{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T18:03:50Z","timestamp":1775066630716,"version":"3.50.1"},"reference-count":48,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T00:00:00Z","timestamp":1687219200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Meta Inc."}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>Robots operating in human environments require a diverse set of skills, including slow and fast walking, turning, side-stepping, and more. However, developing robot controllers capable of exhibiting such a broad range of behaviors is a challenging problem that necessitates meticulous investigation for each task. To address this challenge, we introduce a trajectory optimization method that resolves the kinematic infeasibility of reference animal motions. This method, combined with a model-based controller, results in a unified data-driven model-based control framework capable of imitating various animal gaits without the need for expensive simulation training or real-world fine-tuning. Our framework is capable of imitating a variety of motor skills such as trotting, pacing, turning, and side-stepping with ease. It shows superior tracking capabilities in both simulations and the real world compared to other imitation controllers, including a model-based one and a learning-based motion imitation technique.<\/jats:p>","DOI":"10.3390\/robotics12030090","type":"journal-article","created":{"date-parts":[[2023,6,21]],"date-time":"2023-06-21T02:30:51Z","timestamp":1687314651000},"page":"90","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["FastMimic: Model-Based Motion Imitation for Agile, Diverse and Generalizable Quadrupedal Locomotion"],"prefix":"10.3390","volume":"12","author":[{"given":"Tianyu","family":"Li","sequence":"first","affiliation":[{"name":"School of Interactive Computing, Georgia Institute of Technology, Atlanta, GA 30332, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jungdam","family":"Won","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, Seoul National University, Seoul 08826, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9185-0283","authenticated-orcid":false,"given":"Jeongwoo","family":"Cho","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sehoon","family":"Ha","sequence":"additional","affiliation":[{"name":"School of Interactive Computing, Georgia Institute of Technology, Atlanta, GA 30332, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Akshara","family":"Rai","sequence":"additional","affiliation":[{"name":"Meta AI, Menlo Park, CA 94025, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1145\/3197517.3201311","article-title":"Deepmimic: Example-guided deep reinforcement learning of physics-based character skills","volume":"37","author":"Peng","year":"2018","journal-title":"ACM Trans. Graph. (TOG)"},{"key":"ref_2","unstructured":"Peng, X.B., Coumans, E., Zhang, T., Lee, T.W., Tan, J., and Levine, S. (2020). Learning agile robotic locomotion skills by imitating animals. arXiv."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1177\/0278364917694244","article-title":"High-speed bounding with the MIT Cheetah 2: Control design and experiments","volume":"36","author":"Park","year":"2017","journal-title":"Int. J. Robot. Res."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Bledt, G., Powell, M.J., Katz, B., Di Carlo, J., Wensing, P.M., and Kim, S. (2018, January 1\u20135). MIT Cheetah 3: Design and control of a robust, dynamic quadruped robot. Proceedings of the 2018 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Madrid, Spain.","DOI":"10.1109\/IROS.2018.8593885"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Di Carlo, J., Wensing, P.M., Katz, B., Bledt, G., and Kim, S. (2018, January 1\u20135). Dynamic locomotion in the mit cheetah 3 through convex model-predictive control. Proceedings of the 2018 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Madrid, Spain.","DOI":"10.1109\/IROS.2018.8594448"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1145\/3355089.3356501","article-title":"Learning Predict-and-simulate Policies from Unorganized Human Motion Data","volume":"38","author":"Park","year":"2019","journal-title":"ACM Trans. Graph. (TOG)"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1145\/3355089.3356536","article-title":"DReCon: Data-driven Responsive Control of Physics-based Characters","volume":"38","author":"Bergamin","year":"2019","journal-title":"ACM Trans. Graph. (TOG)"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1145\/3386569.3392381","article-title":"A scalable approach to control diverse behaviors for physically simulated characters","volume":"39","author":"Won","year":"2020","journal-title":"ACM Trans. Graph. (TOG)"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1145\/3478513.3480527","article-title":"SuperTrack: Motion tracking for physically simulated characters using supervised learning","volume":"40","author":"Fussell","year":"2021","journal-title":"ACM Trans. Graph. (TOG)"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1145\/3072959.3073663","article-title":"Phase-functioned neural networks for character control","volume":"36","author":"Holden","year":"2017","journal-title":"ACM Trans. Graph. (TOG)"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1162\/NECO_a_00393","article-title":"Dynamical movement primitives: Learning attractor models for motor behaviors","volume":"25","author":"Ijspeert","year":"2013","journal-title":"Neural Comput."