Oriented exploration in non-oriented sparse environments

The use of relaxation methods for calculation of harmonic potentials has proved to be a powerful technique for path planning in a known environment and recently for exploration of unknown environments. In the latter case, the potential is calculated on partial versions of the map represented on an occupancy grid, and it indicates safe paths towards the unexplored regions. Here, we show that exploration based on potentials functions calculated from boundary value problems works fairly well in sparse environments provided that we no longer use harmonic potentials. We propose different families of potentials that improve the exploration process in this kind of environment, while keeping the important property of not having dynamical local minima.