A hierarchical on-line path planning scheme using wavelets

We present an algorithm for solving the shortest (collision-free) path planning problem for an agent (e.g., wheeled vehicle, UAV) operating in a partially known environment. The agent has detailed knowledge of the environment and the obstacles only in the vicinity of its current position. Far away obstacles or the final destination are only partially known and may even change dynamically at each instant of time. We obtain an approximation of the environment at different levels of fidelity using a wavelet approximation scheme. This allows the construction of a directed weighted graph of the obstacle-free space in a computationally efficient manner. In addition, the dimension of the graph can be adapted to the on-board computational resources. By searching this graph we find the desired shortest path to the final destination using Dijkstra's algorithm, provided that such a path exists. Simulations are presented to test the efficiency of the algorithm using non trivial scenarios.