{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T10:02:32Z","timestamp":1777716152202,"version":"3.51.4"},"reference-count":41,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2024,7,23]],"date-time":"2024-07-23T00:00:00Z","timestamp":1721692800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"name":"D. Dan and Betty Kahn Michigan-Israel Partnership for Research and Education","award":["Autonomous Systems Mega-Project"],"award-info":[{"award-number":["Autonomous Systems Mega-Project"]}]},{"DOI":"10.13039\/100000147","name":"Division of Civil, Mechanical and Manufacturing Innovation","doi-asserted-by":"publisher","award":["CMMI 1825918"],"award-info":[{"award-number":["CMMI 1825918"]}],"id":[{"id":"10.13039\/100000147","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000183","name":"Army Research Office","doi-asserted-by":"publisher","award":["W911NF-17-1-0306"],"award-info":[{"award-number":["W911NF-17-1-0306"]}],"id":[{"id":"10.13039\/100000183","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000183","name":"Army Research Office","doi-asserted-by":"publisher","award":["W911NF-17-1-0243"],"award-info":[{"award-number":["W911NF-17-1-0243"]}],"id":[{"id":"10.13039\/100000183","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000083","name":"Directorate for Computer and Information Science and Engineering","doi-asserted-by":"publisher","award":["CPS 2038432"],"award-info":[{"award-number":["CPS 2038432"]}],"id":[{"id":"10.13039\/100000083","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2025,2]]},"abstract":"<jats:p>Multi-legged robots with six or more legs are not in common use, despite designs with superior stability, maneuverability, and a low number of actuators being available for over 20 years. This may be in part due to the difficulty in modeling multi-legged motion with slipping and producing reliable predictions of body velocity. Here, we present a detailed measurement of the foot contact forces in a hexapedal robot with multiple sliding contacts, and provide an algorithm for predicting these contact forces and the body velocity. The algorithm relies on the recently published observation that even while slipping, multi-legged robots are principally kinematic, and employ a friction law ansatz that allows us to compute the shape-change to body-velocity connection and the foot contact forces. This results in the ability to simulate motion plans for a large number of contacts, each potentially with slipping. Furthermore, in homogeneous environments, this kind of simulation can run in (parallel) logarithmic time of the planning horizon.<\/jats:p>","DOI":"10.1177\/02783649241263114","type":"journal-article","created":{"date-parts":[[2024,7,23]],"date-time":"2024-07-23T13:06:26Z","timestamp":1721739986000},"page":"196-215","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":6,"title":["Modeling multi-legged robot locomotion with slipping and its experimental validation"],"prefix":"10.1177","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4543-6815","authenticated-orcid":false,"given":"Ziyou","family":"Wu","sequence":"first","affiliation":[{"name":"Robotics, University of Michigan, Ann Arbor, MI, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0095-0818","authenticated-orcid":false,"given":"Dan","family":"Zhao","sequence":"additional","affiliation":[{"name":"Mechanical Engineering, University of Michigan, Ann Arbor, MI, USA"},{"name":"Now at RoboForce Inc., CA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shai","family":"Revzen","sequence":"additional","affiliation":[{"name":"Robotics, University of Michigan, Ann Arbor, MI, USA"},{"name":"Ecology and Evolutionary Biology, University of Michigan, Ann Arbor, MI, USA"},{"name":"Applied Physics Program, University of Michigan, Ann