{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T10:03:49Z","timestamp":1777716229265,"version":"3.51.4"},"reference-count":33,"publisher":"SAGE Publications","issue":"5","license":[{"start":{"date-parts":[[2012,3,28]],"date-time":"2012-03-28T00:00:00Z","timestamp":1332892800000},"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":[[2012,4]]},"abstract":"<jats:p>The speed and maneuverability at which legged animals can travel across rough and cluttered landscapes has provided inspiration for the development of legged robots with similar capabilities. Researchers have developed a number of robots that can run over rough terrain, but there is currently no universally accepted measure for stability in an unstructured environment. This paper considers the effectiveness of a number of stability metrics in predicting the disturbance-rejection behavior of three spring-loaded inverted pendulum (SLIP)-like systems ranging from simple reduced-order models to a one-legged mechanical hopping robot. We show that the gait stability norm utilizing leg-centric indicators and a two-step decay ratio utilizing body-centric indicators provide the best correlation between step response behavior and how the systems perform when running over unknown, uneven terrain. By providing a cross-platform stability comparison, this paper facilitates the development and evaluation of robots and control schemes, such as the active energy removal approach utilized in this paper, that aim to improve the stability of running systems.<\/jats:p>","DOI":"10.1177\/0278364912439613","type":"journal-article","created":{"date-parts":[[2012,3,28]],"date-time":"2012-03-28T22:52:56Z","timestamp":1332975176000},"page":"573-587","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":18,"title":["Quantifying disturbance rejection of SLIP-like running systems"],"prefix":"10.1177","volume":"31","author":[{"given":"Bruce","family":"Miller","sequence":"first","affiliation":[{"name":"Florida State University, Mechanical Engineering, Florida, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"John","family":"Schmitt","sequence":"additional","affiliation":[{"name":"Bend Research, Inc., Bend, Oregon, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jonathan E","family":"Clark","sequence":"additional","affiliation":[{"name":"Florida State University, Mechanical Engineering, Florida, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2012,3,28]]},"reference":[{"key":"bibr1-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1111\/j.1469-7998.1975.tb05983.x"},{"key":"bibr2-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1023\/A:1012426720699"},{"key":"bibr3-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1088\/1748-3182\/6\/2\/026009"},{"key":"bibr4-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1007\/BF00197760"},{"key":"bibr5-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1109\/ROBOT.1998.677408"},{"key":"bibr6-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1177\/0278364909340446"},{"key":"bibr7-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1152\/ajpregu.1977.233.5.R243"},{"key":"bibr8-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1177\/0278364902021010837"},{"key":"bibr9-0278364912439613","volume-title":"proceedings of the 9th international conference on climbing and walking robots","author":"Clark J","year":"2006"},{"key":"bibr10-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0601473103"},{"key":"bibr11-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.01986"},{"key":"bibr12-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1155\/2009\/743713"},{"key":"bibr13-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.202.23.3325"},{"key":"bibr14-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1093\/icb\/42.1.149"},{"key":"bibr15-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1137\/S1111111102408311"},{"key":"bibr16-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2007.904908"},{"key":"bibr17-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.205.18.2803"},{"key":"bibr18-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1177\/0278364911408631"},{"key":"bibr19-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1177\/02783649922066655"},{"key":"bibr20-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1098\/rspb.1990.0030"},{"key":"bibr21-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1177\/027836499000900206"},{"key":"bibr22-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1109\/MEX.1986.4307016"},{"key":"bibr23-0278364912439613","doi-asserted-by":"publisher","DOI":"10.3182\/20080706-5-KR-1001.01833"},{"key":"bibr24-0278364912439613","unstructured":"Revzen S (2009) Neuromechanical control architectures in arthropod locomotion. PhD thesis, University of California, Berkeley."},{"key":"bibr25-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1115\/1.2338650"},{"key":"bibr26-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1115\/DETC2007-35740"},{"key":"bibr27-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1088\/1748-3182\/4\/4\/046005"},{"key":"bibr28-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1007\/s004220000181"},{"key":"bibr29-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9290(01)00245-7"},{"key":"bibr30-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.00463"},{"key":"bibr31-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.012385"},{"key":"bibr32-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1115\/1.2800760"},{"key":"bibr33-0278364912439613","doi-asserted-by":"publisher","DOI":"10.1109\/ROBOT.2004.1307381"}],"container-title":["The International Journal of Robotics Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0278364912439613","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0278364912439613","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T10:17:44Z","timestamp":1777457864000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/0278364912439613"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3,28]]},"references-count":33,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2012,4]]}},"alternative-id":["10.1177\/0278364912439613"],"URL":"https:\/\/doi.org\/10.1177\/0278364912439613","relation":{},"ISSN":["0278-3649","1741-3176"],"issn-type":[{"value":"0278-3649","type":"print"},{"value":"1741-3176","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,3,28]]}}}