3D Map Exploration via Learning Submodular Functions in the Fourier Domain

Abstract

3D map exploration is one of key technologies in robotics. However, finding an optimal exploration path is a challenge since the environment is unknown. This research proposed the submodular exploration (SE) algorithm to enable an unmanned aerial vehicle (UAV) to explore 3D environments. The algorithm learns the submodular function in the Fourier domain and reconstructs the submodular function in the spatial domain via the compressed sensing techniques. Since the objective function of spatial exploration is reformulated as a maximizing submodular function with path constraints, greedy algorithms can achieve 1/2(1-e <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> ) of the optimum. Experiments conducted with this algorithm demonstrate that the UAV can explore more voxels in the environments than the benchmark approach.