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This work presents an safe and efficient methodology for autonomous indoorexploration with aerial robots using Harmonic Potential Fields (HPF). Thechallenge of applying HPF in complex 3D environments rests on highcomputational load involved in solving the Laplace equation. To address thisissue, the proposed solution utilizes the Fast Multiple accelerated BoundaryElement Method with boundary values controlled to ensure both safety andconvergence. The methodology is validated through simulations, whichdemonstrate its properties of efficiency, safety and convergence.

Harmonic Field-based Provable Exploration of 3D Indoor Environments