Implementation of Efficient Algorithms for Globally Optimal Trajectories ∗

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 <2, and minimizes a cost function of the form ∫ T 0 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 [Tsi93]. Here we develop some new label correcting-like methods based on the Small Label First methods of Bertsekas [Ber93], and Bertsekas et. al. [BGM94]. We prove the finite termination of these methods, and we present computational results showing that they are competitive and often superior to the Dijkstra-like method. ∗Research Supported by NSF Grant No 9300494-DMI. †Ph.D. Candidate, Laboratory for Information and Decision Systems, M.I.T., Cambridge, MA, 02139. ‡Professor, Laboratory for Information and Decision Systems, M.I.T., Cambridge, MA, 02139