  This work presents an safe and efficient methodology for autonomous indoor
exploration with aerial robots using Harmonic Potential Fields (HPF). The
challenge of applying HPF in complex 3D environments rests on high
computational load involved in solving the Laplace equation. To address this
issue, the proposed solution utilizes the Fast Multiple accelerated Boundary
Element Method with boundary values controlled to ensure both safety and
convergence. The methodology is validated through simulations, which
demonstrate its properties of efficiency, safety and convergence.