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Hansen, N. (2006). The CMA evolution strategy: A comparing review. Towards a New Evolutionary Computation, Springer Science & Business Media.","DOI":"10.1007\/3-540-32494-1_4"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Raibert, M.H. (1986). Legged Robots That Balance, MIT Press.","DOI":"10.1109\/MEX.1986.4307016"},{"key":"ref_14","unstructured":"(2023, March 03). Unitree Robotics. Available online: http:\/\/www.unitree.cc\/."},{"key":"ref_15","unstructured":"Kang, D., Zimmermann, S., and Coros, S. (October, January 27). Animal Gaits on Quadrupedal Robots Using Motion Matching and Model Based Control. Proceedings of the IROS, Prague, Czech Republic."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Won, J., and Lee, J. (2019). Learning Body Shape Variation in Physics-based Characters. ACM Trans. Graph. (TOG), 38.","DOI":"10.1145\/3355089.3356499"},{"key":"ref_17","unstructured":"Merel, J., Tassa, Y., TB, D., Srinivasan, S., Lemmon, J., Wang, Z., Wayne, G., and Heess, N. (2017). Learning human behaviors from motion capture by adversarial imitation. arXiv."},{"key":"ref_18","unstructured":"Merel, J., Hasenclever, L., Galashov, A., Ahuja, A., Pham, V., Wayne, G., Teh, Y.W., and Heess, N. (2019, January 6\u20139). Neural Probabilistic Motor Primitives for Humanoid Control. Proceedings of the ICLR, New Orleans, LA, USA."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Xie, Z., Berseth, G., Clary, P., Hurst, J., and van de Panne, M. (2018, January 1\u20135). Feedback Control for Cassie with Deep Reinforcement Learning. Proceedings of the IROS, Madrid, Spain.","DOI":"10.1109\/IROS.2018.8593722"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1145\/3386569.3392433","article-title":"CARL: Controllable Agent with Reinforcement Learning for Quadruped Locomotion","volume":"39","author":"Luo","year":"2020","journal-title":"ACM Trans. Graph. (TOG)"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Exarchos, I., Jiang, Y., Yu, W., and Liu, C.K. (June, January 30). Policy Transfer via Kinematic Domain Randomization and Adaptation. Proceedings of the 2021 IEEE International Conference on Robotics and Automation (ICRA), Xi\u2019an, China.","DOI":"10.1109\/ICRA48506.2021.9561982"},{"key":"ref_22","unstructured":"Schwind, W.J. (1998). Spring Loaded Inverted Pendulum Running: A Plant Model, University of Michigan."},{"key":"ref_23","first-page":"3926","article-title":"Learning Spring Mass Locomotion: Guiding Policies with a Reduced-Order Model","volume":"6","author":"Green","year":"2021","journal-title":"IEEE RAL"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Gong, Y., and Grizzle, J. (2020). Angular momentum about the contact point for control of bipedal locomotion: Validation in a lip-based controller. arXiv.","DOI":"10.1109\/ICRA48506.2021.9560821"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Li, T., Geyer, H., Atkeson, C.G., and Rai, A. (2019, January 20\u201324). Using deep reinforcement learning to learn high-level policies on the atrias biped. Proceedings of the 2019 International Conference on Robotics and Automation (ICRA 2019), Montreal, QC, Canada.","DOI":"10.1109\/ICRA.2019.8793864"},{"key":"ref_26","unstructured":"Kim, D., Di Carlo, J., Katz, B., Bledt, G., and Kim, S. (2019). Highly dynamic quadruped locomotion via whole-body impulse control and model predictive control. arXiv."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Xie, Z., Da, X., Babich, B., Garg, A., and van de Panne, M. (2021). GLiDE: Generalizable Quadrupedal Locomotion in Diverse Environments with a Centroidal Model. arXiv.","DOI":"10.1007\/978-3-031-21090-7_31"},{"key":"ref_28","unstructured":"Da, X., Xie, Z., Hoeller, D., Boots, B., Anandkumar, A., Zhu, Y., Babich, B., and Garg, A. (2020). Learning a contact-adaptive controller for robust, efficient legged locomotion. arXiv."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2682","DOI":"10.1109\/LRA.2021.3062342","article-title":"Planning in Learned Latent Action Spaces for Generalizable Legged Locomotion","volume":"6","author":"Li","year":"2021","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Kormushev, P., Calinon, S., and Caldwell, D.G. (2010, January 18\u201322). Robot motor skill coordination with EM-based reinforcement learning. Proceedings of the 2010 IEEE\/RSJ International Conference on Intelligent Robots and Systems, Taipei, Taiwan.","DOI":"10.1109\/IROS.2010.5649089"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1177\/0278364912472380","article-title":"Learning to select and generalize striking movements in robot table tennis","volume":"32","author":"Kober","year":"2013","journal-title":"Int. J. Robot. Res."