{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,10]],"date-time":"2026-09-10T05:08:02Z","timestamp":1789016882126,"version":"build-2803163510"},"reference-count":46,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T00:00:00Z","timestamp":1788825600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Beijing Natural Science Foundation","award":["L2608056"],"award-info":[{"award-number":["L2608056"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biomimetics"],"abstract":"<jats:p>Humanoid robots are highly susceptible to structural damage during irrecoverable falls due to high landing velocity, short impact duration, and high peak impact force. Inspired by human protective strategies, namely instinctive postural adjustment and soft-tissue energy absorption, this paper proposes a passive\u2013active cooperative fall-protection method that combines pre-impact motion regulation with post-impact structural energy absorption. On the passive protection side, high-risk contact regions are identified through multi-directional fall simulations, and a multi-region, multilayer protective suit is optimized considering impact energy absorption, peak-force reduction, anti-bottoming safety, added mass, and thickness constraints. On the active protection side, a variable height inverted pendulum (VHIP) model is used to optimize the center of pressure and center of mass trajectories, reducing the terminal impact energy before ground contact. The residual impact energy is then matched with the absorption capacity of the passive protective layers, forming a unified framework that integrates pre-impact motion unloading and post-impact energy absorption. Numerical validation is performed on a MATLAB\u2013CoppeliaSim co-simulation platform, and physical experiments are conducted on the FCR humanoid robot (approx. 50 kg, 1.65 m, 22 DOF). Compared with the unprotected case, the proposed method reduces the peak equivalent impact force from 4819.1 N to 1038.2 N, i.e., a reduction of 78.5%, demonstrating its effectiveness in attenuating impact loads and enhancing protection capability.<\/jats:p>","DOI":"10.3390\/biomimetics11090644","type":"journal-article","created":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T08:10:22Z","timestamp":1788855022000},"page":"644","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Passive\u2013Active Cooperative Design Method for Fall Protection in Humanoid Robot"],"prefix":"10.3390","volume":"11","author":[{"given":"Tian","family":"Mu","sequence":"first","affiliation":[{"name":"School of Mechatronics Engineering, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"}]},{"given":"Junyao","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Mechatronics Engineering, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"resources","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6223-3147","authenticated-orcid":false,"given":"Weilong","family":"Zuo","sequence":"additional","affiliation":[{"name":"School of Mechatronics Engineering, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"visualization","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"}]},{"given":"Leilei","family":"Xie","sequence":"additional","affiliation":[{"name":"School of Mechatronics Engineering, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"visualization","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"104443","DOI":"10.1016\/j.robot.2023.104443","article-title":"A survey on control of humanoid fall over","volume":"166","author":"Subburaman","year":"2023","journal-title":"Robot. Auton. Syst."},{"key":"ref_2","unstructured":"Goswami, A., and Kallem, V. (May, January 26). Rate of change of angular momentum and balance maintenance of biped robots. Proceedings of the 2004 IEEE International Conference on Robotics and Automation (ICRA), New Orleans, LA, USA."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Pratt, J., Carff, J., Drakunov, S., and Goswami, A. (2006, January 4\u20136). Capture point: A step toward humanoid push recovery. Proceedings of the 2006 6th IEEE-RAS International Conference on Humanoid Robots, Genova, Italy.","DOI":"10.1109\/ICHR.2006.321385"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/s10514-013-9343-2","article-title":"Direction-changing fall control of humanoid robots: Theory and experiments","volume":"36","author":"Goswami","year":"2014","journal-title":"Auton. Robot."