{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T21:53:53Z","timestamp":1770069233362,"version":"3.49.0"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2021,8,11]],"date-time":"2021-08-11T00:00:00Z","timestamp":1628640000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,8,11]],"date-time":"2021-08-11T00:00:00Z","timestamp":1628640000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001871","name":"funda\u00e7\u00e3o para a ci\u00eancia e a tecnologia","doi-asserted-by":"publisher","award":["SFRH\/BD\/118438\/2016"],"award-info":[{"award-number":["SFRH\/BD\/118438\/2016"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["SN Appl. Sci."],"published-print":{"date-parts":[[2021,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Biped robots are inherently unstable because of their complex kinematics as well as dynamics. Despite many research efforts in developing biped locomotion, the performance of biped locomotion is still far from the expectations. This paper proposes a model-based framework to generate stable biped locomotion. The core of this framework is an abstract dynamics model which is composed of three masses to consider the dynamics of stance leg, torso, and swing leg for minimizing the tracking problems. According to this dynamics model, we propose a modular walking reference trajectories planner which takes into account obstacles to plan all the references. Moreover, this dynamics model is used to formulate the controller as a Model Predictive Control\u00a0(MPC) scheme which can consider some constraints in the states of the system, inputs, outputs, and also mixed input-output. The performance and the robustness of the proposed framework are validated by performing several numerical simulations using\u00a0MATLAB. Moreover, the framework is deployed on a simulated torque-controlled humanoid to verify its performance and robustness. The simulation results show that the proposed framework is capable of generating biped locomotion robustly.<\/jats:p>","DOI":"10.1007\/s42452-021-04752-9","type":"journal-article","created":{"date-parts":[[2021,8,11]],"date-time":"2021-08-11T20:02:33Z","timestamp":1628712153000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A modular framework to generate robust biped locomotion: from planning to control"],"prefix":"10.1007","volume":"3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4932-1457","authenticated-orcid":false,"given":"Mohammadreza","family":"Kasaei","sequence":"first","affiliation":[]},{"given":"Ali","family":"Ahmadi","sequence":"additional","affiliation":[]},{"given":"Nuno","family":"Lau","sequence":"additional","affiliation":[]},{"given":"Artur","family":"Pereira","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,8,11]]},"reference":[{"key":"4752_CR1","doi-asserted-by":"crossref","unstructured":"Abreu M, Reis LP, Lau N (2019) Learning to run faster in a humanoid robot soccer environment through reinforcement learning. In: Robot world cup. Springer, pp 3\u201315","DOI":"10.1007\/978-3-030-35699-6_1"},{"issue":"2","key":"4752_CR2","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1023\/A:1022600522613","volume":"36","author":"A Albert","year":"2003","unstructured":"Albert A, Gerth W (2003) Analytic path planning algorithms for bipedal robots without a trunk. J Intell Rob Syst 36(2):109\u2013127","journal-title":"J Intell Rob Syst"},{"key":"4752_CR3","doi-asserted-by":"crossref","unstructured":"Brasseur C, Sherikov A, Collette C, Dimitrov D, Wieber PB (2015) A robust linear MPC approach to online generation of 3d biped walking motion. In: 2015 IEEE-RAS 15th international conference on humanoid robots (Humanoids), pp 595\u2013601","DOI":"10.1109\/HUMANOIDS.2015.7363423"},{"key":"4752_CR4","doi-asserted-by":"crossref","unstructured":"Chang