{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T09:51:29Z","timestamp":1777715489748,"version":"3.51.4"},"reference-count":68,"publisher":"SAGE Publications","issue":"5","license":[{"start":{"date-parts":[[2015,10,25]],"date-time":"2015-10-25T00:00:00Z","timestamp":1445731200000},"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":[[2016,4]]},"abstract":"<jats:p>\n                    We present the first asymptotically optimal feedback planning algorithm for nonholonomic systems and additive cost functionals. Our algorithm is based on three well-established numerical practices: 1) positive coefficient numerical approximations of the Hamilton-Jacobi-Bellman equations; 2) the Fast Marching Method, which is a fast nonlinear solver that utilizes Bellman\u2019s dynamic programming principle for efficient computations; and 3) an adaptive mesh-refinement algorithm designed to improve the resolution of an initial simplicial mesh and reduce the solution numerical error. By refining the discretization mesh globally, we compute a sequence of numerical solutions that converges to the true viscosity solution of the Hamilton-Jacobi-Bellman equations. In order to reduce the total computational cost of the proposed planning algorithm, we find that it is sufficient to refine the discretization within a small region in the vicinity of the optimal trajectory. Numerical experiments confirm our theoretical findings and establish that our algorithm outperforms previous asymptotically optimal planning algorithms, such as PRM\n                    <jats:sup>*<\/jats:sup>\n                    and RRT\n                    <jats:sup>*<\/jats:sup>\n                    .\n                  <\/jats:p>","DOI":"10.1177\/0278364915602958","type":"journal-article","created":{"date-parts":[[2015,10,26]],"date-time":"2015-10-26T20:18:42Z","timestamp":1445890722000},"page":"565-584","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":13,"title":["Asymptotically optimal feedback planning using a numerical Hamilton-Jacobi-Bellman solver and an adaptive mesh refinement"],"prefix":"10.1177","volume":"35","author":[{"given":"Dmitry S.","family":"Yershov","sequence":"first","affiliation":[{"name":"Massachusetts Institute of Technology, Cambridge, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Emilio","family":"Frazzoli","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology, Cambridge, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2015,10,25]]},"reference":[{"key":"bibr1-0278364915602958","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827597323373"},{"key":"bibr2-0278364915602958","doi-asserted-by":"publisher","DOI":"10.1109\/ICRA.2013.6630906"},{"key":"bibr3-0278364915602958","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-003-2952-3"},{"key":"bibr4-0278364915602958","doi-asserted-by":"publisher","DOI":"10.1137\/0715049"},{"key":"bibr5-0278364915602958","doi-asserted-by":"publisher","DOI":"10.1016\/0378-4754(80)90098-1"},{"key":"bibr6-0278364915602958","doi-asserted-by":"publisher","DOI":"10.1016\/0899-8248(91)90006-G"},{"key":"bibr7-0278364915602958","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1998.6007"},{"key":"bibr8-0278364915602958","unstructured":"Bellman R (1957)\n                      Dynamic Programming\n                      . 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