{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,15]],"date-time":"2026-09-15T05:03:02Z","timestamp":1789448582946,"version":"build-2803163510"},"reference-count":29,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2026,9,15]],"date-time":"2026-09-15T00:00:00Z","timestamp":1789430400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Robot. AI"],"abstract":"<jats:p>Achieving both high-precision trajectory tracking and compliant physical interaction in collaborative robot joints equipped with 3K planetary gear reducers remains challenging under torque-sensorless conditions. This paper proposes a physics-informed data-driven joint dynamics modeling method and an associated meta-policy-optimized adaptive variable impedance control scheme to address this limitation. First, a hybrid dynamics model combining lumped rigid-body dynamics with a Multilayer Perceptron (MLP) for residual loss estimation is established. By incorporating power-flow direction features, the network identifies and predicts the time-varying transmission efficiency and nonlinear friction losses of the 3K reducer across motoring and generating quadrants. Second, a model-based feedforward torque compensation scheme is designed, and a variable-gain generalized momentum observer is developed to achieve stable estimation of external interaction torques. Building upon this, a force-responsive variable-stiffness impedance control law is formulated, and a proximal policy optimization (PPO) algorithm is employed within a contextual reinforcement learning architecture to search for optimal high-level meta-parameters, enabling adaptive adjustment of impedance parameters. Multi-condition dynamic interaction simulations demonstrate that the proposed hybrid modeling approach achieves a 40% improvement in joint torque prediction accuracy compared to the conventional momentum disturbance observer (MDOB) baseline. Furthermore, the adaptive variable stiffness control law actively adjusts the joint stiffness in response to estimated external forces, satisfying the dual requirements of high-precision tracking in free space and high compliance in contact space.<\/jats:p>","DOI":"10.3389\/frobt.2026.1923729","type":"journal-article","created":{"date-parts":[[2026,9,15]],"date-time":"2026-09-15T04:27:56Z","timestamp":1789446476000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Sensorless variable impedance control of robot joints with 3K gear reducers based on hybrid dynamics model and meta-policy optimization"],"prefix":"10.3389","volume":"13","author":[{"given":"Jiyu","family":"Sun","sequence":"first","affiliation":[{"name":"The School of Automation Science and Electrical Engineering, Beihang University","place":["Beijing, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoshan","family":"Gao","sequence":"additional","affiliation":[{"name":"The School of Automation Science and Electrical Engineering, Beihang University","place":["Beijing, China"]},{"name":"The Ningbo Institute of Technology, Beihang University","place":["Ningbo, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liang","family":"Yan","sequence":"additional","affiliation":[{"name":"The School of Automation Science and Electrical Engineering, Beihang University","place":["Beijing, China"]},{"name":"The Ningbo Institute of Technology, Beihang University","place":["Ningbo, China"]},{"name":"Tianmushan Laboratory","place":["Hangzhou, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1965","published-online":{"date-parts":[[2026,9,15]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"2666","DOI":"10.1109\/ROBOT.2004.1307463","article-title":"A passivity based cartesian impedance controller for flexible joint robots \u2013 part II: full state feedback, impedance design and experiments","volume":"3","author":"Albu-Sch\u00e4ffer","year":"2004","journal-title":"Proc. IEEE Int. Conf. Robot. Autom. (ICRA)"},{"key":"B2","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1177\/0278364907073776","article-title":"A unified passivity-based control framework for position, torque and impedance control of flexible joint robots","volume":"26","author":"Albu-Sch\u00e4ffer","year":"2007","journal-title":"Int. J. Robot. Res."