Parallel Shortest Paths Methods for Globally Optimal Trajectories

In this paper we consider a special type of trajectory optimization problem that can be viewed as a continuous-space analog of the classical shortest path problem. This problem is approached by space discretization and solution of a discretized version of the associated Hamilton-Jacobi equation. It was recently shown by Tsitsiklis [1] that some of the ideas of classical shortest path methods, such as those underlying Dijkstra's algorithm, can be applied to solve the discretized Hamilton-Jacobi equation. In more recent work, Polymenakos, Bertsekas and Tsitsiklis [2] have carried this analogy further to show that some efficient label correcting methods for shortest path problems, the SLF and SLF/LLL methods of [3] and [4], can be fruitfully adapted to solve the discretized Hamilton-Jacobi equation. In this paper we discuss parallel asynchronous implementations of these methods on a shared memory multiprocessor, the Alliant FX/80. Our results show that these methods are well suited for parallelization and achieve excellent speedup.