{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,24]],"date-time":"2026-10-24T00:35:08Z","timestamp":1792802108807,"version":"4.5.0"},"reference-count":41,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T00:00:00Z","timestamp":1770768000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62373217"],"award-info":[{"award-number":["62373217"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biomimetics"],"abstract":"<jats:p>Legged robots inspired by animal locomotion require actuators with high power density, fast response, and robust force control, yet traditional valve-controlled hydraulic systems suffer from substantial energy losses and weak regeneration performance. Motivated by role allocation across gait phases in animal legs, where in-air positioning requires far less actuation effort than ground contact support and force modulation, this work proposes a novel gas\u2013oil hybrid servo actuator, denoted GOhsa, for quadruped knee joints. GOhsa utilizes pre-charged high-pressure gas to pressurize hydraulic oil, converting the conventional dual-chamber pressure servo control into a single-chamber configuration while preserving the original piston stroke. This architecture enables bidirectional position\u2013force control, enhances energy regeneration applicability, and improves operational efficiency. Theoretical modeling is conducted to analyze hydraulic stiffness and frequency-response characteristics, and a linearization-based force controller with dynamic compensation is developed to handle system nonlinearities. Experimental validation on a single-leg platform demonstrates significant energy-saving performance: under no-load conditions (simulating the swing phase), GOhsa achieves a maximum power reduction of 79.1%, with average reductions of 15.2% and 11.5% at inflation pressures of 3 MPa and 4 MPa, respectively. Under loaded conditions (simulating the stance phase), the maximum reduction reaches 28.0%, with average savings of 10.0% and 9.8%. Tracking accuracy is comparable to traditional actuators, with reduced maximum errors (13.7 mm\/16.5 mm at 3 MPa; 15.0 mm\/17.8 mm at 4 MPa) relative to the 16.6 mm and 18.1 mm errors of the conventional system, confirming improved motion stability under load. These results verify that GOhsa provides high control performance with markedly enhanced energy efficiency.<\/jats:p>","DOI":"10.3390\/biomimetics11020131","type":"journal-article","created":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T11:13:15Z","timestamp":1770808395000},"page":"131","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["An Energy-Efficient Gas\u2013Oil Hybrid Servo Actuator with Single-Chamber Pressure Control for Biomimetic Quadruped Knee Joints"],"prefix":"10.3390","volume":"11","author":[{"given":"Mingzhu","family":"Yao","sequence":"first","affiliation":[{"name":"School of Artificial Intelligence, Anhui University of Science & Technology, Hefei 231131, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zisen","family":"Hua","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Anhui University of Science & Technology, Hefei 231131, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Huimin","family":"Qian","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Anhui University of Science & Technology, Hefei 231131, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2017","DOI":"10.1016\/j.asej.2020.11.005","article-title":"Development of quadruped walking robots: A review","volume":"12","author":"Biswal","year":"2021","journal-title":"Ain Shams Eng. J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"105448","DOI":"10.1016\/j.mechmachtheory.2023.105448","article-title":"A study on quadruped mobile robots","volume":"190","author":"Taheri","year":"2023","journal-title":"Mech. Mach. Theory"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4857","DOI":"10.1007\/s12206-023-0838-2","article-title":"Energy efficiency onboard hydraulic power for quadruped robot based on high-low double pumps supply","volume":"37","author":"Hua","year":"2023","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Harper, M.Y., Nicholson, J.V., Collins, E.G., Pusey, J., and Clark, J.E. (2019, January 20\u201324). Energy efficient navigation for running legged robots. Proceedings of the 2019 International Conference on Robotics and Automation (ICRA), Montreal, QC, Canada.","DOI":"10.1109\/ICRA.2019.8793599"},{"key":"ref_5","first-page":"88","article-title":"What\u2019s the difference between pneumatic, hydraulic, and electrical actuators","volume":"87","author":"Gonzalez","year":"2015","journal-title":"Mach. Des."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"eaau5872","DOI":"10.1126\/scirobotics.aau5872","article-title":"Learning agile and dynamic motor skills for legged robots","volume":"4","author":"Hwangbo","year":"2019","journal-title":"Sci. Robot."