{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T21:28:47Z","timestamp":1772832527394,"version":"3.50.1"},"reference-count":57,"publisher":"SAGE Publications","issue":"13","license":[{"start":{"date-parts":[[2013,10,21]],"date-time":"2013-10-21T00:00:00Z","timestamp":1382313600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2013,11]]},"abstract":"<jats:p> Contact mechanics plays an important role in the design, performance analysis, simulation, and control of legged robots. The Hunt\u2013Crossley model and the Coulomb friction model are often used as black-box models with limited consideration of the properties of the terrain and the feet. This paper analyzes the foot\u2013terrain interaction based on the knowledge of terramechanics and reveals the relationship between the parameters of the conventional models and the terramechanics models. The proposed models are derived in three categories: deformable foot on hard terrain, hard foot on deformable terrain, and deformable foot on deformable terrain. A novel model of tangential forces as the function of displacement is proposed on the basis of an in-depth understanding of the terrain properties. Methods for identifying the model parameters are also developed. Extensive foot\u2013soil interaction experiments have been carried out, and the experimental results validate the high fidelity of the derived models. <\/jats:p>","DOI":"10.1177\/0278364913498122","type":"journal-article","created":{"date-parts":[[2013,10,22]],"date-time":"2013-10-22T01:24:25Z","timestamp":1382405065000},"page":"1585-1606","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":147,"title":["Foot\u2013terrain interaction mechanics for legged robots: Modeling and experimental validation"],"prefix":"10.1177","volume":"32","author":[{"given":"Liang","family":"Ding","sequence":"first","affiliation":[{"name":"State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin, Heilongjiang, the People\u2019s Republic of China."}]},{"given":"Haibo","family":"Gao","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin, Heilongjiang, the People\u2019s Republic of China."}]},{"given":"Zongquan","family":"Deng","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin, Heilongjiang, the People\u2019s Republic of China."}]},{"given":"Jianhu","family":"Song","sequence":"additional","affiliation":[{"name":"Antenna and Servo Department, the 54th Research Institute of China Electronics Technology Group Corporation, Shijiazhuang, Hebei, the People\u2019s Republic of China."}]},{"given":"Yiqun","family":"Liu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin, Heilongjiang, the People\u2019s Republic of China."}]},{"given":"Guangjun","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Aerospace Engineering, Ryerson University, Toronto, ON, Canada."}]},{"given":"Karl","family":"Iagnemma","sequence":"additional","affiliation":[{"name":"Laboratory for Manufacturing and Productivity, Massachusetts Institute of Technology, Cambridge, MA, USA"}]}],"member":"179","published-online":{"date-parts":[[2013,10,21]]},"reference":[{"key":"bibr1-0278364913498122","unstructured":"Ackerman E (2012) DARPA selects Boston Dynamics\u2019 humanoid for robotics challenge. http:\/\/spectrum.ieee.org\/automaton\/robotics\/humanoids\/darpa-selects-boston-dynamics-humanoid-for-robotics-challenge (accessed 1 September 2012)."},{"key":"bibr2-0278364913498122","volume-title":"Introduction to terrain\u2013vehicle systems","author":"Bekker G","year":"1969"},{"key":"bibr3-0278364913498122","doi-asserted-by":"publisher","DOI":"10.1109\/IROS.2005.1545529"},{"key":"bibr4-0278364913498122","unstructured":"BostonDynamics (2012a) LS3\u2014Legged Squad Support Systems. http:\/\/www.bostondynamics.com\/robot_ls3.html (accessed 1 September 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