchiorri, C., and Luca, A.D. (2008, January 19\u201323). On the feedback linearization of robots with variable joint stiffness. Proceedings of the IEEE International Conference on Robotics and Automation, Pasadena, CA, USA.","DOI":"10.1109\/ROBOT.2008.4543454"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Petit, F., and Albu-Sch\u00e4ffer, A. (2011, January 9\u201313). State feedback damping control for a multi DOF variable stiffness robot arm. Proceedings of the 2011 IEEE International Conference on Robotics and Automation, Shanghai, China.","DOI":"10.1109\/ICRA.2011.5980207"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Miyazaki, F., Kawamura, S., Matsumori, M., and Arimoto, S. (1986, January 10\u201312). Learning control scheme for a class of robot systems with elasticity. Proceedings of the 25th IEEE Conference on Decision and Control, Athens, Greece.","DOI":"10.1109\/CDC.1986.267157"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1109\/TRO.2013.2244787","article-title":"Gain Scheduling Control for a Class of Variable Stiffness Actuators Based on Lever Mechanisms","volume":"29","author":"Sardellitti","year":"2013","journal-title":"IEEE Trans. Robot."},{"key":"ref_23","unstructured":"Petit, F., Ott, C., and Albu-Sch\u00e4ffer, A. (June, January 31). A model-free approach to vibration suppression for intrinsically elastic robots. Proceedings of the IEEE International Conference on Robotics and Automation, Hong Kong, China."},{"key":"ref_24","first-page":"139","article-title":"Residual Vibration Suppression of a Flexible Joint System Using a Systematic Command Shaping Technique","volume":"31","author":"Kapucu","year":"2006","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3197","DOI":"10.1109\/TIE.2009.2038398","article-title":"Robust Tracking and Vibration Suppression for a Two-Inertia System by Combining Backstepping Approach With Disturbance Observer","volume":"57","author":"Bang","year":"2010","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2947","DOI":"10.21595\/jve.2016.16725","article-title":"A review of command shaping techniques for elimination of residual vibrations in flexible-joint manipulators","volume":"18","author":"Conker","year":"2016","journal-title":"J. Vibroeng."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Dang, J., Ni, F., Gu, Y., Jin, M., and Liu, H. (2009, January 19\u201323). A highly integrated and flexible joint test system based on DSP\/FPGA-FPGA. Proceedings of the IEEE International Conference on Robotics and Biomimetics, Guilin, China.","DOI":"10.1109\/ROBIO.2009.5420551"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"612","DOI":"10.1016\/j.mechmachtheory.2006.04.013","article-title":"The modular multisensory DLR-HIT-Hand","volume":"42","author":"Liu","year":"2007","journal-title":"Mech. Mach. Theory"},{"key":"ref_29","unstructured":"Yoon, S.-S., Kang, S., Kim, S.-J., Kim, Y.-H., Kim, M., and Lee, C.-W. (2003, January 27\u201331). Safe arm with MR-based passive compliant joints and visco-elastic covering for service robot applications. Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems, Las Vegas, NV, USA."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1115\/1.4007695","article-title":"A Novel Compact Torsional Spring for Series Elastic Actuators for Assistive Wearable Robots","volume":"134","author":"Carpino","year":"2012","journal-title":"J. Mech. Des."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/j.conengprac.2015.09.008","article-title":"Design and control of an active knee orthosis driven by a rotary Series Elastic Actuator","volume":"58","author":"Caurin","year":"2017","journal-title":"Control Eng. Pract."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1007\/s00422-004-0484-4","article-title":"A model of force and impedance in human arm movements","volume":"90","author":"Tee","year":"2004","journal-title":"Biol. Cybern."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Wolf, S., Eiberger, O., and Hirzinger, G. (2011, January 9\u201313). The DLR FSJ: Energy based design of a variable stiffness joint. Proceedings of the IEEE International Conference on Robotics and Automation, Shanghai, China.","DOI":"10.1109\/ICRA.2011.5980303"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Sariyildiz, E., Yu, H., Yu, K., and Ohnishi, K. (2015, January 6\u20138). A nonlinear stability analysis for the robust position control problem of robot manipulators via disturbance observer. Proceedings of the IEEE International Conference on Mechatronics (ICM), Nagoya, Japan.","DOI":"10.1109\/ICMECH.2015.7083943"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1900","DOI":"10.1109\/TIE.2015.2512228","article-title":"An Acceleration-Based Robust Motion Controller Design for a Novel Series Elastic Actuator","volume":"63","author":"Sariyildiz","year":"2016","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1109\/TIE.2014.2327009","article-title":"Stability and Robustness of Disturbance-Observer-Based Motion Control Systems","volume":"62","author":"Sariyildiz","year":"2015","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_37","unstructured":"Yuki, K., Murakami, T., and Ohnishi, K. (1993, January 15\u201319). Vibration control of 2 mass resonant system by resonance ratio control. Proceedings of the International Conference on Industrial Electronics, Maui, HI, USA."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/6\/1869\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:07:45Z","timestamp":1760195265000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/6\/1869"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,7]]},"references-count":37,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2018,6]]}},"alternative-id":["s18061869"],"URL":"https:\/\/doi.org\/10.3390\/s18061869","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,6,7]]}}}