Computationally Efficient Harmonic-Based Reactive Exploration

Although Harmonic Potential Fields constitute a powerful tool for tackling the autonomous robot exploration problem, yet their applicability is limited by the heavy computational load involved in solving the Laplace equation in real time. In this letter, we propose a computationally efficient exploration scheme employing a Fast Multipole accelerated Boundary Element Method, which enjoys both linear complexity w.r.t. The boundary's size as well as linear memory requirements. Furthermore, we devise an adaptive control law for the specified boundary conditions that allows us to tune the robot's behavior without affecting the inherent safety and convergence properties of the underlying potential field. Finally, we validate the performance of the proposed exploration scheme through extensive realistic simulations.