{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T11:46:09Z","timestamp":1770551169224,"version":"3.49.0"},"reference-count":47,"publisher":"SAGE Publications","issue":"8","license":[{"start":{"date-parts":[[2005,8,1]],"date-time":"2005-08-01T00:00:00Z","timestamp":1122854400000},"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":[[2005,8]]},"abstract":"<jats:p>\n                    <jats:italic toggle=\"yes\">We analyze a simple model for running: a three-dimensional spring-loaded                     inverted pendulum carrying a point mass (3D-SLIP). Our formulation reduces to                     the sagittal plane SLIP and horizontal plane lateral leg spring (LLS) models in                     the appropriate limits. Using the intrinsic geometry and symmetries and                     appealing to the case of stiff springs, in which gravity may be neglected during                     stance, we derive an explicit approximate mapping describing stride-to-stride                     behavior. We thereby show that all left-right symmetric periodic gaits are                     unstable, deriving a particularly simple mapping for sagittal plane dynamics.                     Continuation to fixed points for the \u201cexact\u201d mapping                     confirms instability of these gaits, and we describe a simple feedback                     stabilization scheme for leg placement at touchdown.<\/jats:italic>\n                  <\/jats:p>","DOI":"10.1177\/0278364905056194","type":"journal-article","created":{"date-parts":[[2005,8,15]],"date-time":"2005-08-15T09:28:04Z","timestamp":1124098084000},"page":"657-674","source":"Crossref","is-referenced-by-count":100,"title":["Running in Three Dimensions: Analysis of a Point-mass Sprung-leg Model"],"prefix":"10.1177","volume":"24","author":[{"given":"Justin E.","family":"Seipel","sequence":"first","affiliation":[{"name":"Department of Mechanical and Aerospace Engineering, Princeton University,                         Princeton, NJ 08544, USA"}]},{"given":"Philip","family":"Holmes","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Aerospace Engineering, and Program in                         Applied and Computational Mathematics, Princeton University, Princeton, NJ                         08544, USA"}]}],"member":"179","published-online":{"date-parts":[[2005,8]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"crossref","unstructured":"Altendorfer R. Saranli U. Komsuoglu H. Koditschek D. E. Brown B. Buehler M. Moore E. McMordie D. and Full R. J. 2002. Evidence for spring loaded inverted pendulum running in a hexapod robot. Experimental Robotics VII Springer-Verlag Berlin pp. 291-302.","DOI":"10.1007\/3-540-45118-8_30"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1177\/0278364904047389"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1177\/0278364904047390"},{"key":"e_1_2_1_4_1","doi-asserted-by":"crossref","unstructured":"Back A. Guckenheimer J. and Myers M. 1993. A dynamical simulation facility for hybrid systems. Lecture Notes in Computer Science Springer-Verlag Berlin Vol. 736 pp. 255-267.","DOI":"10.1007\/3-540-57318-6_32"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9290(00)00101-9"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9290(89)90224-8"},{"key":"e_1_2_1_7_1","first-page":"509","volume":"173","year":"1993","unstructured":"Blickhan, R. and Full, R. J. 1993. Similarity in multi-legged locomotion: bouncing like a monopode . Journal of Comparative Physiology A 173: 509-517 .","journal-title":"Journal of Comparative Physiology A"},{"key":"e_1_2_1_8_1","unstructured":"Carver S. 2003. Control of a Spring Mass Hopper. Ph.D. Thesis Cornell University."},{"key":"e_1_2_1_9_1","first-page":"R243","volume":"233","year":"1977","unstructured":"Cavagna, G. A., Heglund, N. C., and Taylor, C. R. 1977. Mechanical work in terrestrial locomotion: two basic mechanisms for minimizing energy expenditure . American Journal of Physiology 233(5): R243-R261 .","journal-title":"American Journal of Physiology"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1177\/0278364902021010837"},{"key":"e_1_2_1_11_1","first-page":"1","volume":"4","year":"1999","unstructured":"Coleman, M. J. and Holmes, P. 1999. Motions and stability of a piecewise holonomic system: the discrete Chaplygin sleigh . Regular and Chaotic Dynamics 4(2): 1-23 .","journal-title":"Regular and Chaotic Dynamics"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.80.3658"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1080\/02681119708806242"},{"key":"e_1_2_1_14_1","first-page":"1082","volume":"305","year":"2005","unstructured":"Collins, S. H., Ruina, A., Tedrake, R., and Wisse, M. 2005. Efficient bipedal robots based on passive-dynamic walkers . Science 305: 1082-1085 .","journal-title":"Science"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127491000397"},{"key":"e_1_2_1_16_1","unstructured":"Dudek D. M. and Full R.J. 2005. Resilience and impedance of legs in running insects. Manuscript in preparation."