Numerical algorithms for continuous optimal trajectories

We consider the problem of computing minimum-cost trajectories in continuous space. We focus on two classes of problems: isotropic cost problems where the cost depends only on the position, and anisotropic cost problems where the cost depends on the position and direction of the trajectory. Using stochastic control discretization, we evaluate the performance of different value iteration techniques for solving the dynamic programming equations. For isotropic problems, our results show that the recently developed fast-sweeping algorithms offer significant computation advantages over Dijkstra-type algorithms and adaptive label correcting algorithms. However, for anisotropic problems, adaptive label correcting algorithms are fastest. We also investigate the accuracy of discrete graph approximations, and approaches for computing the optimal continuous trajectories from the discrete stochastic control solution.