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"She, J., Feng, X., Xu, B., Chen, L., Wang, Y., Liu, N., Zou, W., Ma, G., Yu, B., and Ba, K. (2025). Bionic Energy-Efficient Inverse Kinematics Method Based on Neural Networks for the Legs of Hydraulic Legged Robots. Biomimetics, 10.","DOI":"10.3390\/biomimetics10060403"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1109\/TMECH.2019.2893235","article-title":"Improving legged robot hopping by using coupling-based series elastic actuation","volume":"24","author":"Guenther","year":"2019","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3631","DOI":"10.1109\/LRA.2021.3061390","article-title":"Design of a compact embedded hydraulic power unit for bipedal robots","volume":"6","author":"Cho","year":"2021","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"86","DOI":"10.7746\/jkros.2021.16.2.086","article-title":"Energy efficient control of onboard hydraulic power unit for hydraulic bipedal robots","volume":"16","author":"Cho","year":"2021","journal-title":"J. Korea Robot. Soc."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1109\/TMECH.2022.3190506","article-title":"Energy-efficient hydraulic pump control for legged robots using model predictive control","volume":"28","author":"Cho","year":"2022","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"63538","DOI":"10.1109\/ACCESS.2021.3072986","article-title":"Planning and analysis of centroid fluctuation gait for hydraulic hexapod robot","volume":"9","author":"Dong","year":"2021","journal-title":"IEEE Access"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Zhuang, Y., Wang, Y., and Ding, Y. (2025, January 19\u201323). Kinodynamic Model Predictive Control for Energy-Efficient Locomotion of Legged Robots with Parallel Elasticity. Proceedings of the 2025 IEEE International Conference on Robotics and Automation (ICRA), Atlanta, GA, USA.","DOI":"10.1109\/ICRA55743.2025.11128416"},{"key":"ref_14","unstructured":"Tanfener, E. (2022). Design and Experimental Verification of a Clutched Parallel Elastic Actuation Mechanism for Legged Locomotion. [Master\u2019s Thesis, Middle East Technical University]."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Culha, U., and Saranli, U. (2011, January 9\u201313). Quadrupedal bounding with an actuated spinal joint. Proceedings of the 2011 IEEE International Conference on Robotics and Automation, Shanghai, China.","DOI":"10.1109\/ICRA.2011.5980176"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Chu, Z., Luo, J., and Fu, Y. (2016, January 7\u201310). Variable stiffness control and implementation of hydraulic sea based on virtual spring leg. Proceedings of the 2016 IEEE International Conference on Mechatronics and Automation, Harbin, China.","DOI":"10.1109\/ICMA.2016.7558644"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Zhou, S., Chen, G., Gong, M., Liu, J., Xu, P., Liu, B., and Yin, N. (2025). Bio-Inspired Compliant Joints and Economic MPC Co-Design for Energy-Efficient, High-Speed Locomotion in Snake-like Robots. Biomimetics, 10.","DOI":"10.3390\/biomimetics10060389"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Zhao, H., Zhou, J., Ma, S., Du, S., Liu, H., and Han, L. (2023). Design and experiments of electro-hydrostatic actuator for wheel-legged robot with fast force control response. Machines, 11.","DOI":"10.3390\/machines11070685"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"130417","DOI":"10.1016\/j.energy.2024.130417","article-title":"Research on the energy transfer and efficiency performance of an electro-hydrostatic actuator for a wheel\u2013legged robot joint","volume":"291","author":"Du","year":"2024","journal-title":"Energy"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"119041","DOI":"10.1016\/j.enconman.2024.119041","article-title":"Application and progress of high-efficiency electro-hydrostatic actuator technology with energy recovery: A comprehensive review","volume":"321","author":"Du","year":"2024","journal-title":"Energy Convers. Manag."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Fan, W., Liu, T., Yi, J., Huang, X., Zhang, B., Zhang, X., and Wang, S. (June, January 30). A passive hydraulic auxiliary system designed for increasing legged robot payload and efficiency. Proceedings of the 2021 IEEE International Conference on Robotics and Automation (ICRA), Xi\u2019an, China.","DOI":"10.1109\/ICRA48506.2021.9561581"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1445","DOI":"10.1080\/01691864.2014.946447","article-title":"Energy efficient fluid power in autonomous legged robotics based on bionic multi-stage energy supply","volume":"28","author":"Xue","year":"2014","journal-title":"Adv. Robot."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3459","DOI":"10.1177\/0954406215570106","article-title":"Design and optimization of a new kind of hydraulic cylinder for mobile robots","volume":"229","author":"Xue","year":"2015","journal-title":"Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Guglielmino, E., Semini, C., Yang, Y., Caldwell, D., Kogler, H., and Scheidl, R. (2009, January 12\u201314). Energy efficient fluid power in autonomous legged robotics. Proceedings of the Dynamic Systems and Control Conference, Hollywood, CA, USA.","DOI":"10.1115\/DSCC2009-2522"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"108571","DOI":"10.1016\/j.est.2023.108571","article-title":"Research on energy saving system of hydraulic excavator based on three-chamber accumulator","volume":"72","author":"Yang","year":"2023","journal-title":"J. Energy Storage"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"113196","DOI":"10.1016\/j.enconman.2020.113196","article-title":"Analysis of energy characteristic and working performance of novel controllable hydraulic accumulator with simulation and experimental methods","volume":"221","author":"Liu","year":"2020","journal-title":"Energy Convers. Manag."