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"480","DOI":"10.1007\/s42235-024-00643-y","article-title":"A review of fall coping strategies for humanoid robots","volume":"22","author":"Zhang","year":"2025","journal-title":"J. Bionic Eng."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Mungai, M.E., Prabhakaran, G., and Grizzle, J.W. (2024, January 13\u201317). Fall prediction for bipedal robots: The standing phase. Proceedings of the 2024 IEEE International Conference on Robotics and Automation (ICRA), Yokohama, Japan.","DOI":"10.1109\/ICRA57147.2024.10611387"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"104995","DOI":"10.1016\/j.robot.2025.104995","article-title":"Fall analysis and prediction for humanoids","volume":"190","author":"Zhang","year":"2025","journal-title":"Robot. Auton. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1420301","DOI":"10.1007\/s11431-024-2872-7","article-title":"DCM-based dynamic stable walking under terrain-induced time-varying disturbances for humanoid robots","volume":"68","author":"Luo","year":"2025","journal-title":"Sci. China Technol. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/s10846-025-02327-z","article-title":"Enhancing humanoid robot stability on uneven terrain with online foothold planning based on ground scanning","volume":"111","author":"Frizza","year":"2025","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zhang, Z., Huang, Q., Liu, H., Zhang, W., Chen, X., and Yu, Z. (2016, January 7\u201310). Passive buffering arm for a humanoid robot against falling damage. Proceedings of the 2016 IEEE International Conference on Mechatronics and Automation (ICMA), Harbin, China.","DOI":"10.1109\/ICMA.2016.7558725"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Kajita, S., Cisneros, R., Benallegue, M., Sakaguchi, T., Nakaoka, S.-I., Morisawa, M., Kaneko, K., and Kanehiro, F. (2016, January 15\u201317). Impact acceleration of falling humanoid robot with an airbag. Proceedings of the 2016 IEEE-RAS 16th International Conference on Humanoid Robots (Humanoids), Cancun, Mexico.","DOI":"10.1109\/HUMANOIDS.2016.7803341"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Lee, J., Choi, W., Kanoulas, D., Subburaman, R., Caldwell, D.G., and Tsagarakis, N.G. (2016, January 15\u201317). An active compliant impact protection system for humanoids: Application to WALK-MAN hands. Proceedings of the 2016 IEEE-RAS 16th International Conference on Humanoid Robots (Humanoids), Cancun, Mexico.","DOI":"10.1109\/HUMANOIDS.2016.7803362"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"796","DOI":"10.1016\/j.robot.2009.03.011","article-title":"Learning to fall: Designing low damage fall sequences for humanoid soccer robots","volume":"57","author":"Marchant","year":"2009","journal-title":"Robot. Auton. Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"021005","DOI":"10.1115\/1.4006783","article-title":"Fall on backpack: Damage minimization of humanoid robots by falling on targeted body segments","volume":"8","author":"Lee","year":"2013","journal-title":"J. Comput. Nonlinear Dyn."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1729881417728016","DOI":"10.1177\/1729881417728016","article-title":"A minimized falling damage method for humanoid robots","volume":"14","author":"Li","year":"2017","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Zhou, Y., Chen, X., Liu, H., Yu, Z., Zhang, W., and Huang, Q. (2016, January 3\u20137). Falling protective method for humanoid robots using arm compliance to reduce damage. Proceedings of the 2016 IEEE International Conference on Robotics and Biomimetics (ROBIO), Qingdao, China.","DOI":"10.1109\/ROBIO.2016.7866624"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.egypro.2017.05.118","article-title":"Internal fall protection mechanism in non-compliant humanoid robot","volume":"117","author":"Anurag","year":"2017","journal-title":"Energy Procedia"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"6741","DOI":"10.1109\/LRA.2021.3094234","article-title":"Dynamic fall recovery motion generation on biped robot with shell protector","volume":"6","author":"Nguyen","year":"2021","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_19","first-page":"1793","article-title":"Predicting falls of a humanoid robot through machine learning","volume":"24","author":"Kalyanakrishnan","year":"2010","journal-title":"Proc. AAAI Conf. Artif. Intell."