| Summary: | Fast Marching is a widely used method in path planning, especially continuity is demanded due to kinodynamic constraints of automatic vehicles. However, its application in real environment with obstacles and perturbations requires simplifications to be made, resulting in non-optimal or even unfeasible path. We introduce a risk function ζ to describe the effect of obstacles to the safety of a generated path. Combined with the physical law based description of external flow perturbation, we formulate the path planning problem in realistic environment as a wave front propagation in terms of an extended Eikonal equation. Inspired by the underlying mechanism of the numerical recipe of Fast Marching algorithm, we transform the equation into its canonical form based on the physical rules behind. This enables solutions of the equation without any simplification nor introduction of additional complexity. Comparing to the classical fast marching based method in anisotropic environment, numerical simulations show that the proposed method is more efficient and robust to external flow perturbations, especially in the case of weak or strong external flow environment.
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