{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,7]],"date-time":"2026-08-07T17:17:17Z","timestamp":1786123037695,"version":"build-2736575974"},"reference-count":45,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2026,8,7]],"date-time":"2026-08-07T00:00:00Z","timestamp":1786060800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biomimetics"],"abstract":"<jats:p>Existing quadruped robots typically place their center of mass (CoM) near the geometric center of the body to achieve structural symmetry and simplify control design. In contrast, many quadrupedal animals capable of agile running exhibit a pronounced anteriorly biased mass distribution, with the CoM located closer to the front of the body. This biological characteristic motivates a re-examination of whether a geometrically centered CoM necessarily corresponds to dynamically balanced loading between the fore- and hindlimbs during high-speed locomotion. To address this question, this study investigates the influence of longitudinal CoM position on load distribution during high-speed straight-line locomotion of quadruped robots. A unified analytical framework is established by combining whole-body force and pitch moment equilibrium, sagittal-plane kinematics, and Jacobian-based force-to-torque mapping, thereby linking longitudinal CoM position, foot-end support forces, and joint loads. Simulation validation is conducted on the Black Panther 2 quadruped robot using four central-body CoM configurations, denoted as \u00d70, \u00d75, \u00d710, and \u00d715. In the primary evaluation at 5 m\/s, shifting the CoM forward from \u00d70 to \u00d715 reduces the absolute median fore\u2013hindlimb differences in support force and joint torque by approximately 86.6% and 93.4%, respectively, indicating a transition from hindlimb-dominated loading toward cooperative load sharing between the fore and hindlimbs. Independent training runs with multiple random seeds further confirm the robustness of this load-redistribution trend to reinforcement learning variability. Consistent behavior is also observed at 8 m\/s, while no evident degradation in turning response or locomotion stability is found under the tested turning and randomly generated rough-terrain conditions. These results demonstrate that a moderate forward shift of the longitudinal CoM can alleviate hindlimb load concentration and promote a more balanced fore\u2013hindlimb load distribution, providing a theoretical basis for the morphological design and control optimization of high-speed quadruped robots.<\/jats:p>","DOI":"10.3390\/biomimetics11080565","type":"journal-article","created":{"date-parts":[[2026,8,7]],"date-time":"2026-08-07T13:20:16Z","timestamp":1786108816000},"page":"565","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Influence of Longitudinal Center of Mass Position on Load Distribution in High-Speed Quadrupedal Locomotion"],"prefix":"10.3390","volume":"11","author":[{"given":"Kaixin","family":"Lan","sequence":"first","affiliation":[{"name":"Center for X-Mechanics, Zhejiang University, Hangzhou 310012, China"},{"name":"State Key Laboratory of Fluid Power and Mechatronic System, Zhejiang University, Hangzhou 310012, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-3467-4626","authenticated-orcid":false,"given":"Lei","family":"Jiang","sequence":"additional","affiliation":[{"name":"Center for X-Mechanics, Zhejiang University, Hangzhou 310012, China"},{"name":"State Key Laboratory of Fluid Power and Mechatronic System, Zhejiang University, Hangzhou 310012, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yucheng","family":"Tao","sequence":"additional","affiliation":[{"name":"Center for X-Mechanics, Zhejiang University, Hangzhou 310012, China"},{"name":"State Key Laboratory of Fluid Power and Mechatronic System, Zhejiang University, Hangzhou 310012, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-6770-3155","authenticated-orcid":false,"given":"Chaojie","family":"Fu","sequence":"additional","affiliation":[{"name":"Center for X-Mechanics, Zhejiang University, Hangzhou 310012, China"},{"name":"State Key Laboratory of Fluid Power and Mechatronic System, Zhejiang University, Hangzhou 