{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T09:55:57Z","timestamp":1777715757740,"version":"3.51.4"},"reference-count":43,"publisher":"SAGE Publications","issue":"6","license":[{"start":{"date-parts":[[2000,6,1]],"date-time":"2000-06-01T00:00:00Z","timestamp":959817600000},"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":[[2000,6]]},"abstract":"<jats:p>A new control strategy is used to stabilize numerical simulations of a horse model in the trotting quadrupedal gait. Several well-established experimental findings are predicted by the model, including how stride frequency and stride length change with forward running speed. Mass is distributed throughout the model's legs, trunk, and head in a realistic manner. Leg and trunk flexion is modeled using four flexible legs, a back joint, and a neck joint. In the control model, pitch stabilization is achieved without directly controlling body pitch, but rather by controlling both the aerial time and the foot speed of each stance leg. The legs behave as ideal springs while in contact with the ground, enabling the model to rebound from the ground with each trotting step. Numerical experiments are conducted to test the model's capacity to overcome a change in ground impedance. Model stability is maximized and the metabolic cost of trotting is minimized within a narrow range of leg stiffness where trotting horses of similar body size have been observed to operate. This work suggests that a horselike robot will exhibit behavior that is mechanically similar to that of a trotting horse if it operates in a narrow range of leg stiffness and employs simple control strategies where postural stabilization is an emergent property of the system.<\/jats:p>","DOI":"10.1177\/027836490001900602","type":"journal-article","created":{"date-parts":[[2004,12,17]],"date-time":"2004-12-17T20:23:10Z","timestamp":1103314990000},"page":"566-581","source":"Crossref","is-referenced-by-count":53,"title":["A Trotting Horse Model"],"prefix":"10.1177","volume":"19","author":[{"given":"Hugh M.","family":"Herr","sequence":"first","affiliation":[{"name":"The Leg Laboratory, Massachusetts Institute of Technology, 545 Technology                         Square, NE43-006, Cambridge, Massachusetts 02139, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thomas A.","family":"McMahon","sequence":"additional","affiliation":[{"name":"Division of Engineering and Applied Science, Harvard University, Pierce                         Hall 322, Cambridge, Massachusetts 02138, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2000,6,1]]},"reference":[{"key":"atypb1","unstructured":"Alexander, R. McN. 1977. Mechanics and scaling of terrestrial locomotion. In Scale Effects in Animal Locomotion, ed. T. J. Pedley, 93-110. New York: Academic Press ."},{"key":"atypb2","doi-asserted-by":"crossref","unstructured":"Alexander, R. McN. 1985. Elastic structures in the back and their role in galloping in some mammals . J. Zool. Lond. (A) 207: 467-482 .","DOI":"10.1111\/j.1469-7998.1985.tb04944.x"},{"key":"atypb3","unstructured":"Bair, I. R. 1959. Amphibious walking vehicle. U.S. Patent number 2,918,738."},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1126\/science.2740914"},{"key":"atypb5","doi-asserted-by":"crossref","unstructured":"Cavagna, G. A., Heglund, N. C., and Taylor, C. R. 1977. Mechanical work in terrestrial locomotion: Two basic mechanisms for minimizing energy expenditure . Am. J. Physiol. 233: R243-R261 .","DOI":"10.1152\/ajpregu.1977.233.5.R243"},{"key":"atypb6","unstructured":"Corson, P. E. 1958. Walking tractor. U.S. Patent number 2,822,878."},{"key":"atypb7","unstructured":"Ehrlich, A. 1928. Vehicle propelled by steppers. US Patent number 1,691,233."},{"key":"atypb8","unstructured":"Eyzaguirre, C., and Fidone, S. J. 1975. Physiology of the nervous system. 2d ed. Year Book Medical. Chicago, IL ."},{"key":"atypb9","doi-asserted-by":"crossref","unstructured":"Farley, C. T., Glasheen, J., and McMahon, T. A. 1993. Running springs: Speed and animal size . J. Exp. Biol. 185: 71-86 .","DOI":"10.1242\/jeb.185.1.71"},{"key":"atypb10","doi-asserted-by":"crossref","unstructured":"Fedak, M. A., Heglund, N. C., and Taylor, C. R. 1982. Energetics and mechanics of terrestrial locomotion II. Kinetic energy changes of the limbs and body as a function of speed and body size in birds and mammals . J. Exp. Biol. 79: 23-40 .","DOI":"10.1242\/jeb.97.1.23"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1007\/BF02477183"},{"key":"atypb12","unstructured":"Gray, J. 1968. Animal Locomotion. London: Weidenfeld & Nicolson ."