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Li, Z., Zhou, C., Castano, J., Wang, X., Negrello, F., Tsagarakis, N.G., and Caldwell, D.G. (2015, January 26\u201330). Fall prediction of legged robots based on energy state and its implication of balance augmentation: A study on the humanoid. Proceedings of the 2015 IEEE International Conference on Robotics and Automation (ICRA), Seattle, WA, USA.","DOI":"10.1109\/ICRA.2015.7139908"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Subburaman, R., Lee, J., Caldwell, D.G., and Tsagarakis, N.G. (2016, January 19\u201321). Multi-sensor based fall prediction method for humanoid robots. Proceedings of the 2016 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI), Baden-Baden, Germany.","DOI":"10.1109\/MFI.2016.7849474"},{"key":"ref_22","unstructured":"Fujiwara, K., Kanehiro, F., Kajita, S., Kaneko, K., Yokoi, K., and Hirukawa, H. (October, January 30). UKEMI: Falling motion control to minimize damage to biped humanoid robot. Proceedings of the 2002 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS 2002), Lausanne, Switzerland."},{"key":"ref_23","unstructured":"Fujiwara, K., Kanehiro, F., Kajita, S., Yokoi, K., Saito, H., Harada, K., Kaneko, K., and Hirukawa, H. (2003, January 27\u201331). The first human-size humanoid that can fall over safely and stand-up again. Proceedings of the 2003 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Las Vegas, NV, USA."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Fujiwara, K., Kajita, S., Harada, K., Kaneko, K., Morisawa, M., Kanehiro, F., Nakaoka, S., and Hirukawa, H. (November, January 29). An optimal planning of falling motions of a humanoid robot. Proceedings of the 2007 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), San Diego, CA, USA.","DOI":"10.1109\/IROS.2007.4399327"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Ogata, K., Terada, K., and Kuniyoshi, Y. (2008, January 1\u20133). Real-time selection and generation of fall damage reduction actions for humanoid robots. Proceedings of the 2008 8th IEEE-RAS International Conference on Humanoid Robots, Daejeon, Republic of Korea.","DOI":"10.1109\/ICHR.2008.4755950"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Ding, W., Chen, X., Yu, Z., Meng, L., Ceccarelli, M., and Huang, Q. (2018, January 6\u20139). Fall protection of humanoids inspired by human fall motion. Proceedings of the 2018 IEEE-RAS 18th International Conference on Humanoid Robots (Humanoids), Beijing, China.","DOI":"10.1109\/HUMANOIDS.2018.8625074"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Yun, S.-K., and Goswami, A. (June, January 31). Tripod fall: Concept and experiments of a novel approach to humanoid robot fall damage reduction. Proceedings of the 2014 IEEE International Conference on Robotics and Automation (ICRA), Hong Kong, China.","DOI":"10.1109\/ICRA.2014.6907260"},{"key":"ref_28","unstructured":"Wang, J., Whitman, E.C., and Stilman, M. (2012, January 27\u201329). Whole-body trajectory optimization for humanoid falling. Proceedings of the 2012 American Control Conference (ACC), Montreal, QC, Canada."},{"key":"ref_29","unstructured":"Ha, S., and Liu, C.K. (October, January 28). Multiple contact planning for minimizing damage of humanoid falls. Proceedings of the 2015 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Hamburg, Germany."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Wang, S., and Hauser, K. (2018, January 6\u20139). Unified multi-contact fall mitigation planning for humanoids via contact transition tree optimization. Proceedings of the 2018 IEEE-RAS 18th International Conference on Humanoid Robots (Humanoids), Beijing, China.","DOI":"10.1109\/HUMANOIDS.2018.8625018"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Samy, V., Bouyarmane, K., and Kheddar, A. (June, January 29). QP-based adaptive-gains compliance control in humanoid falls. Proceedings of the 2017 IEEE International Conference on Robotics and Automation (ICRA), Singapore.","DOI":"10.1109\/ICRA.2017.7989553"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Samy, V., Caron, S., Bouyarmane, K., and Kheddar, A. (2017, January 15\u201317). Post-impact adaptive compliance for humanoid falls using predictive control of a reduced model. Proceedings of the 2017 IEEE-RAS 17th International Conference on Humanoid Robotics (Humanoids), Birmingham, UK.","DOI":"10.1109\/HUMANOIDS.2017.8246942"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Subburaman, R., Lee, J., Caldwell, D.G., and Tsagarakis, N.G. (2018, January 21\u201325). Online falling-over control of humanoids exploiting energy shaping and