Implementation of efficient algorithms for globally optimal trajectories Export

@article{citeulike:2795191, abstract = {We consider a continuous space shortest path problem in a two-dimensional plane. This is the problem of finding a trajectory that starts at a given point, ends at the boundary of a compact set of \ℜ ², and minimizes a cost function of the form \∫_O^T r(x(t)) dt+q(x(T)). For a discretized version of this problem, a Dijkstra-like method that requires one iteration per discretization point has been developed by Tsitsiklis (1995). Here we develop some new label correcting-like methods based on the small label first methods of Bertsekas (1993) and Bertsekas et al. (1996). We prove the finite termination of these methods, and present computational results showing that they are competitive and often superior to the Dijkstra-like method and are also much faster than the traditional Jacobi and Gauss-Seidel methods}, author = {Polymenakos, L. C. and Bertsekas, D. P. and Tsitsiklis, J. N.}, booktitle = {Automatic Control, IEEE Transactions on}, citeulike-article-id = {2795191}, citeulike-linkout-0 = {http://dx.doi.org/10.1109/9.661081}, citeulike-linkout-1 = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=661081}, doi = {10.1109/9.661081}, journal = {Automatic Control, IEEE Transactions on}, keywords = {dijktsra, distance, eikonal, fast, geodesic, marching, optimal, path}, number = {2}, pages = {278--283}, posted-at = {2008-05-13 15:41:14}, priority = {5}, title = {Implementation of efficient algorithms for globally optimal trajectories}, url = {http://dx.doi.org/10.1109/9.661081}, volume = {43}, year = {1998} }

TY - JOUR ID - citeulike:2795191 L3 - citeulike-article-id:2795191 N2 - We consider a continuous space shortest path problem in a two-dimensional plane. This is the problem of finding a trajectory that starts at a given point, ends at the boundary of a compact set of ℜ ², and minimizes a cost function of the form ∫_O^T r(x(t)) dt+q(x(T)). For a discretized version of this problem, a Dijkstra-like method that requires one iteration per discretization point has been developed by Tsitsiklis (1995). Here we develop some new label correcting-like methods based on the small label first methods of Bertsekas (1993) and Bertsekas et al. (1996). We prove the finite termination of these methods, and present computational results showing that they are competitive and often superior to the Dijkstra-like method and are also much faster than the traditional Jacobi and Gauss-Seidel methods IS - 2 JF - Automatic Control, IEEE Transactions on EP - 283 TI - Implementation of efficient algorithms for globally optimal trajectories VL - 43 T2 - Automatic Control, IEEE Transactions on SP - 278 KW - dijktsra KW - distance KW - eikonal KW - fast KW - geodesic KW - marching KW - optimal KW - path AU - Polymenakos, LC AU - Bertsekas, DP AU - Tsitsiklis, JN PY - 1998/// UR - http://dx.doi.org/10.1109/9.661081 ER -