This paper proposes a 3D autonomous exploration scheme designed for a flying vehicle to build a topological map representing the complex environment of the surface of Mars. The environment is modeled as a uniform grid, and the measurements from depth scans are utilized to determine the probability of occupancy at every cell within the scanned area. Shannon's entropy serves as a measure of map uncertainty, where the motion of the aerial vehicle is guided to minimize entropy, thereby maximizing map information. We propose a novel technique to predict future map entropy from depth sensors capable of scanning 3D spaces, and formulate autonomous exploration as an optimization problem based on map information gain subject to inequality constraints to avoid collision. The proposed approach is demonstrated with numerical simulations using contour data from the surface of Mars.
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