A comparative study of implementing Fast Marching Method and A* SEARCH for mobile robot path planning in grid environment: Effect of map resolution

Theoretically both of Fast Marching Method (FMM) and A* SEARCH have the same time complexity of O(N log N) , where N is the number of grid points in a map, and guarantee to find an optimal solution if this path exists. This paper examines the effect of alteration of resolution of map on the performance of path planning by A* and FMM on 2D rectangular grid environments. Our observations on the basis of comparative simulations in three test environments at different resolutions are that: A* is more focused and thus faster to generate a polygonal line (continuous but not smooth) path, while FMM generates a better curvature-control, generally smoother and shorter path that is a numerically consistent approximation to the true shortest continuous path as the resolution of map is finer and finer. The difference of path quality for these two methods is more significant as the resolution is finer.