310012, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yongbin","family":"Jin","sequence":"additional","affiliation":[{"name":"Center for X-Mechanics, Zhejiang University, Hangzhou 310012, China"},{"name":"State Key Laboratory of Fluid Power and Mechatronic System, Zhejiang University, Hangzhou 310012, China"},{"name":"ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 311200, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongtao","family":"Wang","sequence":"additional","affiliation":[{"name":"Center for X-Mechanics, Zhejiang University, Hangzhou 310012, China"},{"name":"State Key Laboratory of Fluid Power and Mechatronic System, Zhejiang University, Hangzhou 310012, China"},{"name":"ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 311200, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Raibert, M.H. (1986). Legged Robots That Balance, MIT Press.","DOI":"10.1109\/MEX.1986.4307016"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Bledt, G., Powell, M.J., Katz, B., Di Carlo, J., Wensing, P.M., and Kim, S. (2018). 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, 1\u20135 October 2018, IEEE.","DOI":"10.1109\/IROS.2018.8593885"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Di Carlo, J., Wensing, P.M., Katz, B., Bledt, G., and Kim, S. (2018). 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, 1\u20135 October 2018, IEEE.","DOI":"10.1109\/IROS.2018.8594448"},{"key":"ref_4","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_5","doi-asserted-by":"crossref","first-page":"eadi7566","DOI":"10.1126\/scirobotics.adi7566","article-title":"ANYmal Parkour: Learning Agile Navigation for Quadrupedal Robots","volume":"9","author":"Hoeller","year":"2024","journal-title":"Sci. Robot."},{"key":"ref_6","unstructured":"Makoviychuk, V., Wawrzyniak, L., Guo, Y., Lu, M., Storey, K., Macklin, M., Hoeller, D., Rudin, N., Allshire, A., and Handa, A. (2021). Isaac Gym: High Performance GPU-Based Physics Simulation for Robot Learning. arXiv."},{"key":"ref_7","first-page":"91","article-title":"Learning to Walk in Minutes Using Massively Parallel Deep Reinforcement Learning","volume":"Volume 164","author":"Rudin","year":"2022","journal-title":"Proceedings of the 5th Conference on Robot Learning, London, UK, 8\u201311 November 2021"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Nahrendra, I.M.A., Yu, B., and Myung, H. (2023). DreamWaQ: Learning Robust Quadrupedal Locomotion with Implicit Terrain Imagination via Deep Reinforcement Learning. Proceedings of the 2023 IEEE International Conference on Robotics and Automation (ICRA), London, UK, 29 May\u20132 June 2023, IEEE.","DOI":"10.1109\/ICRA48891.2023.10161144"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Kumar, A., Fu, Z., Pathak, D., and Malik, J. (2021, January 12\u201316). RMA: Rapid Motor Adaptation for Legged Robots. Proceedings of the Robotics: Science and Systems XVII, Virtual.","DOI":"10.15607\/RSS.2021.XVII.011"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"eabc5986","DOI":"10.1126\/scirobotics.abc5986","article-title":"Learning Quadrupedal Locomotion over Challenging Terrain","volume":"5","author":"Lee","year":"2020","journal-title":"Sci. Robot."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"eabk2822","DOI":"10.1126\/scirobotics.abk2822","article-title":"Learning Robust Perceptive Locomotion for Quadrupedal Robots in the Wild","volume":"7","author":"Miki","year":"2022","journal-title":"Sci. Robot."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"572","DOI":"10.1177\/02783649231224053","article-title":"Rapid Locomotion via Reinforcement Learning","volume":"43","author":"Margolis","year":"2024","journal-title":"Int. J. Robot. Res."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1038\/s42256-024-00861-3","article-title":"Lifelike Agility and Play in Quadrupedal Robots Using Reinforcement Learning and Generative Pre-Trained Models","volume":"6","author":"Han","year":"2024","journal-title":"Nat. Mach. Intell."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3073","DOI":"10.1038\/s41467-024-47443-w","article-title":"Viability Leads to the Emergence of Gait Transitions in Learning Agile Quadrupedal Locomotion on Challenging Terrains","volume":"15","author":"Shafiee","year":"2024","journal-title":"Nat. Commun."