Arbor, MI, USA"},{"name":"Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2024,7,23]]},"reference":[{"key":"e_1_3_5_2_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.87.012717"},{"key":"e_1_3_5_3_1","doi-asserted-by":"publisher","unstructured":"BIRDS-Lab (2021a) Birds Lab multipod robot motion tracking data - processed data and code. DOI: 10.7302\/0fpj-dz57.","DOI":"10.7302\/0fpj-dz57"},{"key":"e_1_3_5_4_1","doi-asserted-by":"publisher","unstructured":"BIRDS-Lab (2021b) Birds lab multipod robot motion tracking data - raw dataset. DOI: 10.7302\/m05a-0d90.","DOI":"10.7302\/m05a-0d90"},{"key":"e_1_3_5_5_1","doi-asserted-by":"publisher","unstructured":"BIRDS-Lab (2021c) Birds lab multipod robot motion tracking data - videos. DOI: 10.7302\/1y3q-1b42.","DOI":"10.7302\/1y3q-1b42"},{"key":"e_1_3_5_6_1","doi-asserted-by":"publisher","unstructured":"BIRDS-Lab (2023) Force\/torque bigant processed data. DOI: 10.7302\/1y3q-1b42.","DOI":"10.7302\/1y3q-1b42"},{"key":"e_1_3_5_7_1","volume-title":"Dynamic Walking. Internet: Dynamic Walking","author":"Bittner BA","year":"2020","unstructured":"Bittner BA, Revzen S (2020) A robot made of tree branches can learn to move in 15 minutes. In Dynamic Walking. Internet: Dynamic Walking. URL https:\/\/youtu.be\/iRBT3RkhdTU?t=3656."},{"key":"e_1_3_5_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-018-4466-9"},{"key":"e_1_3_5_9_1","doi-asserted-by":"publisher","unstructured":"Bloesch M Gehring C Fankhauser P et al. (2013) State Estimation for Legged Robots on Unstable and Slippery Terrain. In: 2013 IEEE\/RSJ International Conference on Intelligent Robots and Systems. Tokyo Japan 2013 pp. 6058\u20136064. DOI:10.1109\/IROS.2013.6697236.","DOI":"10.1109\/IROS.2013.6697236"},{"key":"e_1_3_5_10_1","doi-asserted-by":"publisher","unstructured":"Carlton R Bartholet S (1987) The evolution of the application of mobile robotics to nuclear facility operations and maintenance. IEEE International Conference on Robotics and Automation Raleigh NC USA pp. 720\u2013726 DOI: 10.1109\/ROBOT.1987.1087979.","DOI":"10.1109\/ROBOT.1987.1087979"},{"key":"e_1_3_5_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-022-07481-9"},{"key":"e_1_3_5_12_1","doi-asserted-by":"publisher","unstructured":"Chong B Aydin YO Rieser JM et al. (2021) A general locomotion control framework for serially connected multi-legged robots. CoRR abs\/2112.00662. DOI: 10.48550\/arXiv.2112.00662.","DOI":"10.48550\/arXiv.2112.00662"},{"key":"e_1_3_5_13_1","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2207.10604"},{"key":"e_1_3_5_14_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2118456119"},{"key":"e_1_3_5_15_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.106.044404"},{"key":"e_1_3_5_16_1","doi-asserted-by":"crossref","unstructured":"Erez T Tassa Y Todorov E (2015) Simulation tools for model-based robotics: comparison of bullet havok mujoco ode and physx. In: 2015 IEEE International Conference on Robotics and Automation (ICRA). WA USA 2015 IEEE 4397\u20134404.","DOI":"10.1109\/ICRA.2015.7139807"},{"key":"e_1_3_5_17_1","doi-asserted-by":"publisher","DOI":"10.1109\/MRA.2016.2639058"},{"key":"e_1_3_5_18_1","doi-asserted-by":"publisher","DOI":"10.1177\/027836499000900202"},{"key":"e_1_3_5_19_1","doi-asserted-by":"publisher","DOI":"10.1177\/0278364910394392"},{"key":"e_1_3_5_20_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0812533106"},{"key":"e_1_3_5_21_1","doi-asserted-by":"publisher","unstructured":"Kao CJ Chen CS Lin PC (2019) Reactive force analysis and modulation of the individual legs in a running hexapod robot. In: 2019 IEEE\/ASME International Conference on Advanced Intelligent Mechatronics (AIM) Hongkong China 2019 370\u2013375. DOI: 