{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T13:32:14Z","timestamp":1778160734112,"version":"3.51.4"},"reference-count":42,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2011,1,25]],"date-time":"2011-01-25T00:00:00Z","timestamp":1295913600000},"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":[[2011,2]]},"abstract":"<jats:p>We present a novel approach to legged locomotion over rough terrain that is thoroughly rooted in optimization. This approach relies on a hierarchy of fast, anytime algorithms to plan a set of footholds, along with the dynamic body motions required to execute them. Components within the planning framework coordinate to exchange plans, cost-to-go estimates, and \u2018certificates\u2019 that ensure the output of an abstract high-level planner can be realized by lower layers of the hierarchy. The burden of careful engineering of cost functions to achieve desired performance is substantially mitigated by a simple inverse optimal control technique. Robustness is achieved by real-time re-planning of the full trajectory, augmented by reflexes and feedback control. We demonstrate the successful application of our approach in guiding the LittleDog quadruped robot over a variety of types of rough terrain. Other novel aspects of our past research efforts include a variety of pioneering inverse optimal control techniques as well as a system for planning using arbitrary pre-recorded robot behavior.<\/jats:p>","DOI":"10.1177\/0278364910392608","type":"journal-article","created":{"date-parts":[[2011,1,25]],"date-time":"2011-01-25T05:53:25Z","timestamp":1295934805000},"page":"175-191","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":100,"title":["Optimization and learning for rough terrain legged locomotion"],"prefix":"10.1177","volume":"30","author":[{"given":"Matt","family":"Zucker","sequence":"first","affiliation":[{"name":"Department of Engineering, Swarthmore College, 500 College Avenue, Swarthmore, PA 19081, USA,"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nathan","family":"Ratliff","sequence":"additional","affiliation":[{"name":"Intel Research, 4720 Forbes Avenue Suite 410, Pittsburgh, PA 15213, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martin","family":"Stolle","sequence":"additional","affiliation":[{"name":"Google, Inc., Brandschenkestrasse 110, 8002 Z\u00fcrich, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joel","family":"Chestnutt","sequence":"additional","affiliation":[{"name":"Digital Human Research Center, National Institute of Advanced, Industrial Science and Technology, 2-3-26, Aomi, Koto-ku, Tokyo 135-0064, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J Andrew","family":"Bagnell","sequence":"additional","affiliation":[{"name":"The Robotics Institute, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christopher G","family":"Atkeson","sequence":"additional","affiliation":[{"name":"The Robotics Institute, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"James","family":"Kuffner","sequence":"additional","affiliation":[{"name":"Google, Inc., 1600 Amphitheatre Parkway, Mountain View, CA 94043, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2011,1,25]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1002\/rob.8116"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1177\/0278364902021012002"},{"key":"atypb3","volume-title":"Proceedings IEEE\/RSJ International Conference on Intelligent Robots and Systems","author":"Buchli J."},{"key":"atypb4","author":"Buehler M.","year":"2005","journal-title":"Proceedings International Symposium on Adaptive Motion in Animals and Machines"},{"key":"atypb5","volume-title":"Navigation Planning for Legged Robots","author":"Chestnutt J.","year":"2007"},{"key":"atypb6","volume-title":"Proceedings IEEE International Conference on Robotics and Automation","author":"Chestnutt J."},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.2307\/2372560"},{"key":"atypb8","volume-title":"Distance Transforms of Sampled Functions. 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