Level set and Fat Fast Marching Method for normal and dynamic path planning of pursuit-evasion problem

This paper proposes a modified version of the Fast Marching Method (FMM), called Fat Fast Marching Method (FFMM), which produces a much more accurate path than the path generated by the original FMM with the approximated ODE solution. Given a complicated environment which has a long optimal path and a very large maximum cost value that results in high gradients, FFMM is faster than FMM. Furthermore, the tree structure result, a TP diagram of FFMM with path recovery rules, makes dynamic path planning of pursuit-evasion problems possible. By providing the shortest path produced by the path recovery rules in every time slot and the avoidance of re-planning in most situations, the pursuer now has a greater chance to intercept the evader in real time spectrum.