Optimal path planning under full state and map knowledge is often accomplished using some variant of Dijkstra's algorithm, despite the fact that it represents the path domain as a discrete graph rather than as a continuous space. We compare Dijkstra's discrete algorithm with a variant (often called the Fast Marching Method) which more accurately treats the underlying continuous space. Analytically, both generate a value function free of local minima, so that optimal path generation merely requires gradient descent. We also investigate the use of optimality metrics other than Euclidean distance for both algorithms. These different norms better represent optimal paths for some types of problems, as demonstrated by planning optimal collision-free paths for multiple robot scenarios. More details can be found in our ICRA 2006 paper and our SINUM paper.
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|One robot in a 2D world. The contours of the value function are shown.||Two robots in a 2D world. The blue robot's goal is on the right and the red robot's goal is on the left.|