Fast Path Planning using Multi-Resolution Boundary Value Problems

BVP Path Planners generate potential fields through a differential equation whose gradient descent represents navigation routes from any point of the environment to a goal position. Resulting paths are smooth and free from local minima. In spite of these advantages, this kind of planners consumes a lot of time to produce a solution. In this paper, we present a new approach that combines our BVP Path Planner with the Full Multigrid Method, which solves elliptic partial differential equations using a hierarchical strategy. Our new approach, called Hierarchical BVP Path Planner, enables real-time performance on large environments. Results show that our proposal spends less than 1% of the time needed to compute a solution using our original planner in several environments.