{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T21:52:06Z","timestamp":1759701126698},"reference-count":22,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2007,3,22]],"date-time":"2007-03-22T00:00:00Z","timestamp":1174521600000},"content-version":"vor","delay-in-days":6199,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Robotic Syst."],"published-print":{"date-parts":[[1990,4]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Crab walking is as important as forward walking as applied to walking machine control. Crab walking is especially important to a quadruped since a quadruped has a similar leg geometric layout in both longitudinal and lateral directions. In the studies of forward walking gaits, the wave gait was found to be the optimally stable. In this article, the wave gait is applied to the crab walking of a quadruped and it is modified into four types of wave\u2010crab gaits according to the range of crab angle. The stability formulae of these wave\u2010crab gaits are then derived analytically based on the following three stability measurements: stability margin (<jats:italic>S<\/jats:italic><jats:italic><jats:sub>m<\/jats:sub><\/jats:italic>), body\u2010longitudinal (or lateral) stability margin (<jats:italic>S<\/jats:italic><jats:sub>bl<\/jats:sub> or <jats:italic>S<\/jats:italic><jats:sub>bt<\/jats:sub>) and crab longitudinal stability margin (<jats:italic>S<\/jats:italic><jats:sub>cl<\/jats:sub>). <jats:italic>S<\/jats:italic><jats:sub>m<\/jats:sub> is the true stability index under quasi\u2010static walking condition. However, the equations are more complicated. <jats:italic>S<\/jats:italic><jats:sub>bl<\/jats:sub> (or <jats:italic>S<\/jats:italic><jats:sub>bt<\/jats:sub>) is simpler and can be used as a good approximation of <jats:italic>S<\/jats:italic><jats:sub>m<\/jats:sub>. <jats:italic>S<\/jats:italic><jats:sub>cl<\/jats:sub> was commonly adopted as the stability index in the previous gait studies. Nevertheless, <jats:italic>S<\/jats:italic><jats:sub>cl<\/jats:sub> is found to be misleading for a large portion of crab angle range. The analytical results derived in this paper are useful to the geometric design and to the real\u2010time control of a quadruped.<\/jats:p>","DOI":"10.1002\/rob.4620070208","type":"journal-article","created":{"date-parts":[[2007,7,6]],"date-time":"2007-07-06T09:50:09Z","timestamp":1183715409000},"page":"243-276","source":"Crossref","is-referenced-by-count":56,"title":["Stability analysis of wave\u2010crab gaits of a quadruped"],"prefix":"10.1002","volume":"7","author":[{"given":"Chang\u2010De","family":"Zhang","sequence":"first","affiliation":[]},{"given":"Shin\u2010Min","family":"Song","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2007,3,22]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Animals in Motion","author":"Muybridge E.","year":"1957"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(68)90090-4"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.150.3697.701"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(68)90007-2"},{"key":"e_1_2_1_6_2","volume-title":"The basic motion regulation system for a quadruped walking machine","author":"Hirose S.","year":"1980"},{"key":"e_1_2_1_7_2","volume-title":"Proceedings of Symposium on Theory and Practice of Robots and Manipulators","author":"Bessenov A. 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S.Sun \u201cA theoretical study of gaits for legged locomotion system \u201d Ph.D. Dissertation The Ohio State University Columbus Ohio March1974."}],"container-title":["Journal of Robotic Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Frob.4620070208","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/rob.4620070208","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T16:12:41Z","timestamp":1697991161000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/rob.4620070208"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,4]]},"references-count":22,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1990,4]]}},"alternative-id":["10.1002\/rob.4620070208"],"URL":"https:\/\/doi.org\/10.1002\/rob.4620070208","archive":["Portico"],"relation":{},"ISSN":["0741-2223","1097-4563"],"issn-type":[{"value":"0741-2223","type":"print"},{"value":"1097-4563","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,4]]}}}