10.1109\/AIM.2019.8868826.","DOI":"10.1109\/AIM.2019.8868826"},{"key":"e_1_3_5_22_1","doi-asserted-by":"publisher","DOI":"10.1177\/0278364906069150"},{"key":"e_1_3_5_23_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-00196-3_36"},{"key":"e_1_3_5_24_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-019-05121-3"},{"key":"e_1_3_5_25_1","doi-asserted-by":"publisher","unstructured":"Lin T Zhang R Yu J et al. (2021) Deep multi-modal contact estimation for invariant observer design on quadruped robots. CoRR abs\/2106.15713. DOI: 10.48550\/arXiv.2106.15713.","DOI":"10.48550\/arXiv.2106.15713"},{"key":"e_1_3_5_26_1","doi-asserted-by":"publisher","DOI":"10.1177\/027836499801700701"},{"key":"e_1_3_5_27_1","unstructured":"Quinn RD Nelson GM Bachmann RJ et al. (2001) Insect designs for improved robot mobility. In: Proceedings of 4th International Conference on Climbing and Walking Robots. Germany 2001 69\u201376."},{"key":"e_1_3_5_28_1","volume-title":"Dynamic Walking","author":"Revzen S","year":"2018","unstructured":"Revzen S, Sachdeva V (2018) Towards a simple model for multi-legged slipping. In: Dynamic Walking. URL https:\/\/youtu.be\/sbAZoN_4BRI."},{"key":"e_1_3_5_29_1","volume-title":"Dynamic Walking. Dynamic Walking","author":"Revzen S","year":"2021","unstructured":"Revzen S, Zhao D, Bittner B, et al. (2021a) Bridging walking and slithering - stokesian locomotion. In: Dynamic Walking. Dynamic Walking."},{"key":"e_1_3_5_30_1","doi-asserted-by":"publisher","DOI":"10.7302\/4323"},{"key":"e_1_3_5_31_1","doi-asserted-by":"publisher","DOI":"10.1177\/02783640122067570"},{"key":"e_1_3_5_32_1","doi-asserted-by":"publisher","DOI":"10.1017\/S002211208900025X"},{"key":"e_1_3_5_33_1","doi-asserted-by":"publisher","unstructured":"Todorov E Erez T Tassa Y (2012) Mujoco: A Physics Engine for Model-Based Control. In: 2012 IEEE\/RSJ International Conference on Intelligent Robots and Systems. Algarve Portugal 2012 pp. 5026\u20135033. DOI:10.1109\/IROS.2012.6386109.","DOI":"10.1109\/IROS.2012.6386109"},{"key":"e_1_3_5_34_1","doi-asserted-by":"publisher","DOI":"10.1098\/rsbl.2018.0137"},{"key":"e_1_3_5_35_1","doi-asserted-by":"publisher","DOI":"10.7302\/7633"},{"key":"e_1_3_5_36_1","doi-asserted-by":"publisher","DOI":"10.1115\/1.4042696.054501"},{"key":"e_1_3_5_37_1","doi-asserted-by":"publisher","DOI":"10.3390\/app13020680"},{"key":"e_1_3_5_38_1","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2014.2382981"},{"key":"e_1_3_5_39_1","doi-asserted-by":"publisher","DOI":"10.1117\/12.2176780"},{"key":"e_1_3_5_40_1","volume-title":"Locomotion of Low-DoF Multi-Legged Robots","author":"Zhao D","year":"2021","unstructured":"Zhao D (2021) Locomotion of Low-DoF Multi-Legged Robots. PhD Thesis. University of Michigan."},{"key":"e_1_3_5_41_1","doi-asserted-by":"publisher","DOI":"10.1088\/1748-3190\/ab84c0"},{"key":"e_1_3_5_42_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2113222119"}],"container-title":["The International Journal of Robotics Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/02783649241263114","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/02783649241263114","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/02783649241263114","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/02783649241263114","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T10:17:30Z","timestamp":1777457850000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/02783649241263114"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,23]]},"references-count":41,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,2]]}},"alternative-id":["10.1177\/02783649241263114"],"URL":"https:\/\/doi.org\/10.1177\/02783649241263114","relation":{},"ISSN":["0278-3649","1741-3176"],"issn-type":[{"value":"0278-3649","type":"print"},{"value":"1741-3176","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7,23]]}}}