Globally Optimal Path Planning with Anisotropic Running Costs.

摘要

There are many diverse numerical methods that can be applied to solving path planning problems, however, most of these are either not valid or impractical for solving anisotropic (direction-dependent) path planning problems. Ordered Upwind Methods (OUM) are a family of numerical methods for approximating the viscosity solution of static Hamilton-Jacobi-Bellman equations, and have been tailored to solve anisotropic optimal control problems. There is little information in the literature regarding the implementation of OUM, and a wide range of computational techniques and meticulous algorithmic considerations are required to successfully implement OUM. A comprehensive, generic implementation of OUM is documented in this report, with the intention of minimizing the technical barriers to employing OUM in real-world applications.