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1141","DOI":"10.1038\/s42256-025-01065-z","article-title":"Learning to Adapt through Bio-Inspired Gait Strategies for Versatile Quadruped Locomotion","volume":"7","author":"Humphreys","year":"2025","journal-title":"Nat. Mach. Intell."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"11262","DOI":"10.1038\/s41598-025-94163-2","article-title":"Hierarchical Reinforcement Learning with Central Pattern Generator for Enabling a Quadruped Robot Simulator to Walk on a Variety of Terrains","volume":"15","author":"Watanabe","year":"2025","journal-title":"Sci. Rep."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"eade2256","DOI":"10.1126\/scirobotics.ade2256","article-title":"Learning Quadrupedal Locomotion on Deformable Terrain","volume":"8","author":"Choi","year":"2023","journal-title":"Sci. Robot."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"eads6192","DOI":"10.1126\/scirobotics.ads6192","article-title":"High-Speed Control and Navigation for Quadrupedal Robots on Complex and Discrete Terrain","volume":"10","author":"Kim","year":"2025","journal-title":"Sci. Robot."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1198","DOI":"10.1038\/s42256-022-00576-3","article-title":"High-Speed Quadrupedal Locomotion by Imitation\u2013Relaxation Reinforcement Learning","volume":"4","author":"Jin","year":"2022","journal-title":"Nat. Mach. Intell."},{"key":"ref_20","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). ANYmal\u2014A Highly Mobile and Dynamic Quadrupedal Robot. Proceedings of the 2016 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Daejeon, Republic of Korea, 9\u201314 October 2016, IEEE.","DOI":"10.1109\/IROS.2016.7758092"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Katz, B., Di Carlo, J., and Kim, S. (2019). Mini Cheetah: A Platform for Pushing the Limits of Dynamic Quadruped Control. Proceedings of the 2019 International Conference on Robotics and Automation (ICRA), Montreal, QC, Canada, 20\u201324 May 2019, IEEE.","DOI":"10.1109\/ICRA.2019.8793865"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2300783","DOI":"10.1002\/aisy.202300783","article-title":"A Review of Quadruped Robots: Structure, Control, and Autonomous Motion","volume":"6","author":"Fan","year":"2024","journal-title":"Adv. Intell. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1278","DOI":"10.1016\/j.jbiomech.2014.02.024","article-title":"The Effect of Centre of Mass Location on Sagittal Plane Moments around the Centre of Mass in Trotting Horses","volume":"47","author":"Hobbs","year":"2014","journal-title":"J. Biomech."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1093\/af\/vfac025","article-title":"The Olympic Motto through the Lens of Equestrian Sports","volume":"12","author":"Hobbs","year":"2022","journal-title":"Anim. Front."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1002\/ar.24407","article-title":"A 60:40 Split: Differential Mass Support in Dogs","volume":"304","author":"Fish","year":"2021","journal-title":"Anat. Rec."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1715","DOI":"10.1242\/jeb.00947","article-title":"Effects of Mass Distribution on the Mechanics of Level Trotting in Dogs","volume":"207","author":"Lee","year":"2004","journal-title":"J. Exp. Biol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1111\/j.1469-7998.1978.tb03334.x","article-title":"Mechanics of Locomotion of Dogs (Canis familiaris) and Sheep (Ovis aries)","volume":"185","author":"Jayes","year":"1978","journal-title":"J. Zool."