{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T04:10:12Z","timestamp":1791346212771,"version":"4.3.1"},"reference-count":61,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"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":[[2017,1]]},"abstract":"<jats:p>Quasistatic legged locomotion over uneven terrains requires characterization of the legged robot equilibrium postures as well as an understanding of the non-static motion modes that can develop at the contacts. This paper characterizes the frictional multi-legged equilibrium postures on a generic class called \u2018tame stances\u2019, which satisfy a generalized support polygon principle. To characterize the equilibrium postures, the paper lumps the legged mechanism\u2019s kinematic structure into a rigid body having a variable center of mass and maintaining the same contacts with the terrain. The equilibrium postures associated with a given set of contacts correspond to the locations of the center of mass at which the body is supported in static equilibrium by the same contacts under the influence of gravity. This paper thus characterizes the feasible equilibrium region of a rigid body having a variable center of mass and supported by multiple frictional contacts under the influence of gravity. The paper establishes that the feasible equilibrium region forms a convex set which has five types of boundary curves. These boundary curves are formulated analytically, illustrated with graphical examples, and associated with the onset of five non-static motion modes at the contacts. The paper also compares the analytical results against experimental measurements conducted on a legged mechanism prototype.<\/jats:p>","DOI":"10.1177\/0278364916679719","type":"journal-article","created":{"date-parts":[[2017,1,21]],"date-time":"2017-01-21T12:11:38Z","timestamp":1485000698000},"page":"105-128","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":12,"title":["Characterization of frictional multi-legged equilibrium postures on uneven terrains"],"prefix":"10.1177","volume":"36","author":[{"given":"Yizhar","family":"Or","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Technion, Israel Institute of Technology, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Elon","family":"Rimon","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Technion, Israel Institute of Technology, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2017,1,19]]},"reference":[{"key":"bibr1-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1177\/02783649922066475"},{"key":"bibr2-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1177\/02783640122068119"},{"key":"bibr3-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539797326289"},{"key":"bibr4-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1109\/ROBOT.2006.1641858"},{"key":"bibr5-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2008.2001360"},{"key":"bibr6-0278364916679719","doi-asserted-by":"publisher","DOI":"10.15607\/RSS.2015.XI.028"},{"key":"bibr7-0278364916679719","first-page":"41","volume":"10","author":"Dandurand A","year":"1984","journal-title":"Structural Topology"},{"key":"bibr8-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511530173"},{"key":"bibr9-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1177\/027836499801700502"},{"key":"bibr10-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1177\/027836499601500203"},{"key":"bibr11-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1109\/ICRA.2012.6224670"},{"key":"bibr12-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1109\/TRA.2002.999649"},{"key":"bibr13-0278364916679719","volume-title":"Differential Topology","author":"Guillemin V","year":"1974"},{"key":"bibr14-0278364916679719","unstructured":"Guizzo E, Ackerman E (2012) DARPA Robotics challenge: Here are the official details. Available at: http:\/\/spectrum.ieee.org\/automaton\/robotics\/humanoids\/darpa-robotics-challenge-here-are-the-official-details"},{"key":"bibr15-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1109\/70.897778"},{"key":"bibr16-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1177\/0278364908098447"},{"key":"bibr17-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1109\/ROBOT.1998.677288"},{"key":"bibr18-0278364916679719","first-page":"310","volume-title":"International conference on robotics and systems (IROS)","author":"Hirose M","year":"2001"},{"key":"bibr19-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1115\/1.2179462"},{"key":"bibr20-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1109\/IROS.2011.6094465"},{"key":"bibr21-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1177\/027836499601500204"},{"key":"bibr22-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1109\/ROBOT.2001.932631"},{"key":"bibr23-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-007-9244-z"},{"key":"bibr24-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1109\/ROBOT.2002.1014295"},{"key":"bibr25-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1007\/s10846-012-9670-0"},{"key":"bibr26-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1002\/zamm.19810611202"},{"key":"bibr27-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1177\/027836499601500602"},{"key":"bibr28-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1109\/ROBOT.1992.220257"},{"key":"bibr29-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1109\/ROBOT.1997.620082"},{"key":"bibr30-0278364916679719","volume-title":"Robots Hands and the Mechanics of Manipulation","author":"Mason MT","year":"1985"},{"key":"bibr31-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1109\/ROBOT.1988.12105"},{"key":"bibr32-0278364916679719","volume-title":"Introduction to Theoretical Kinematics","author":"McCarthy JM","year":"1990"},{"key":"bibr33-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(68)90090-4"},{"key":"bibr34-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.1979.4310180"},{"key":"bibr35-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1109\/ROBOT.1994.351378"},{"key":"bibr36-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1177\/0278364910387457"},{"key":"bibr37-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1177\/0278364910390538"},{"key":"bibr38-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1177\/027836498800700301"},{"key":"bibr39-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1109\/70.833187"},{"key":"bibr40-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1177\/0278364906072038"},{"key":"bibr41-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1177\/0278364909347783"},{"key":"bibr42-0278364916679719","volume-title":"Computation of frictional multi-contact equilibrium stances and postures on 3D uneven tame terrains","author":"Or Y","year":"2014"},{"key":"bibr43-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1109\/ROBOT.2000.844083"},{"key":"bibr44-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1109\/ROBOT.2001.932951"},{"key":"bibr45-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1109\/ROBOT.2007.363870"},{"key":"bibr46-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1177\/027836499701600102"},{"key":"bibr47-0278364916679719","first-page":"1601","volume-title":"IEEE international conference on robotics and automation","author":"Prete AD","year":"2016"},{"key":"bibr48-0278364916679719","first-page":"671","volume-title":"IEEE international conference on robotics and automation","author":"Rajan VT","year":"1987"},{"key":"bibr49-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1109\/ROBOT.2007.363191"},{"key":"bibr50-0278364916679719","first-page":"103","volume-title":"IEEE international conference on robotics and automation","author":"Schlegl T","year":"2001"},{"key":"bibr51-0278364916679719","volume-title":"15th international symposium on robotics research (ISRR)","author":"Sentis L","year":"2011"},{"key":"bibr52-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2014.2305792"},{"key":"bibr53-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1109\/70.938387"},{"key":"bibr54-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1109\/ROBOT.2003.1241572"},{"key":"bibr55-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1109\/ROBOT.2009.5152768"},{"key":"bibr56-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-016-3247-6"},{"key":"bibr57-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1142\/S0219843604000083"},{"key":"bibr58-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1002\/rob.20193"},{"key":"bibr59-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1109\/ROBOT.2004.1307172"},{"key":"bibr60-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1177\/0278364904042194"},{"key":"bibr61-0278364916679719","doi-asserted-by":"publisher","DOI":"10.1109\/ROBOT.2002.1014811"}],"container-title":["The International Journal of Robotics Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0278364916679719","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/0278364916679719","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0278364916679719","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T10:15:24Z","timestamp":1777457724000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/0278364916679719"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1]]},"references-count":61,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["10.1177\/0278364916679719"],"URL":"https:\/\/doi.org\/10.1177\/0278364916679719","relation":{},"ISSN":["0278-3649","1741-3176"],"issn-type":[{"value":"0278-3649","type":"print"},{"value":"1741-3176","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1]]}}}