CH, Huang HP, Hsu HK, Cheng CA (2015) Humanoid robot push-recovery strategy based on cmp criterion and angular momentum regulation. In: 2015 IEEE international conference on advanced intelligent mechatronics (AIM), pp 761\u2013766","DOI":"10.1109\/AIM.2015.7222629"},{"key":"4752_CR5","doi-asserted-by":"crossref","unstructured":"Dasgupta A, Nakamura Y (1999). Making feasible walking motion of humanoid robots from human motion capture data. In: Proceedings 1999 IEEE international conference on robotics and automation (Cat. No. 99CH36288C), vol\u00a02. IEEE, pp 1044\u20131049","DOI":"10.1109\/ROBOT.1999.772454"},{"key":"4752_CR6","doi-asserted-by":"crossref","unstructured":"Erbatur K, Okazaki A, Obiya K, Takahashi T, Kawamura A (2002) A study on the zero moment point measurement for biped walking robots. In: 7th International workshop on advanced motion control. proceedings (Cat. No. 02TH8623). IEEE, pp 431\u2013436","DOI":"10.1109\/AMC.2002.1026959"},{"issue":"4","key":"4752_CR7","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1177\/0278364917708248","volume":"36","author":"S Faraji","year":"2017","unstructured":"Faraji S, Ijspeert AJ (2017) 3lp: a linear 3d-walking model including torso and swing dynamics. Int J Robot Res 36(4):436\u2013455","journal-title":"Int J Robot Res"},{"key":"4752_CR8","doi-asserted-by":"crossref","unstructured":"Griffin RJ, Wiedebach G, McCrory S, Bertrand S, Lee I, Pratt J (2019) Footstep planning for autonomous walking over rough terrain. arXiv preprint arXiv:1907.08673","DOI":"10.1109\/Humanoids43949.2019.9035046"},{"issue":"5\u20136","key":"4752_CR9","doi-asserted-by":"publisher","first-page":"719","DOI":"10.1163\/016918610X493552","volume":"24","author":"A Herdt","year":"2010","unstructured":"Herdt A, Diedam H, Wieber PB, Dimitrov D, Mombaur K, Diehl M (2010) Online walking motion generation with automatic footstep placement. Adv Robot 24(5\u20136):719\u2013737","journal-title":"Adv Robot"},{"key":"4752_CR10","doi-asserted-by":"crossref","unstructured":"Herdt A, Perrin N, Wieber PB (2010). Walking without thinking about it. In: 2010 IEEE\/RSJ International conference on intelligent robots and systems (IROS). IEEE, pp 190\u2013195","DOI":"10.1109\/IROS.2010.5654429"},{"key":"4752_CR11","doi-asserted-by":"crossref","unstructured":"Hornung A, Bennewitz M (2012) Adaptive level-of-detail planning for efficient humanoid navigation. In: 2012 IEEE international conference on robotics and automation. IEEE, pp 997\u20131002","DOI":"10.1109\/ICRA.2012.6224898"},{"key":"4752_CR12","doi-asserted-by":"crossref","unstructured":"Kajita S, Kanehiro F, Kaneko K, Fujiwara K, Harada K, Yokoi K, Hirukawa H (2003) Biped walking pattern generation by using preview control of zero-moment point. In: Robotics and automation, 2003. Proceedings. ICRA\u201903. IEEE international conference on, vol\u00a02. IEEE, pp 1620\u20131626","DOI":"10.1109\/ROBOT.2003.1241826"},{"key":"4752_CR13","doi-asserted-by":"crossref","unstructured":"Kajita S, Matsumoto O, Saigo M (2001) Real-time 3D walking pattern generation for a biped robot with telescopic legs. In: Robotics and automation, 2001. Proceedings 2001 ICRA. IEEE international conference on, vol\u00a03. IEEE, pp 2299\u20132306","DOI":"10.1109\/ROBOT.2001.932965"},{"key":"4752_CR14","doi-asserted-by":"crossref","unstructured":"Kasaei M, Ahmadi A, Lau N, Pereira A (2020) A robust model-based biped locomotion framework based on three-mass model: from planning to control. In: 2020 IEEE international conference on autonomous robot systems and competitions (ICARSC). IEEE, pp 257\u2013262","DOI":"10.1109\/ICARSC49921.2020.9096150"},{"key":"4752_CR15","doi-asserted-by":"crossref","unstructured":"Kasaei M, Lau N, Pereira A (2018) An optimal closed-loop framework to