{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T09:46:30Z","timestamp":1777715190536,"version":"3.51.4"},"reference-count":26,"publisher":"SAGE Publications","issue":"6","license":[{"start":{"date-parts":[[1991,12,1]],"date-time":"1991-12-01T00:00:00Z","timestamp":691545600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[1991,12]]},"abstract":"<jats:p>This article offers some analytical results concerning sim plified models of Raibert's hopper. We represent the task of achieving a recurring hopping height for an actuated \"ball\" robot as a stability problem in a nonlinear discrete dynamical control system. We model the properties of Raibert's control scheme in a simplified fashion and argue that his strategy leads to closed-loop dynamics governed by a well-known class of functions, the unimodal maps. The rich mathematical literature on this subject greatly advances our ability to determine the presence of an essentially globally attracting fixed point-the formal ren dering of what we intuitively mean by a \"correct\" strat egy. The motivation for this work is the hope that it will facilitate the development of general design principles for \"dynamically dexterous\" robots.<\/jats:p>","DOI":"10.1177\/027836499101000601","type":"journal-article","created":{"date-parts":[[2007,3,4]],"date-time":"2007-03-04T20:24:06Z","timestamp":1173039846000},"page":"587-605","source":"Crossref","is-referenced-by-count":197,"title":["Analysis of a Simplified Hopping Robot"],"prefix":"10.1177","volume":"10","author":[{"given":"Daniel E.","family":"Koditschek","sequence":"first","affiliation":[{"name":"Center for Systems Science Department of Electrical Engineering Yale University New Haven, Connecticut 06520-1968"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martin","family":"B\u00fchler","sequence":"additional","affiliation":[{"name":"Center for Systems Science Department of Electrical Engineering Yale University New Haven, Connecticut 06520-1968"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[1991,12,1]]},"reference":[{"key":"atypb1","first-page":"1290","author":"Aboaf, E.W.","year":"1989","journal-title":"Proc. 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