},{"key":"e_1_2_1_17_1","first-page":"181","volume":"29","year":"1995","unstructured":"Farley, C. T. and Gonz\u00e1lez, O. 1995. Leg stiffness and stride frequency in human running . Journal of Biomechanics 29(2): 181-186 .","journal-title":"Journal of Biomechanics"},{"key":"e_1_2_1_18_1","doi-asserted-by":"crossref","unstructured":"Full R. J. and Farley C. T. 2000. Musculoskeletal dynamics in rhythmic systems\u2014A comparative approach to legged locomotion. Biomechanics and Neural Control of Movement J. M. Winters and P. E. Crago editors Springer-Verlag New York pp. 192-205.","DOI":"10.1007\/978-1-4612-2104-3_13"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.202.23.3325"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1115\/1.2798313"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2004.08.015"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1111111102408311"},{"key":"e_1_2_1_22_2","doi-asserted-by":"crossref","unstructured":"(Updated version to appear as SIGEST featured article in 2005 SIAM Review 47(3)).","DOI":"10.1137\/SIREAD000047000003000517000001"},{"key":"e_1_2_1_23_1","unstructured":"Goldstein H. 1980. Classical Mechanics 2nd edition Addison-Wesley Reading MA ."},{"key":"e_1_2_1_24_1","unstructured":"Guckenheimer J. and Holmes P. 1990. Nonlinear Oscillations Dynamical Systems and Bifurcations of Vector Fields Springer-Verlag New York ."},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1177\/027836499101000601"},{"key":"e_1_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.asd.2004.06.003"},{"key":"e_1_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1098\/rstb.1999.0437"},{"key":"e_1_2_1_28_1","doi-asserted-by":"publisher","DOI":"10.1177\/02783649922066655"},{"key":"e_1_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.1098\/rspb.1990.0030"},{"key":"e_1_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1177\/027836499000900206"},{"key":"e_1_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9290(90)90042-2"},{"key":"e_1_2_1_32_1","doi-asserted-by":"publisher","DOI":"10.1177\/0278364904050917"},{"key":"e_1_2_1_33_1","doi-asserted-by":"crossref","unstructured":"Raibert M. 1986. Legged Robots that Balance MIT Press Cambridge MA .","DOI":"10.1109\/MEX.1986.4307016"},{"key":"e_1_2_1_34_1","doi-asserted-by":"crossref","unstructured":"Ringrose R. 1997. Self-stabilizing running . Proceedings of the IEEE International Conference on Robotics and Automation Albuquerque NM pp. 487-493 .","DOI":"10.1109\/ROBOT.1997.620084"},{"key":"e_1_2_1_35_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0034-4877(98)80006-2"},{"key":"e_1_2_1_36_1","doi-asserted-by":"crossref","unstructured":"Saranli U. and Koditschek D. E. 2003. Template based control of hexapedal running . Proceedings of the IEEE International Conference on Robotics and Automation Taipei Taiwan Vol. 1 pp. 1374-1379 .","DOI":"10.1109\/ROBOT.2003.1241783"},{"key":"e_1_2_1_37_1","doi-asserted-by":"publisher","DOI":"10.1177\/02783640122067570"},{"key":"e_1_2_1_38_1","doi-asserted-by":"publisher","DOI":"10.1007\/s004220000181"},{"key":"e_1_2_1_39_1","doi-asserted-by":"publisher","DOI":"10.1007\/s004220000180"},{"key":"e_1_2_1_40_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00422-001-0300-3"},{"key":"e_1_2_1_41_1","unstructured":"Schwind W. J. 1998. Spring Loaded Inverted Pendulum Running: A Plant Model. Ph.D. Thesis University of Michigan at Ann Arbor."},{"key":"e_1_2_1_42_1","doi-asserted-by":"publisher","DOI":"10.1007\/s004530010001"},{"key":"e_1_2_1_43_1","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1007\/s00422-004-0498-y","volume":"91","year":"2004","unstructured":"Seipel, J., Holmes, P., and Full, R. J. 2004. Dynamics and stability of insect locomotion: a hexapedal model for horizontal plane motions . Biological Cybernetics 91: 76-90 .","journal-title":"Biological Cybernetics"},{"key":"e_1_2_1_44_1","unstructured":"Seipel J. and Holmes P. 2005. Three-dimensional dynamics of multi-legged runners. Manuscript in preparation."},{"key":"e_1_2_1_45_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127491000026"},{"key":"e_1_2_1_46_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9290(01)00245-7"}],"container-title":["The International Journal of Robotics Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0278364905056194","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0278364905056194","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T05:18:43Z","timestamp":1767676723000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/0278364905056194"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,8]]},"references-count":47,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2005,8]]}},"alternative-id":["10.1177\/0278364905056194"],"URL":"https:\/\/doi.org\/10.1177\/0278364905056194","relation":{},"ISSN":["0278-3649","1741-3176"],"issn-type":[{"value":"0278-3649","type":"print"},{"value":"1741-3176","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,8]]}}}