},{"key":"B3","doi-asserted-by":"publisher","first-page":"4313","DOI":"10.1109\/LRA.2022.3150523","article-title":"Characterization of open-loop impedance control and efficiency in wearable robots","volume":"7","author":"Azocar","year":"2022","journal-title":"IEEE Robot. Autom. Lett."},{"key":"B4","doi-asserted-by":"publisher","first-page":"613","DOI":"10.1109\/TMECH.2015.2465849","article-title":"A review of algorithms for compliant control of stiff and fixed-compliance robots","volume":"21","author":"Calanca","year":"2016","journal-title":"IEEE Trans. Mechatron."},{"key":"B5","doi-asserted-by":"publisher","first-page":"3628","DOI":"10.1109\/LRA.2025.3543967","article-title":"Sensor-based adaptive robust torque control for flexible joints","volume":"10","author":"Dai","year":"2025","journal-title":"IEEE Robot. Autom. Lett."},{"key":"B6","doi-asserted-by":"publisher","first-page":"1623","DOI":"10.1109\/IROS.2006.282053","article-title":"Collision detection and safe reaction with the DLR-III lightweight manipulator arm","author":"De Luca","year":"2006","journal-title":"Proc. IEEE\/RSJ Int. Conf. Intell. Robots Syst. (IROS)"},{"key":"B7","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1177\/02783649211053650","article-title":"Enabling impedance-based physical human\u2013multi\u2013robot collaboration: experiments with four torque-controlled manipulators","volume":"41","author":"Dehio","year":"2022","journal-title":"Int. J. Robot. Res."},{"key":"B8","doi-asserted-by":"publisher","first-page":"105495","DOI":"10.1016\/j.mechmachtheory.2023.105495","article-title":"A 3k planetary gear train with a flexure-based anti-backlash carrier for collaborative robots","volume":"191","author":"Du","year":"2024","journal-title":"Mech. Mach. Theory"},{"key":"B9","doi-asserted-by":"publisher","first-page":"2065","DOI":"10.1007\/s10845-023-02137-w","article-title":"Collaborative robots in manufacturing and assembly systems: literature review and future research agenda","volume":"35","author":"Keshvarparast","year":"2024","journal-title":"J. Intell. Manuf."},{"key":"B10","doi-asserted-by":"publisher","first-page":"1508","DOI":"10.1109\/TRO.2019.2926496","article-title":"Model-free friction observers for flexible joint robots with torque measurements","volume":"35","author":"Kim","year":"2019","journal-title":"IEEE Trans. Robot."},{"key":"B11","doi-asserted-by":"publisher","first-page":"091004","DOI":"10.1115\/1.4050504","article-title":"A robust impedance controller for improved safety in human\u2013robot interaction","volume":"143","author":"Laubscher","year":"2021","journal-title":"ASME J. Dyn. Syst. Meas. Control"},{"key":"B12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/ICIEA65512.2025.11149202","article-title":"Accurate impedance control for robot joints with 3k gear reducers based on transmission efficiency","author":"Liu","year":"2025","journal-title":"Proc. IEEE 20th Conf. Ind. Electron. Appl. (ICIEA)"},{"key":"B13","doi-asserted-by":"publisher","first-page":"103","DOI":"10.3389\/frobt.2020.00103","article-title":"Compact gearboxes for modern robotics: a review","volume":"7","author":"Lopez Garcia","year":"2020","journal-title":"Front. Robot."},{"key":"B14","doi-asserted-by":"publisher","first-page":"2659","DOI":"10.1109\/ROBOT.2004.1307462","article-title":"A passivity based cartesian impedance controller for flexible joint robots \u2013 part I: torque feedback and gravity compensation","volume":"3","author":"Ott","year":"2004","journal-title":"Proc. IEEE Int. Conf. Robot. Autom. (ICRA)"},{"key":"B15","first-page":"1","article-title":"On the interaction force sensing accuracy of franka emika panda robot","volume-title":"IECON 2021 \u2013 47th Annual Conference of the IEEE Industrial Electronics Society","author":"Petrea","year":"2021"},{"key":"B16","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1016\/j.mechatronics.2014.02.009","article-title":"Modeling, observation, and control of hysteresis torsion in elastic robot joints","volume":"24","author":"Ruderman","year":"2014","journal-title":"Mechatronics"},{"key":"B17","doi-asserted-by":"publisher","first-page":"1178","DOI":"10.1109\/TASE.2017.2748386","article-title":"Collaborative assembly in hybrid manufacturing cells: an integrated framework for human\u2013robot interaction","volume":"15","author":"Sadrfaridpour","year":"2018","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"B18","volume-title":"Proximal Policy Optimization Algorithms","author":"Schulman","year":"2017"},{"key":"B19","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1016\/j.robot.2019.06.009","article-title":"An introductory review of active compliant control","volume":"119","author":"Schumacher","year":"2019","journal-title":"Robot. Auton. Syst."