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The fast marching method (FMM) has proved to be a very efficient algorithm for solving the isotropic Eikonal equation. Because it is a minor modification of Dijkstra's algorithm for finding the shortest path through a discrete graph, FMM is also easy to implement. In this paper we describe a new class of Hamilton–Jacobi (HJ) PDEs with axis-aligned… (More)

We define a-causal discretization of static convex Hamilton-Jacobi Partial Differential Equations (HJ PDEs) such that the solution value at a grid node is dependent only on solution values that are smaller by at least. We develop a Monotone Acceptance Ordered Upwind Method (MAOUM) that first determines a consistent,-causal stencil for each grid node and… (More)

— We present an efficient dynamic programming algorithm to solve the problem of optimal multi-location robot rendezvous. The rendezvous problem considered can be struc-tured as a tree, with each node representing a meeting of robots, and the algorithm computes optimal meeting locations and connecting robot trajectories. The tree structure is exploited by… (More)

— We present a semi-parametric control policy representation and use it to solve a series of nonholonomic control problems with input state spaces of up to 7 dimensions. A nearest-neighbor control policy is represented by a set of nodes that induce a Voronoi partitioning of the input space. The Voronoi cells then define local control actions. Direct policy… (More)

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