{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T09:59:34Z","timestamp":1777715974228,"version":"3.51.4"},"reference-count":41,"publisher":"SAGE Publications","issue":"10-11","license":[{"start":{"date-parts":[[2004,10,1]],"date-time":"2004-10-01T00:00:00Z","timestamp":1096588800000},"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":[[2004,10]]},"abstract":"<jats:p>In this paper we present the system design of a machine that we have constructed to study a quadrupedal gallop gait. The gallop gait is the preferred high-speed gait of most cursorial quadrupeds. To gallop, an animal must generate ballistic trajectories with characteristic strong impacts, coordinate leg movements with asymmetric footfall phasing, and effectively use compliant members, all the while maintaining dynamic stability. In this paper we seek to further understand the primary biological features necessary for galloping by building and testing a robotic quadruped similar in size to a large goat or antelope. These features include high-speed actuation, energy storage, on-line learning control, and high-performance attitude sensing. Because body dynamics are primarily influenced by the impulses delivered by the legs, the successful design and control of single leg energetics is a major focus of this work. The leg stores energy during flight by adding tension to a spring acting across an articulated knee. During stance, the spring energy is quickly released using a novel capstan design. As a precursor to quadruped control, two intelligent strategies have been developed for verification on a one-legged system. The Levenberg-Marquardt on-line learning method is applied to a simple heuristic controller and provides good control over height and forward velocity. Direct adaptive fuzzy control, which requires no system modeling but is more computationally expensive, exhibits better response. Using these techniques we have been successful in operating one leg at speeds necessary for a dynamic gallop of a machine of this scale. Another necessary component of quadruped locomotion is high-resolution and high-bandwidth attitude sensing. The large ground impact accelerations, which cause problems for any single traditional sensor, are overcome through the use of an inertial sensing approach using updates from optical sensors and vehicle kinematics.<\/jats:p>","DOI":"10.1177\/0278364904047391","type":"journal-article","created":{"date-parts":[[2004,9,27]],"date-time":"2004-09-27T01:22:25Z","timestamp":1096248145000},"page":"1013-1027","source":"Crossref","is-referenced-by-count":94,"title":["System Design of a Quadrupedal Galloping Machine"],"prefix":"10.1177","volume":"23","author":[{"given":"J. Gordon","family":"Nichol","sequence":"first","affiliation":[{"name":"Stanford University, 424 Panama Mall, Bldg 560, Stanford, CA 94305, USA,"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Surya P.N.","family":"Singh","sequence":"additional","affiliation":[{"name":"Stanford University, 424 Panama Mall, Bldg 560, Stanford, CA 94305, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kenneth J.","family":"Waldron","sequence":"additional","affiliation":[{"name":"Stanford University, 424 Panama Mall, Bldg 560, Stanford, CA 94305, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"suffix":"III","given":"Luther R.","family":"Palmer","sequence":"additional","affiliation":[{"name":"Ohio State University, Department of Electrical and Computer Engineering,                         2015 Neil Avenue, Columbus, OH 43210, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David E.","family":"Orin","sequence":"additional","affiliation":[{"name":"Ohio State University, Department of Electrical and Computer Engineering,                         2015 Neil Avenue, Columbus, OH 43210, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2004,10,1]]},"reference":[{"key":"atypb1","unstructured":"Alexander, R.M. 1988. Elastic Mechanisms in Animal Movement, Cambridge University Press, Cambridge ."},{"key":"atypb2","unstructured":"Analytic Sciences Corporation, Technical Staff. 