develop stable walking for humanoid robot. In: 2018 IEEE international conference on autonomous robot systems and competitions (ICARSC). IEEE, pp 30\u201335","DOI":"10.1109\/ICARSC.2018.8374156"},{"key":"4752_CR16","doi-asserted-by":"crossref","unstructured":"Kasaei M, Lau N, Pereira A (2019) A fast and stable omnidirectional walking engine for the nao humanoid robot. In: Robot world cup. Springer, pp 99\u2013111","DOI":"10.1007\/978-3-030-35699-6_8"},{"key":"4752_CR17","doi-asserted-by":"crossref","unstructured":"Kasaei M, Lau N, Pereira A (2019) A robust biped locomotion based on linear-quadratic-Gaussian controller and divergent component of motion. In: 2019 IEEE\/RSJ international conference on intelligent robots and systems. IEEE, pp 1429\u20131434","DOI":"10.1109\/IROS40897.2019.8967778"},{"key":"4752_CR18","doi-asserted-by":"crossref","unstructured":"Kasaei SM, Lau N, Pereira A (2017) A reliable hierarchical omnidirectional walking engine for a bipedal robot by using the enhanced lip plus flywheel. In: Human-centric robotics-proceedings of the 20th international conference Clawar 2017. World Scientific, p 399","DOI":"10.1142\/9789813231047_0049"},{"key":"4752_CR19","doi-asserted-by":"publisher","first-page":"5","DOI":"10.3389\/fnbot.2013.00005","volume":"7","author":"C Li","year":"2013","unstructured":"Li C, Lowe R, Ziemke T (2013) Humanoids learning to walk: a natural cpg-actor-critic architecture. Front Neurorobot 7:5","journal-title":"Front Neurorobot"},{"issue":"10","key":"4752_CR20","doi-asserted-by":"publisher","first-page":"1750","DOI":"10.1017\/S0263574719000237","volume":"37","author":"J Luo","year":"2019","unstructured":"Luo J, Su Y, Ruan L, Zhao Y, Kim D, Sentis L, Fu C (2019) Robust bipedal locomotion based on a hierarchical control structure. Robotica 37(10):1750\u20131767","journal-title":"Robotica"},{"key":"4752_CR21","doi-asserted-by":"crossref","unstructured":"Luo RC, Lee KC, Spalanzani A (2016). Humanoid robot walking pattern generation based on five-mass with angular momentum model. In: 2016 IEEE 25th international symposium on industrial electronics (ISIE). IEEE, pp 375\u2013380","DOI":"10.1109\/ISIE.2016.7744919"},{"key":"4752_CR22","doi-asserted-by":"crossref","unstructured":"Mirjalili R, Yousefi-Korna A, Shirazi FA, Nikkhah A, Nazemi F, Khadiv M (2018) A whole-body model predictive control scheme including external contact forces and COM height variations. In: 2018 IEEE-RAS 18th international conference on humanoid robots (Humanoids). IEEE, pp 1\u20136","DOI":"10.1109\/HUMANOIDS.2018.8624963"},{"key":"4752_CR23","doi-asserted-by":"crossref","unstructured":"Pratt J, Carff J, Drakunov S, Goswami A (2006). Capture point: a step toward humanoid push recovery. In: 2006 6th IEEE-RAS international conference on humanoid robots. IEEE, pp 200\u2013207","DOI":"10.1109\/ICHR.2006.321385"},{"issue":"1","key":"4752_CR24","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/s10846-016-0407-3","volume":"85","author":"CP Santos","year":"2017","unstructured":"Santos CP, Alves N, Moreno JC (2017) Biped locomotion control through a biomimetic cpg-based controller. J Intell Robot Syst 85(1):47\u201370","journal-title":"J Intell Robot Syst"},{"key":"4752_CR25","doi-asserted-by":"publisher","first-page":"418","DOI":"10.1016\/j.procs.2019.09.196","volume":"159","author":"AA Saputra","year":"2019","unstructured":"Saputra AA, Botzheim J, Sulistijono IA, Kubota N (2019) Layered neural-based locomotion for biped robot movement with carrying dynamic payload. Procedia Computer Science 159:418\u2013427","journal-title":"Procedia Computer Science"},{"issue":"2","key":"4752_CR26","doi-asserted-by":"publisher","first-page":"376","DOI":"10.1109\/TIE.2010.2052535","volume":"58","author":"T Sato","year":"2010","unstructured":"Sato