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This paper deals with the bilateral teleoperation of underactuated aerial robots by means of a haptic interface. In particular, we propose a switching-based state mapping and control algorithm between a rate-based passive controller, which addresses the workspace incompatibility between the master and slave systems, and a pose-based passive controller, which is required for precise operation. The overall control architecture provides the possibility of changing the scaling factor of the mapping online, while preserving the passivity of the complete system. In our formulation, we use the port-Hamiltonian framework, in which energetic considerations play a determinant role for passivity and, thereby stability of the overall system. Simulation and experimental results illustrating the effectiveness of the proposed algorithm are also presented.