},{"key":"B20","doi-asserted-by":"publisher","first-page":"3789","DOI":"10.1109\/IROS.2008.4651049","article-title":"Friction observer and compensation for control of robots with joint torque measurement","author":"Tien","year":"2008","journal-title":"Proc. IEEE\/RSJ Int. Conf. Intell. Robots Syst. (IROS)"},{"key":"B21","doi-asserted-by":"publisher","first-page":"040802","DOI":"10.1115\/1.4046238","article-title":"Collaborative robotics: a survey","volume":"143","author":"Vicentini","year":"2020","journal-title":"J. Mech. Des."},{"key":"B22","doi-asserted-by":"publisher","first-page":"1890","DOI":"10.1109\/TMECH.2023.3272364","article-title":"Compliant control of flexible joint by dual-disturbance observer and predictive feedforward","volume":"28","author":"Wan","year":"2023","journal-title":"IEEE Trans. Mechatron."},{"key":"B23","doi-asserted-by":"publisher","first-page":"783","DOI":"10.1109\/ICRA.2018.8460613","article-title":"Extending a dynamic friction model with nonlinear viscous and thermal dependency for a motor and harmonic drive gear","author":"Wolf","year":"2018","journal-title":"Proc. IEEE Int. Conf. Robot. Autom. (ICRA)"},{"key":"B24","doi-asserted-by":"publisher","first-page":"4862","DOI":"10.1109\/ICRA46639.2022.9812458","article-title":"Dynamic modeling and digital twin of a harmonic drive based collaborative robot joint","author":"Yang","year":"2022","journal-title":"Proc. IEEE Int. Conf. Robot. Autom. (ICRA)"},{"key":"B25","doi-asserted-by":"publisher","first-page":"4909","DOI":"10.1109\/LRA.2022.3151401","article-title":"Whole-body fuzzy based impedance control of a humanoid wheeled robot","volume":"7","author":"Yang","year":"2022","journal-title":"IEEE Robot. Autom. Lett."},{"key":"B26","doi-asserted-by":"publisher","first-page":"538","DOI":"10.1109\/LRA.2019.2891434","article-title":"Interconnection and damping assignment passivity-based impedance control of a compliant assistive robot for physical human\u2013robot interactions","volume":"4","author":"Zhang","year":"2019","journal-title":"IEEE Robot. Autom. Lett."},{"key":"B27","doi-asserted-by":"publisher","first-page":"117380","DOI":"10.1016\/j.jsv.2022.117380","article-title":"Non-random vibration analysis of rotate vector reducer","volume":"542","author":"Zhang","year":"2023","journal-title":"J. Sound. Vib."},{"key":"B28","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/ICIEA61579.2024.10664908","article-title":"Sensorless impedance control of robot joints with 3k gear drives considering transmission efficiencies","author":"Zhang","year":"2024","journal-title":"Proc. IEEE 19th Conf. Ind. Electron. Appl. (ICIEA)"},{"key":"B29","doi-asserted-by":"publisher","first-page":"113653","DOI":"10.1109\/ACCESS.2021.3099692","article-title":"Fuzzy adaptive sliding mode impedance control of fracture reduction robot","volume":"9","author":"Zheng","year":"2021","journal-title":"IEEE Access"}],"container-title":["Frontiers in Robotics and AI"],"original-title":[],"link":[{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/frobt.2026.1923729\/full","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,15]],"date-time":"2026-09-15T04:27:57Z","timestamp":1789446477000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/frobt.2026.1923729\/full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,15]]},"references-count":29,"alternative-id":["10.3389\/frobt.2026.1923729"],"URL":"https:\/\/doi.org\/10.3389\/frobt.2026.1923729","relation":{},"ISSN":["2296-9144"],"issn-type":[{"value":"2296-9144","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,15]]},"article-number":"1923729"}}