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"119620","DOI":"10.1016\/j.enconman.2025.119620","article-title":"Design of lightweight hydraulic power unit for legged robots based on the Sobol sensitivity analysis","volume":"328","author":"Yu","year":"2025","journal-title":"Energy Convers. Manag."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"133730","DOI":"10.1016\/j.energy.2024.133730","article-title":"Design and matching control strategy of electro-hydraulic load-sensitive hydraulic power unit for legged robots","volume":"313","author":"Yu","year":"2024","journal-title":"Energy"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"521","DOI":"10.4142\/jvs.2017.18.4.521","article-title":"Comparative kinematic gait analysis in young and old Beagle dogs","volume":"18","author":"Lorke","year":"2017","journal-title":"J. Vet. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1016\/j.isatra.2020.03.029","article-title":"High-precision motion servo control of double-rod electro-hydraulic actuators with exact tracking performance","volume":"103","author":"Yang","year":"2020","journal-title":"ISA Trans."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1016\/0005-1098(94)90209-7","article-title":"A Survey of Models, Analysis Tools and Compensation Methods for the Control of Machines with Friction","volume":"30","author":"Dupont","year":"1994","journal-title":"Automatica"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1016\/S0947-3580(98)70113-X","article-title":"Friction Models and Friction Compensation","volume":"4","author":"Olsson","year":"1998","journal-title":"Eur. J. Control"},{"key":"ref_33","unstructured":"Merritt, H.E. (1967). Hydraulic Control Systems, John Wiley & Sons."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Ruderman, M. (November, January 29). Full- and Reduced-Order Model of Hydraulic Cylinder for Motion Control. Proceedings of the 43rd Annual Conference of the IEEE Industrial Electronics Society (IECON 2017), Beijing, China.","DOI":"10.1109\/IECON.2017.8217274"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Boaventura, T., Semini, C., Buchli, J., Frigerio, M., Focchi, M., and Caldwell, D.G. (2012, January 14\u201318). Dynamic torque control of a hydraulic quadruped robot. Proceedings of the 2012 IEEE International Conference on Robotics and Automation, Saint Paul, MN, USA.","DOI":"10.1109\/ICRA.2012.6224628"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Levine, W.S. (2018). The Control Handbook (Three Volume Set), CRC Press. [3rd ed.].","DOI":"10.1201\/9781315218694"},{"key":"ref_37","first-page":"218","article-title":"Co-simulation of a quadruped robot\u2019s mechanical and hydraulic systems based on ADAMS and AMESim","volume":"25","author":"Han","year":"2016","journal-title":"J. Beijing Inst. Technol."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"17298814211062006","DOI":"10.1177\/17298814211062006","article-title":"Modeling and analysis on low energy consumption foot trajectory for hydraulic actuated quadruped robot","volume":"18","author":"Sun","year":"2021","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2313327","DOI":"10.1002\/adma.202313327","article-title":"Bio-Inspired Dynamically Morphing Microelectronics toward High-Density Energy Applications and Intelligent Biomedical Implants","volume":"36","author":"Merces","year":"2024","journal-title":"Adv. Mater."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"2305611","DOI":"10.1002\/advs.202305611","article-title":"Advanced Neuromorphic Applications Enabled by Synaptic Ion-Gating Vertical Transistors","volume":"11","author":"Merces","year":"2024","journal-title":"Adv. Sci."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"2121","DOI":"10.1038\/s41467-022-29802-7","article-title":"A New Dimension for Magnetosensitive E-Skins: Active Matrix Integrated Micro-Origami Sensor Arrays","volume":"13","author":"Becker","year":"2022","journal-title":"Nat. Commun."}],"container-title":["Biomimetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2313-7673\/11\/2\/131\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T11:57:46Z","timestamp":1770811066000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2313-7673\/11\/2\/131"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,11]]},"references-count":41,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,2]]}},"alternative-id":["biomimetics11020131"],"URL":"https:\/\/doi.org\/10.3390\/biomimetics11020131","relation":{},"ISSN":["2313-7673"],"issn-type":[{"value":"2313-7673","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,11]]}}}