{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T06:14:58Z","timestamp":1776320098456,"version":"3.50.1"},"reference-count":28,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2009,7,27]],"date-time":"2009-07-27T00:00:00Z","timestamp":1248652800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000145","name":"Division of Information and Intelligent Systems","doi-asserted-by":"publisher","award":["HCC-0811902"],"award-info":[{"award-number":["HCC-0811902"]}],"id":[{"id":"10.13039\/100000145","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2009,7,27]]},"abstract":"<jats:p>We present a fully automatic method for generating gaits and morphologies for legged animal locomotion. Given a specific animal's shape we can determine an efficient gait with which it can move. Similarly, we can also adapt the animal's morphology to be optimal for a specific locomotion task. We show that determining such gaits is possible without the need to specify a good initial motion, and without manually restricting the allowed gaits of each animal. Our approach is based on a hybrid optimization method which combines an efficient derivative-aware spacetime constraints optimization with a derivative-free approach able to find non-local solutions in high-dimensional discontinuous spaces. We demonstrate the effectiveness of this approach by synthesizing dynamic locomotions of bipeds, a quadruped, and an imaginary five-legged creature.<\/jats:p>","DOI":"10.1145\/1531326.1531366","type":"journal-article","created":{"date-parts":[[2009,7,28]],"date-time":"2009-07-28T12:43:55Z","timestamp":1248785035000},"page":"1-8","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":104,"title":["Optimal gait and form for animal locomotion"],"prefix":"10.1145","volume":"28","author":[{"given":"Kevin","family":"Wampler","sequence":"first","affiliation":[{"name":"University of Washington"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zoran","family":"Popovi\u0107","sequence":"additional","affiliation":[{"name":"University of Washington"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2009,7,27]]},"reference":[{"key":"e_1_2_2_1_1","volume-title":"Optima for Animals","author":"Alexander M.","unstructured":"Alexander , M. 1996. Optima for Animals . Princeton University Press . Alexander, M. 1996. Optima for Animals. Princeton University Press."},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/225294.225295"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882286"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144504446096"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/280814.280816"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/1276377.1276512"},{"key":"e_1_2_2_7_1","doi-asserted-by":"crossref","unstructured":"H&amp;#228;kkinen K. and Keskinen K. L. 2006. Muscle cross-sectional area and voluntary force production characteristics in elite strength- and endurance-trained athletes and sprinters. European Journal of Applied Physiology (Apr) 215--220.  H&amp;#228;kkinen K. and Keskinen K. L. 2006. Muscle cross-sectional area and voluntary force production characteristics in elite strength- and endurance-trained athletes and sprinters. European Journal of Applied Physiology (Apr) 215--220.","DOI":"10.1007\/BF02386190"},{"key":"e_1_2_2_8_1","doi-asserted-by":"crossref","unstructured":"Hansen N. and \n      Kern S\n  . \n  2004\n  . Evaluating the CMA evolution strategy on multimodal test functions. In Parallel Problem Solving from Nature PPSN VIII Springer X. Yao et al. Eds. vol. \n  3242\n   of \n  LNCS 282--291.  Hansen N. and Kern S. 2004. Evaluating the CMA evolution strategy on multimodal test functions. In Parallel Problem Solving from Nature PPSN VIII Springer X. Yao et al. Eds. vol. 3242 of LNCS 282--291.","DOI":"10.1007\/978-3-540-30217-9_29"},{"key":"e_1_2_2_9_1","unstructured":"Hansen N. Hansen N. Ostermeier A. and Ostermeier A. 1996. Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation. Morgan Kaufmann 312--317.  Hansen N. Hansen N. Ostermeier A. and Ostermeier A. 1996. Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation. Morgan Kaufmann 312--317."},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/1360612.1360626"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/258734.258822"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1038\/440292a"},{"key":"e_1_2_2_13_1","doi-asserted-by":"crossref","unstructured":"Koh B.-I. Reinbolt J. A. George A. D. Haftka R. T. and Fregly B. J. 2008. Limitations of parallel global optimization for large-scale human movement problems. Medical Engineering and Physics.  Koh B.-I. Reinbolt J. A. George A. D. Haftka R. T. and Fregly B. J. 2008. Limitations of parallel global optimization for large-scale human movement problems. Medical Engineering and Physics .","DOI":"10.1016\/j.medengphy.2008.09.010"},{"key":"e_1_2_2_14_1","volume-title":"-P","author":"Kry P. G.","year":"2009","unstructured":"Kry , P. G. , Reveret , L. , Faure , F. , and Cani , M . -P . 2009 . Modal locomotion: Animating virtual characters with natural vibrations. Computer Graphics Forum . Kry, P. G., Reveret, L., Faure, F., and Cani, M.-P. 2009. Modal locomotion: Animating virtual characters with natural vibrations. Computer Graphics Forum."},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/192161.192169"},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073314"},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.5555\/1218064.1218093"},{"key":"e_1_2_2_18_1","volume-title":"In Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS2001","author":"Paul A.","unstructured":"Paul , A. , and Bongard , J. C . 2001. The road less travelled: Morphology in the optimization of biped robot locomotion . In In Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS2001 , IEEE Press, 226--232. Paul, A., and Bongard, J. C. 2001. The road less travelled: Morphology in the optimization of biped robot locomotion. In In Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS2001, IEEE Press, 226--232."},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/311535.311536"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/122718.122755"},{"key":"e_1_2_2_21_1","doi-asserted-by":"crossref","unstructured":"Rose C. Guenter B. Bodenheimer B. and Cohen M. F. 1996. Efficient generation of motion transitions using spacetime constraints. 147--154.  Rose C. Guenter B. Bodenheimer B. and Cohen M. F. 1996. Efficient generation of motion transitions using spacetime constraints. 147--154.","DOI":"10.1145\/237170.237229"},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/1015706.1015754"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/192161.192167"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1038\/nature04113"},{"key":"e_1_2_2_25_1","volume-title":"On Growth and Form: The Complete Revised Edition","author":"Thompson D. W.","unstructured":"Thompson , D. W. 1992. On Growth and Form: The Complete Revised Edition . Dover . Thompson, D. W. 1992. On Growth and Form: The Complete Revised Edition. Dover."},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1109\/38.486679"},{"key":"e_1_2_2_27_1","unstructured":"Weibel E. R. Tayor C. R. and Bolis L. 1998. Principles of Animal Design. Cambridge University Press.  Weibel E. R. Tayor C. R. and Bolis L. 1998. Principles of Animal Design . Cambridge University Press."},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1145\/54852.378507"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1531326.1531366","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1531326.1531366","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T12:23:12Z","timestamp":1750249392000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1531326.1531366"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,7,27]]},"references-count":28,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2009,7,27]]}},"alternative-id":["10.1145\/1531326.1531366"],"URL":"https:\/\/doi.org\/10.1145\/1531326.1531366","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,7,27]]},"assertion":[{"value":"2009-07-27","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}