In this paper, we propose a stochastic differential equation-based exploration algorithm to enable exploration in three-dimensional indoor environments with a payload-constrained micro-aerial vehicle (MAV). We are able to address computation, memory, and sensor limitations by using a map representation which is dense for the known occupied space but sparse for the free space. We determine regions for further exploration based on the evolution of a stochastic differential equation that simulates the expansion of a system of particles with Newtonian dynamics. The regions of most significant particle expansion correlate to unexplored space. After identifying and processing these regions, the autonomous MAV navigates to these locations to enable fully autonomous exploration. The performance of the approach is demonstrated through numerical simulations and experimental results in single- and multi-floor indoor experiments.
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