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"800","DOI":"10.1109\/TRO.2010.2065430","article-title":"Task-specific generalization of discrete and periodic dynamic movement primitives","volume":"26","author":"Ude","year":"2010","journal-title":"IEEE Trans. Robot."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Conkey, A., and Hermans, T. (2019, January 15\u201317). Active learning of probabilistic movement primitives. Proceedings of the Humanoids, Toronto, ON, Canada.","DOI":"10.1109\/Humanoids43949.2019.9035026"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Kober, J., and Peters, J. (2009, January 7\u201310). Learning motor primitives for robotics. Proceedings of the ICRA, Paris, France.","DOI":"10.1109\/ROBOT.2009.5152577"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Pastor, P., Kalakrishnan, M., Chitta, S., Theodorou, E., and Schaal, S. (2011, January 9\u201313). Skill learning and task outcome prediction for manipulation. Proceedings of the Robotics and Automation (ICRA), Shanghai, China.","DOI":"10.1109\/ICRA.2011.5980200"},{"key":"ref_36","unstructured":"Rai, A., Sutanto, G., Schaal, S., and Meier, F. (June, January 29). Learning feedback terms for reactive planning and control. Proceedings of the Robotics and Automation (ICRA), Singapore."},{"key":"ref_37","unstructured":"Stulp, F., and Sigaud, O. (2012). Path integral policy improvement with covariance matrix adaptation. arXiv."},{"key":"ref_38","unstructured":"Bahl, S., Mukadam, M., Gupta, A., and Pathak, D. (2020). Neural dynamic policies for end-to-end sensorimotor learning. arXiv."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Jalics, L., Hemami, H., and Zheng, Y.F. (1997, January 20\u201325). Pattern generation using coupled oscillators for robotic and biorobotic adaptive periodic movement. Proceedings of the Robotics and Automation (ICRA), Albuquerque, NW, USA.","DOI":"10.1109\/ROBOT.1997.620035"},{"key":"ref_40","unstructured":"Kajita, S., Kanehiro, F., Kaneko, K., Fujiwara, K., Yokoi, K., and Hirukawa, H. (2002, January 11\u201315). A realtime pattern generator for biped walking. Proceedings of the Robotics and Automation (ICRA), Washington, DC, USA."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"662","DOI":"10.1139\/y04-070","article-title":"Infant stepping: A window to the behaviour of the human pattern generator for walking","volume":"82","author":"Yang","year":"2004","journal-title":"Can. J. Physiol. Pharmacol."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"642","DOI":"10.1016\/j.neunet.2008.03.014","article-title":"Central pattern generators for locomotion control in animals and robots: A review","volume":"21","author":"Ijspeert","year":"2008","journal-title":"Neural Netw."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Rosado, J., Silva, F., and Santos, V. (2015, January 8\u201310). Adaptation of Robot Locomotion Patterns with Dynamic Movement Primitives. Proceedings of the 2015 IEEE International Conference on Autonomous Robot Systems and Competitions, Vila Real, Portugal.","DOI":"10.1109\/ICARSC.2015.9"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"830","DOI":"10.1111\/j.1469-7580.2009.01083.x","article-title":"The intertarsal joint of the ostrich (Struthio camelus): Anatomical examination and function of passive structures in locomotion","volume":"214","author":"Schaller","year":"2009","journal-title":"J. Anat."},{"key":"ref_45","first-page":"1114","article-title":"The 3-D spring\u2013mass model reveals a time-based deadbeat control for highly robust running and steering in uncertain environments","volume":"29","author":"Wu","year":"2013","journal-title":"IEEE TRO"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1145\/3197517.3201366","article-title":"Mode-adaptive neural networks for quadruped motion control","volume":"37","author":"Zhang","year":"2018","journal-title":"ACM Trans. Graph. (TOG)"},{"key":"ref_47","unstructured":"Coumans, E., and Bai, Y. (2023, March 03). PyBullet. Available online: http:\/\/pybullet.org."},{"key":"ref_48","unstructured":"Schulman, J., Wolski, F., Dhariwal, P., Radford, A., and Klimov, O. (2017). Proximal policy optimization algorithms. arXiv."}],"container-title":["Robotics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2218-6581\/12\/3\/90\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:57:26Z","timestamp":1760126246000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2218-6581\/12\/3\/90"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,20]]},"references-count":48,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,6]]}},"alternative-id":["robotics12030090"],"URL":"https:\/\/doi.org\/10.3390\/robotics12030090","relation":{},"ISSN":["2218-6581"],"issn-type":[{"value":"2218-6581","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6,20]]}}}