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Bishop, K.L., Pai, A.K., and Schmitt, D. (2008). Whole Body Mechanics of Stealthy Walking in Cats. PLoS ONE, 3.","DOI":"10.1371\/journal.pone.0003808"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"522","DOI":"10.1242\/jeb.15.4.522","article-title":"The Dynamics of Quadrupedal Walking","volume":"15","author":"Manter","year":"1938","journal-title":"J. Exp. Biol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"12134","DOI":"10.1109\/LRA.2022.3211785","article-title":"Meta Reinforcement Learning for Optimal Design of Legged Robots","volume":"7","author":"Lee","year":"2022","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1611","DOI":"10.1109\/LRA.2023.3234809","article-title":"Learning-Based Design and Control for Quadrupedal Robots with Parallel-Elastic Actuators","volume":"8","author":"Bjelonic","year":"2023","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2697","DOI":"10.1109\/TMECH.2023.3330427","article-title":"Deep Reinforcement Learning Based Co-Optimization of Morphology and Gait for Small-Scale Legged Robot","volume":"29","author":"Chen","year":"2024","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Dr\u0103goi, M.-V., Nisipeanu, I., Puiu, R.-A., Tache, F.-G., Spiridon-Mocioac\u0103, T.-M., Hank, A., and Cristoiu, C. (2025). An Inclusive Offline Learning Platform Integrating Gesture Recognition and Local AI Models. Biomimetics, 10.","DOI":"10.3390\/biomimetics10100693"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/s10514-013-9341-4","article-title":"Centroidal Dynamics of a Humanoid Robot","volume":"35","author":"Orin","year":"2013","journal-title":"Auton. Robot."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1094","DOI":"10.1177\/0278364912452673","article-title":"Capturability-Based Analysis and Control of Legged Locomotion, Part 1: Theory and Application to Three Simple Gait Models","volume":"31","author":"Koolen","year":"2012","journal-title":"Int. J. Robot. Res."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/TRO.2016.2623338","article-title":"ZMP Support Areas for Multicontact Mobility under Frictional Constraints","volume":"33","author":"Caron","year":"2017","journal-title":"IEEE Trans. Robot."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Mason, M.T. (2001). Mechanics of Robotic Manipulation, MIT Press.","DOI":"10.7551\/mitpress\/4527.001.0001"},{"key":"ref_38","unstructured":"Spong, M.W., Hutchinson, S., and Vidyasagar, M. (2006). Robot Modeling and Control, John Wiley & Sons."},{"key":"ref_39","unstructured":"Murray, R.M., Li, Z., and Sastry, S.S. (1994). A Mathematical Introduction to Robotic Manipulation, CRC Press."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Featherstone, R. (2008). Rigid Body Dynamics Algorithms, Springer.","DOI":"10.1007\/978-1-4899-7560-7"},{"key":"ref_41","unstructured":"Schulman, J., Wolski, F., Dhariwal, P., Radford, A., and Klimov, O. (2017). Proximal Policy Optimization Algorithms. arXiv."},{"key":"ref_42","unstructured":"Kingma, D.P., and Welling, M. (2014, January 14\u201316). Auto-Encoding Variational Bayes. Proceedings of the 2nd International Conference on Learning Representations (ICLR), Banff, AB, Canada. Available online: https:\/\/arxiv.org\/abs\/1312.6114."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1117","DOI":"10.1109\/TMECH.2014.2339013","article-title":"Design Principles for Energy-Efficient Legged Locomotion and Implementation on the MIT Cheetah Robot","volume":"20","author":"Seok","year":"2015","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1891","DOI":"10.1109\/TMECH.2022.3170548","article-title":"Unknown Payload Adaptive Control for Quadruped Locomotion With Proprioceptive Linear Legs","volume":"27","author":"Jin","year":"2022","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Dinev, T., Mastalli, C., Ivan, V., Tonneau, S., and Vijayakumar, S. (2022). A Versatile Co-Design Approach for Dynamic Legged Robots. Proceedings of the 2022 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Kyoto, Japan, 23\u201327 October 2022, IEEE.","DOI":"10.1109\/IROS47612.2022.9981378"}],"container-title":["Biomimetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2313-7673\/11\/8\/565\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,7]],"date-time":"2026-08-07T13:30:34Z","timestamp":1786109434000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2313-7673\/11\/8\/565"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,7]]},"references-count":45,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2026,8]]}},"alternative-id":["biomimetics11080565"],"URL":"https:\/\/doi.org\/10.3390\/biomimetics11080565","relation":{},"ISSN":["2313-7673"],"issn-type":[{"value":"2313-7673","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,7]]}}}