T, Sakaino S, Ohnishi K (2010) Real-time walking trajectory generation method with three-mass models at constant body height for three-dimensional biped robots. IEEE Trans Ind Electron 58(2):376\u2013383","journal-title":"IEEE Trans Ind Electron"},{"issue":"11","key":"4752_CR27","doi-asserted-by":"publisher","first-page":"5137","DOI":"10.1109\/TIE.2012.2221111","volume":"60","author":"S Shimmyo","year":"2013","unstructured":"Shimmyo S, Sato T, Ohnishi K (2013) Biped walking pattern generation by using preview control based on three-mass model. IEEE Trans Ind Electron 60(11):5137\u20135147","journal-title":"IEEE Trans Ind Electron"},{"key":"4752_CR28","doi-asserted-by":"crossref","unstructured":"Spyrakos-Papastavridis E, Medrano-Cerda GA, Tsagarakis NG, Dai JS, Caldwell DG (2013) A push recovery strategy for a passively compliant humanoid robot using decentralized lqr controllers. In: 2013 IEEE international conference on mechatronics (ICM). IEEE, pp 464\u2013470","DOI":"10.1109\/ICMECH.2013.6518581"},{"key":"4752_CR29","doi-asserted-by":"crossref","unstructured":"Takenaka T, Matsumoto T, Yoshiike T (2009) Real time motion generation and control for biped robot-1st report: walking gait pattern generation. In: Intelligent robots and systems, 2009. IROS 2009. IEEE\/RSJ international conference on. IEEE, pp 1084\u20131091","DOI":"10.1109\/IROS.2009.5354662"},{"key":"4752_CR30","unstructured":"Tran DH, Hamker F, Nassour J (2018) A humanoid robot learns to recover perturbation during swinging motion. IEEE Trans Syst Man Cybern Syst"},{"issue":"01","key":"4752_CR31","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1142\/S0219843604000083","volume":"1","author":"M Vukobratovi\u0107","year":"2004","unstructured":"Vukobratovi\u0107 M, Borovac B (2004) Zero-moment point-thirty five years of its life. Int J Humanoid Robot 1(01):157\u2013173","journal-title":"Int J Humanoid Robot"},{"key":"4752_CR32","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1109\/TBME.1970.4502681","volume":"1","author":"M Vukobratovic","year":"1970","unstructured":"Vukobratovic M, Frank A, Juricic D (1970) On the stability of biped locomotion. IEEE Trans Biomed Eng 1:25\u201336","journal-title":"IEEE Trans Biomed Eng"},{"issue":"2","key":"4752_CR33","doi-asserted-by":"publisher","first-page":"613","DOI":"10.1109\/TCYB.2018.2870145","volume":"50","author":"Y Wang","year":"2018","unstructured":"Wang Y, Xue X, Chen B (2018) Matsuoka\u2019s cpg with desired rhythmic signals for adaptive walking of humanoid robots. IEEE Trans Cybern 50(2):613\u2013626","journal-title":"IEEE Trans Cybern"}],"container-title":["SN Applied Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42452-021-04752-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s42452-021-04752-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42452-021-04752-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,8,11]],"date-time":"2021-08-11T20:10:04Z","timestamp":1628712604000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s42452-021-04752-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,11]]},"references-count":33,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2021,9]]}},"alternative-id":["4752"],"URL":"https:\/\/doi.org\/10.1007\/s42452-021-04752-9","relation":{},"ISSN":["2523-3963","2523-3971"],"issn-type":[{"value":"2523-3963","type":"print"},{"value":"2523-3971","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,11]]},"assertion":[{"value":"24 July 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 July 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 August 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"On behalf of all authors, the corresponding author states that there is no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"771"}}