{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T04:03:46Z","timestamp":1775707426333,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2021,7,19]],"date-time":"2021-07-19T00:00:00Z","timestamp":1626652800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Educational Science Planning in Guangdong Province Projects","award":["2018GXJK138"],"award-info":[{"award-number":["2018GXJK138"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>As an important part of the quadruped robot, the leg determines its performance. Flexible legs or flexible joints aid in the buffering and adaptability of robots. At present, most flexible quadruped robots only have two-dimensional flexibility or use complex parallel structures to achieve three-dimensional flexibility. This research will propose a new type of three-dimensional flexible structure. This passive compliant three-dimensional flexibility reduces the weight and complex structure of the robot. The anti-impact performance of the robot is verified by a side impact experiment. The simulation and experiments show that the robot still has good stability even under a simple algorithm and that the flexible leg can reduce the impact on the quadruped robot and improve the environmental adaptability of the robot.<\/jats:p>","DOI":"10.3390\/s21144907","type":"journal-article","created":{"date-parts":[[2021,7,19]],"date-time":"2021-07-19T21:39:15Z","timestamp":1626730755000},"page":"4907","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["A Quadruped Robot with Three-Dimensional Flexible Legs"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3111-7511","authenticated-orcid":false,"given":"Wenkai","family":"Huang","sequence":"first","affiliation":[{"name":"School of Mechanical & Electrical Engineering, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3854-8760","authenticated-orcid":false,"given":"Junlong","family":"Xiao","sequence":"additional","affiliation":[{"name":"School of Mechanical & Electrical Engineering, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Feilong","family":"Zeng","sequence":"additional","affiliation":[{"name":"School of Mechanical & Electrical Engineering, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Puwei","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Mechanical & Electrical Engineering, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guojian","family":"Lin","sequence":"additional","affiliation":[{"name":"School of Mechanical & Electrical Engineering, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Mechanical & Electrical Engineering, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3840-9536","authenticated-orcid":false,"given":"Xuyu","family":"Lin","sequence":"additional","affiliation":[{"name":"School of Mechanical & Electrical Engineering, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1804-0495","authenticated-orcid":false,"given":"Yu","family":"Wu","sequence":"additional","affiliation":[{"name":"Laboratory Center, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3138","DOI":"10.1109\/TIE.2019.2912781","article-title":"Force Sensorless Admittance Control with Neural Learning for Robots with Actuator Saturation","volume":"67","author":"Peng","year":"2020","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"10822","DOI":"10.3182\/20080706-5-KR-1001.01833","article-title":"Bigdog the rough-terrain quadruped robot","volume":"41","author":"Raibert","year":"2008","journal-title":"IFAC Proc. Vol."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Koolen, T., Bertrand, S., Thomas, G., de Boer, T., Wu, T., Smith, J., Englsberger, J., and Pratt, J. (2016). Design of a Momentum-Based Control Framework and Application to the Humanoid Robot Atlas. Int. J. Hum. Robot., 13.","DOI":"10.1142\/S0219843616500079"},{"key":"ref_4","unstructured":"Kanazawa, M., Nozawa, S., Kakiuchi, Y., Kanemoto, Y., Kuroda, M., Okada, K., Inaba, M., and Yoshiike, T. (October, January 28). Robust Vertical Ladder Climbing and Transitioning between Ladder and Catwalk for Humanoid Robots. Proceedings of the IEEE International Conference on Intelligent Robots and Systems, Hamburg, Germany."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Kaneko, K., Kanehiro, F., Morisawa, M., Akachi, K., Miyamori, G., Hayashi, A., and Kanehira, N. (2011, January 25\u201330). Humanoid Robot HRP-4-Humanoid Robotics Platform with Lightweight and Slim Body. Proceedings of the IEEE International Conference on Intelligent Robots and Systems, San Francisco, CA, USA.","DOI":"10.1109\/IROS.2011.6094465"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"17866","DOI":"10.1109\/ACCESS.2021.3053492","article-title":"Design, Construction, and Rough-Terrain Locomotion Control of Novel Hexapod Walking Robot with Four Degrees of Freedom Per Leg","volume":"9","author":"Cizek","year":"2021","journal-title":"IEEE Access"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1007\/s11370-020-00340-9","article-title":"A hybrid tactile sensor-based obstacle overcoming method for hexapod walking robots","volume":"14","author":"Luneckas","year":"2020","journal-title":"Intell. Serv. Robot."