1974. Applied Optimal Estimation, A. Gelb, editor, MIT Press, Cambridge, MA ."},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"Alexander, R.M., and Jayes, A.S. 1983. A dynamic similarity hypothesis for the gaits of quadrupedal mammals . Journal of Zoology, London 201: 135-152 .","DOI":"10.1111\/j.1469-7998.1983.tb04266.x"},{"key":"atypb4","doi-asserted-by":"crossref","unstructured":"Alexander, R.M. 1985. Body support, scaling, and allometry. Functional Vertebrate Morphology, M. Hildebrandet al., editors, Belknap Press, Cambridge , pp. 26-37.","DOI":"10.4159\/harvard.9780674184404.c2"},{"key":"atypb5","unstructured":"Ashley, C.W. 1953. The Ashley Book of Knots, Doubleday, New York ."},{"key":"atypb6","doi-asserted-by":"crossref","unstructured":"Bachmann, E., Yun, X., and McGhee, R. 2003. Sourceless tracking of human posture using small inertial\/magnetic sensors . Proceedings of the IEEE International Symposium on Computational Intelligence in Robotics and Automation, Kobe, Japan, pp. 822-829 .","DOI":"10.1109\/CIRA.2003.1222286"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1109\/70.388775"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1109\/84.982867"},{"key":"atypb9","unstructured":"Bingelis, A. 1986. Sportplane Construction Techniques, Sportplane Builder Publications, Austin, TX ."},{"key":"atypb10","doi-asserted-by":"crossref","unstructured":"Brown, H.B. Jr and Zeglin, G. 1998. The bow leg hopping robot . Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Leuven, Belgium, pp. 781-786 .","DOI":"10.1109\/ROBOT.1998.677072"},{"key":"atypb11","unstructured":"DeMan, H., Lefeber, D., and Vermeulen, J. 1998. Design and control of a robot with one articulated leg forlocomotion on irregular terrain . Proceedings of the12th CISM-IFToMM Symposium on Theory and Practice of Robots and Manipulators, Vienna, Austria, Springer-Verlag, Berlin, pp. 417-424 ."},{"key":"atypb12","unstructured":"Department of Defense. 2004. Metallic Materials and Elements for Aerospace Vehicle Structures, MIL-HDBK-5H."},{"key":"atypb13","unstructured":"Federal Aviation Administration. 2004. Acceptable Methods, Techniques, and Practices\u2014Aircraft Inspection and Repair, AC43.13-1B."},{"key":"atypb14","unstructured":"Gambaryan, P.P. 1974. How Mammals Run: Anatomical Adaptations, Wiley, New York ."},{"key":"atypb15","doi-asserted-by":"crossref","unstructured":"Heglund, N.C., and Taylor, C.R. 1988. Speed, stride frequency and energy cost per stride: how do they change with body size and gait? Journal of Experimental Biology 138: 301-318 .","DOI":"10.1242\/jeb.138.1.301"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1126\/science.186.4169.1112"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.2307\/1379571"},{"key":"atypb18","unstructured":"Honeywell International, Inc. 2002. Spectra Fiber 2000. Available at http:\/\/www.spectrafiber.com\/pdfs\/hon-pfps10-sp2000.pdf."},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1038\/292239a0"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1038\/422493a"},{"key":"atypb21","unstructured":"Jang, J.S.R., and Mizutani, E. 1996. Levenberg-Marquardt learning for ANFIS learning . Proceedings of the 1996 Biennial Conference of the North American Fuzzy Information Processing Society, Berkeley, CA, pp. 87-91 ."},{"key":"atypb22","doi-asserted-by":"crossref","unstructured":"Jenkins, F.A. 1971. Limb posture and locomotion in the Virginia opossum (Didelphis marsupialis) and in other noncursorial mammals . Journal of Zoology, London 165: 303-315 .","DOI":"10.1111\/j.1469-7998.1971.tb02189.x"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008924521542"},{"key":"atypb24","unstructured":"Marhefka, D.W. 2000.\n                      Fuzzy Control and Dynamic Simulation of a Quadruped Galloping Machine\n                      , PhD Thesis, Ohio State University."},{"key":"atypb25","doi-asserted-by":"crossref","unstructured":"Marhefka, D.W., and Orin, D.E. 2000. Fuzzy control of quadrupedal running . Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), San Francisco, CA, pp. 3063-3069 .","DOI":"10.1109\/ROBOT.2000.846493"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1109\/TMECH.2003.820001"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1016\/0921-8890(95)00089-5"},{"key":"atypb28","doi-asserted-by":"crossref","unstructured":"Necsulescu, D., Sasiadek, J., Kim, B., and Green, D. 1993. Fusion of inertial and kinematic navigation systems for autonomous vehicles . Proceedings of the IEEE-IEE Conference on Vehicle Navigation and Information Systems, pp. 462-465 .","DOI":"10.1109\/VNIS.1993.585672"},{"key":"atypb29","unstructured":"Nichol, J.G., and Waldron, K.J. 2002. Biomimetic leg design for untethered quadruped gallop . Proceedings of the 5th International Conference on Climbing and Walking Robots, Paris, France, pp. 49-54 ."},{"key":"atypb30","doi-asserted-by":"crossref","unstructured":"Palmer, L., Orin, D., Marhefka, D., Schmiedeler, J., and Waldron, K. 2003. Intelligent control of an experimental articulated leg for a galloping machine . Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Taipei, Taiwan, pp. 3821-3827 .","DOI":"10.1109\/ROBOT.2003.1242183"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1115\/1.3108436"},{"key":"atypb32","unstructured":"Poulakakis, I., Smith, J.A., and Buehler, M. 2003. On the dynamics of bounding and extensions towards the half-bound and the gallop gaits . Proceedings of the 2nd International Symposium of Adaptive Motion in Animals and Machines (AMAM), Japan."},{"key":"atypb33","doi-asserted-by":"crossref","unstructured":"Raibert, M.H. 1986. Legged Robots that Balance, MIT Press, Cambridge, MA .","DOI":"10.1109\/MEX.1986.4307016"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9290(90)90043-3"},{"key":"atypb35","doi-asserted-by":"crossref","unstructured":"Raibert, M., Chepponis, M., and Brown, B. 1986. Running on four legs as though they were one . IEEE Journal of Robotics and Automation 2(2): 270-282 .","DOI":"10.1109\/JRA.1986.1087044"},{"key":"atypb36","doi-asserted-by":"publisher","DOI":"10.1017\/S0952836902000353"},{"key":"atypb37","unstructured":"Schmiedeler, J.P. 2001.\n                      The Mechanics of and Robotic Design for Quadrupedal Galloping\n                      . PhD dissertation, Department of Mechanical Engineering, Ohio State University."},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.1177\/02783649922067825"},{"key":"atypb39","doi-asserted-by":"crossref","unstructured":"Schmiedeler, J.P., and Waldron, K.J. 2000. Impact analysis as a design tool for the legs of mobile robots. Advances in Robot Kinematics, J. Lenarcic and M.M. Stanisic, editors, Kluwer Academic, Dortrecht , pp. 129-136.","DOI":"10.1007\/978-94-011-4120-8_14"},{"key":"atypb40","doi-asserted-by":"crossref","unstructured":"Schmiedeler, J.P., and Waldron, K.J. 2002. Leg stiffness and articulated leg design for dynamic locomotion . Proceedings of the ASME International Design Engineering Technical Conferences, Montreal, Canada, Vol. 5B, pp. 1105-1112 .","DOI":"10.1115\/DETC2002\/MECH-34331"},{"key":"atypb41","doi-asserted-by":"crossref","unstructured":"Waldron, K., Arkin, R., Bakkum, D., Merril, E., and Abdallah, M. 2003. Proprioceptive control for a robotic vehicle over geometric obstacles . Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Taipei, Taiwan, pp. 109-114 .","DOI":"10.1109\/ROBOT.2003.1241581"}],"container-title":["The International Journal of Robotics Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0278364904047391","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0278364904047391","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T10:17:02Z","timestamp":1777457822000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/0278364904047391"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,10]]},"references-count":41,"journal-issue":{"issue":"10-11","published-print":{"date-parts":[[2004,10]]}},"alternative-id":["10.1177\/0278364904047391"],"URL":"https:\/\/doi.org\/10.1177\/0278364904047391","relation":{},"ISSN":["0278-3649","1741-3176"],"issn-type":[{"value":"0278-3649","type":"print"},{"value":"1741-3176","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,10]]}}}