distribution methods. Proceedings of the 2018 IEEE International Conference on Robotics and Automation (ICRA), Brisbane, QLD, Australia.","DOI":"10.1109\/ICRA.2018.8462880"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Wang, S., and Hauser, K. (2017, January 15\u201317). Real-time stabilization of a falling humanoid robot using hand contact: An optimal control approach. Proceedings of the 2017 IEEE-RAS 17th International Conference on Humanoid Robotics (Humanoids), Birmingham, UK.","DOI":"10.1109\/HUMANOIDS.2017.8246912"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Wang, S., and Hauser, K. (2018, January 21\u201325). Realization of a real-time optimal control strategy to stabilize a falling humanoid robot with hand contact. Proceedings of the 2018 IEEE International Conference on Robotics and Automation (ICRA), Brisbane, QLD, Australia.","DOI":"10.1109\/ICRA.2018.8460500"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"9028","DOI":"10.1109\/LRA.2022.3188884","article-title":"First do not fall: Learning to exploit a wall with a damaged humanoid robot","volume":"7","author":"Anne","year":"2022","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Zuo, W., Gao, J., Liu, J., Wu, T., and Xin, X. (2024). Whole-body dynamics for humanoid robot fall protection trajectory generation with wall support. Biomimetics, 9.","DOI":"10.3390\/biomimetics9040245"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Ma, Y., Farshidian, F., and Hutter, M. (June, January 29). Learning arm-assisted fall damage reduction and recovery for legged mobile manipulators. Proceedings of the 2023 IEEE International Conference on Robotics and Automation (ICRA), London, UK.","DOI":"10.1109\/ICRA48891.2023.10160582"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"5624","DOI":"10.1109\/LRA.2023.3297060","article-title":"Agile and dynamic standing-up control for humanoids using 3D divergent component of motion in multi-contact scenario","volume":"8","author":"Zambella","year":"2023","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"056014","DOI":"10.1088\/1748-3190\/ac1ab9","article-title":"Human inspired fall arrest strategy for humanoid robots based on stiffness ellipsoid optimisation","volume":"16","author":"Cui","year":"2021","journal-title":"Bioinspir. Biomim."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1109\/TRO.2019.2923971","article-title":"Capturability-based pattern generation for walking with variable height","volume":"36","author":"Caron","year":"2020","journal-title":"IEEE Trans. Robot."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Stronge, W.J. (2018). Impact Mechanics, Cambridge University Press. [2nd ed.].","DOI":"10.1017\/9781139050227"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1016\/S0734-743X(00)00060-9","article-title":"Characterization of polymeric structural foams under compressive impact loading by means of energy-absorption diagram","volume":"25","author":"Avalle","year":"2001","journal-title":"Int. J. Impact Eng."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1177\/0021955X06063519","article-title":"Compressive strain at the onset of densification of cellular solids","volume":"42","author":"Li","year":"2006","journal-title":"J. Cell. Plast."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Paredes, V.C., and Hereid, A. (2024, January 8\u201312). Safe whole-body task space control for humanoid robots. Proceedings of the American Control Conference (ACC), Toronto, ON, Canada.","DOI":"10.23919\/ACC60939.2024.10644227"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.triboint.2012.09.015","article-title":"Mathematical modeling of linear viscoelastic impact: Application to drop impact testing of articular cartilage","volume":"63","author":"Argatov","year":"2013","journal-title":"Tribol. Int."}],"container-title":["Biomimetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2313-7673\/11\/9\/644\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,10]],"date-time":"2026-09-10T04:18:58Z","timestamp":1789013938000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2313-7673\/11\/9\/644"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,8]]},"references-count":46,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2026,9]]}},"alternative-id":["biomimetics11090644"],"URL":"https:\/\/doi.org\/10.3390\/biomimetics11090644","relation":{},"ISSN":["2313-7673"],"issn-type":[{"value":"2313-7673","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,8]]}}}