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Zhong, Y., Wang, R., Feng, H., and Chen, Y. (2019). Analysis and research of quadruped robot\u2019s legs: A comprehensive review. Int. J. Adv. Robot. Syst., 16.","DOI":"10.1177\/1729881419844148"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.mechatronics.2018.03.010","article-title":"Onboard hydraulic system controller design for quadruped robot driven by gasoline engine","volume":"52","author":"Yang","year":"2018","journal-title":"Mechatronics"},{"key":"ref_10","first-page":"831","article-title":"Design of HyQ\u2014A hydraulically and electrically actuated quadruped robot","volume":"225","author":"Semini","year":"2011","journal-title":"Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1109\/TMECH.2016.2616284","article-title":"Design of the Hydraulically Actuated, Torque-Controlled Quadruped Robot HyQ2Max","volume":"22","author":"Semini","year":"2017","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Wasista, S., Tjandrasa, H., and Wibisono, W. (2020, January 17\u201318). Swing Trajectory Model for the New Design of Quadruped Robot Using V-REP Simulator. Proceedings of the 2020 International Conference on Computer Engineering, Network, and Intelligent Multimedia (CENIM), Online.","DOI":"10.1109\/CENIM51130.2020.9297912"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1109\/TMECH.2012.2235078","article-title":"A Pneumatically Actuated Quadrupedal Walking Robot","volume":"19","author":"Wait","year":"2014","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Li, M., Wang, X., Guo, W., Wang, P., and Sun, L. (2014). System Design of a Cheetah Robot Toward Ultra-high Speed. Int. J. Adv. Robot. Syst., 11.","DOI":"10.5772\/58563"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Lei, J., Zhu, J., Xie, P., and Tokhi, M.O. (2017). Joint variable stiffness of musculoskeletal leg mechanism for quadruped robot. Adv. Mech. Eng., 9.","DOI":"10.1177\/1687814017690342"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1427","DOI":"10.1109\/TRO.2014.2360493","article-title":"Toward Combining Speed, Efficiency, Versatility, and Robustness in an Autonomous Quadruped","volume":"30","author":"Hutter","year":"2014","journal-title":"IEEE Trans. Robot."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Hutter, M., Gehring, C., Jud, D., Lauber, A., Bellicoso, C.D., Tsounis, V., Hwangbo, J., Bodie, K., Fankhauser, P., and Bloesch, M. (2016, January 9\u201314). Anymal\u2014A highly mobile and dynamic quadrupedal robot. Proceedings of the 2016 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Daejeon, Korea.","DOI":"10.1109\/IROS.2016.7758092"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Gor, M.M., Pathak, P.M., Samantaray, A.K., Alam, K., Kumar, P., Anand, D., Vijay, P., Sarkar, R., Yang, J.M., and Kwak, S.W. (2018). Development of a compliant legged quadruped robot. S\u0101dhan\u0101, 43.","DOI":"10.1007\/s12046-018-0918-7"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1016\/S1672-6529(16)60436-5","article-title":"Effect of Flexible Spine Motion on Energy Efficiency in Quadruped Running","volume":"14","author":"Chen","year":"2017","journal-title":"J. Bionic Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"6683584","DOI":"10.1155\/2021\/6683584","article-title":"Active Disturbance Rejection Control Design Using the Optimization Algorithm for a Hydraulic Quadruped Robot","volume":"2021","author":"Fan","year":"2021","journal-title":"Comput. Intell. Neurosci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/s10514-008-9099-2","article-title":"Self-organized adaptive legged locomotion in a compliant quadruped robot","volume":"25","author":"Buchli","year":"2008","journal-title":"Auton. Robots"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"208240","DOI":"10.1109\/ACCESS.2020.3037250","article-title":"Proximal Actuation of an Elastically Loaded Scissors Mechanism for the Leg Design of a Quadruped Robot","volume":"8","author":"Nizami","year":"2020","journal-title":"IEEE Access"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Geva, Y., and Shapiro, A. (2014). A Novel Design of a Quadruped Robot for Research Purposes. Int. J. Adv. Robot. Syst., 11.","DOI":"10.5772\/57351"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1007\/s10514-008-9096-5","article-title":"Design and control of a planar bipedal robot ERNIE with parallel knee compliance","volume":"25","author":"Yang","year":"2008","journal-title":"Auton. Robots"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Chai, H., Rong, X., Tang, X., and Li, Y. (2017). Gait-Based Quadruped Robot Planar Hopping Control with Energy Planning. Int. J. Adv. Robot. Syst., 13.","DOI":"10.5772\/62140"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1007\/s10846-018-0777-9","article-title":"Hybrid Compliance Control for Locomotion of Electrically Actuated Quadruped Robot","volume":"94","author":"Koco","year":"2018","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2382","DOI":"10.1109\/TSMC.2019.2912900","article-title":"Boundary Disturbance Observer-Based Control of a Vibrating Single-Link Flexible Manipulator","volume":"51","author":"Zhao","year":"2021","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1109\/JAS.2020.1003378","article-title":"Finite-time convergence disturbance rejection control for a flexible Timoshenko manipulator","volume":"8","author":"Zhao","year":"2021","journal-title":"IEEE\/CAA J. Autom. Sin."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"3282","DOI":"10.1109\/TSMC.2019.2920870","article-title":"Force Sensorless Admittance Control for Teleoperation of Uncertain Robot Manipulator Using Neural Networks","volume":"51","author":"Yang","year":"2021","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"5184","DOI":"10.1109\/TIE.2020.2991929","article-title":"Neural-Learning-Based Force Sensorless Admittance Control for Robots with Input Deadzone","volume":"68","author":"Peng","year":"2021","journal-title":"IEEE Trans. Ind. Electron."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/14\/4907\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:32:00Z","timestamp":1760164320000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/14\/4907"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,19]]},"references-count":30,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2021,7]]}},"alternative-id":["s21144907"],"URL":"https:\/\/doi.org\/10.3390\/s21144907","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,7,19]]}}}