{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,27]],"date-time":"2026-06-27T15:32:12Z","timestamp":1782574332516,"version":"3.54.5"},"reference-count":24,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"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":[[2009,1]]},"abstract":"<jats:p>The shortest paths for a mobile robot are a fundamental property of the mechanism, and may also be used as a family of primitives for motion planning in the presence of obstacles. This paper characterizes shortest paths for differential-drive mobile robots, with the goal of classifying solutions in the spirit of Dubins curves and Reeds\u2014Shepp curves for car-like robots. To obtain a well-defined notion of shortest , the total amount of wheel-rotation is optimized. Using the Pontryagin Maximum Principle and other tools, we derive the set of optimal paths, and we give a representation of the extremals in the form of finite automata. It turns out that minimum time for the Reeds\u2014Shepp car is equal to minimum wheel-rotation for the differential-drive, and minimum time curves for the convexified Reeds\u2014Shepp car are exactly the same as minimum wheel-rotation paths for the differential-drive. It is currently unknown whether there is a simpler proof for this fact.<\/jats:p>","DOI":"10.1177\/0278364908096750","type":"journal-article","created":{"date-parts":[[2009,1,5]],"date-time":"2009-01-05T07:13:19Z","timestamp":1231139599000},"page":"66-80","source":"Crossref","is-referenced-by-count":52,"title":["Minimum Wheel-Rotation Paths for Differential-Drive Mobile Robots"],"prefix":"10.1177","volume":"28","author":[{"given":"Hamidreza","family":"Chitsaz","sequence":"first","affiliation":[{"name":"201 N Goodwin Ave Urbana Illinois United States 61801,"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Steven M.","family":"LaValle","sequence":"additional","affiliation":[{"name":"201 N Goodwin Ave Urbana Illinois United States 61801,"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Devin J.","family":"Balkcom","sequence":"additional","affiliation":[{"name":"Dartmouth Computer Science Department Sudikoff Lab: HB 6211 Hanover, NH 03755 USA,"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Matthew T.","family":"Mason","sequence":"additional","affiliation":[{"name":"Carnegie Mellon University, School of Computer Science 5000 Forbes Avenue Pittsburgh PA 15213-3891,"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2009,1,1]]},"reference":[{"key":"atypb1","volume-title":"Proceedings of the ACM Symposium on Computational Geometry","author":"Agarwal, P.K."},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1177\/027836402320556403"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1177\/0278364906069166"},{"key":"atypb4","volume-title":"Proceedings of the ACM Symposium on Computational Geometry","author":"Boissonnat, J.-D."},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8165-5"},{"key":"atypb6","volume-title":"IEEE International Conference on Robotics and Automation","author":"Chitsaz, H."},{"key":"atypb7","volume-title":"IEEE International Conference on Robotics and Automation","author":"Chitsaz, H."},{"key":"atypb8","volume-title":"IEEE International Conference on Methods and Models in Automation and Robotics","author":"Chitsaz, H."},{"key":"atypb9","first-page":"1669","volume":"3","author":"Chyba, M.","year":"1999","journal-title":"IEEE\/RSJ International Conference on Intelligent Robots & Systems"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1177\/027836499801700504"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.2307\/2372560"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511546877"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1177\/027836499601500103"},{"key":"atypb14","volume-title":"The Mathematical Theory of Optimal Processes","author":"Pontryagin, L.S.","year":"1962"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1990.145.367"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1177\/027836499401300103"},{"key":"atypb17","volume-title":"IEEE International Conference on Robotics and Automation","author":"Renaud, M."},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0036072"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1109\/9.489204"},{"key":"atypb20","volume-title":"Proccedings of the 36th IEEE Conference on Decision and Control","author":"Sussmann, H."},{"key":"atypb21","volume-title":"Shortest paths for the Reeds-Shepp car: A worked out example of the use of geometric techniques in nonlinear optimal control. 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