},{"key":"atypb13","doi-asserted-by":"crossref","unstructured":"Gubina, F., Hemami, H., and McGhee, R. B. 1974. On the dynamic stability of biped locomotion . IEEE Trans. Biomedical Engineering BME 21: 102-108 .","DOI":"10.1109\/TBME.1974.324294"},{"key":"atypb14","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? J.xp. Biol. 138: 301-318 .","DOI":"10.1242\/jeb.138.1.301"},{"key":"atypb15","unstructured":"Herr, M. H. 1998.\n                      A Model of Mammalian Quadrupedal Running.\n                      Ph.D. thesis, Harvard University, Department of Biophysics."},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1038\/292239a0"},{"key":"atypb17","unstructured":"Kinch, E. A. 1928. Vehicle propelling device. U.S. Patent number 1,669,906."},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1038\/346265a0"},{"key":"atypb19","unstructured":"Lucas, E. 1894. Huitieme recreation-la machine a marcher . Recreations Mathematiques 4: 198-204 ."},{"key":"atypb20","doi-asserted-by":"crossref","unstructured":"Manter, J. 1938. Dynamics of quadrupedal walking . J. Exp. Biol. 15: 522-539 .","DOI":"10.1242\/jeb.15.4.522"},{"key":"atypb21","unstructured":"McGeer, T. 1989. Passive bipedal running. Technical report CCS-IS TR 89-02, Simon Fraser University ."},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1177\/027836499000900206"},{"key":"atypb23","unstructured":"McGhee, R. B., and Kuhner, M. B. 1969. On the dynamic stability of legged locomotion systems. In Advances in External Control of Human Extremities, ed. M. M. Gavrilovic and A. B. Wilson, Jr, 431-442. Belgrade: Jugoslav Committee for Electronics and Automation ."},{"key":"atypb24","doi-asserted-by":"crossref","unstructured":"McMahon, T. A. 1985. The role of compliance in mammalian running gaits . J. Exp. Biol. 115: 263-282 .","DOI":"10.1242\/jeb.115.1.263"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9290(90)90042-2"},{"key":"atypb26","doi-asserted-by":"crossref","unstructured":"Miura, H., and Shimoyama, I. 1980. Computer control of an unstable mechanism . J. Fac. Eng. 17: 12-13 .","DOI":"10.1109\/MC.1980.1653453"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1177\/027836498400300206"},{"key":"atypb28","unstructured":"Morrison, R. A. 1968. Iron mule train . Proceedings of Off Road Mobility Research Symposium, International Society for Terrain Vehicle Systems, Washington, DC, pp. 381-400 ."},{"key":"atypb29","unstructured":"Muybridge, E. 1979. Muybridge's Complete Human and Animal Locomotion, vol. 3. New York: Dover ."},{"key":"atypb30","unstructured":"Nilson, F. A. 1926. Supporting and propelling mechanism for motor vehicles. US Patent number 1,574,679."},{"key":"atypb31","unstructured":"Raibert, M. H. 1985. Four-legged running with one-legged algorithms. In Second International Symposium on Robotics Research, ed. H. Hanafusa and H. Inoue, 311-315. Cambridge, MA: MIT Press ."},{"key":"atypb32","doi-asserted-by":"crossref","unstructured":"Raibert, M. H. 1986. Legged Robots That Balance. Cambridge, MA: MIT Press .","DOI":"10.1109\/MEX.1986.4307016"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9290(90)90043-3"},{"key":"atypb34","unstructured":"Ringrose, R. 1997.\n                      SellfStabilizing Running.\n                      Ph.D. thesis, MIT, Department of EECS."},{"key":"atypb35","unstructured":"Roberts, T. J. 1995.\n                      Running Economically: Form, Gait, and Muscle Mechanics.\n                      Ph.D. thesis, Harvard University, Department of Organismal and Evolutionary Biology."},{"key":"atypb36","unstructured":"Roberts. T. J. 1997, February. Personal data collection."},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1126\/science.275.5303.1113"},{"key":"atypb38","unstructured":"Rosenthal, D. E., and Sherman, M. A. 1986. High performance multibody simulations via symbolic equation manipulation and Kane's method . Journal of Astronautical Sciences 34(3): 223-239 ."},{"key":"atypb39","unstructured":"Rygg, L. A. 1893. Mechanical horse. US Patent number 491,927."},{"key":"atypb40","unstructured":"Snell, E. 1947. Reciprocating load carrier. U.S. Patent number 2,430,537."},{"key":"atypb41","unstructured":"Urschel, W. E. 1949. Walking tractor. U.S. Patent number 2,491,064."},{"key":"atypb42","doi-asserted-by":"crossref","unstructured":"Vukobratovic, M. 1973. 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