  The Internet of Things (IoT) brings connectivity to a massive number of
devices that demand energy-efficient solutions to deal with limited battery
capacities, uplink-dominant traffic, and channel impairments. In this work, we
explore the use of Unmanned Aerial Vehicles (UAVs) equipped with configurable
antennas as a flexible solution for serving low-power IoT networks. We
formulate an optimization problem to set the position and antenna beamwidth of
the UAV, and the transmit power of the IoT devices subject to
average-Signal-to-average-Interference-plus-Noise Ratio
($\bar{\text{S}}\overline{\text{IN}}\text{R}$) Quality of Service (QoS)
constraints. We minimize the worst-case average energy consumption of the
latter, thus, targeting the fairest allocation of the energy resources. The
problem is non-convex and highly non-linear; therefore, we re-formulate it as a
series of three geometric programs that can be solved iteratively. Results
reveal the benefits of planning the network compared to a random deployment in
terms of reducing the worst-case average energy consumption. Furthermore, we
show that the target $\bar{\text{S}}\overline{\text{IN}}\text{R}$ is limited by
the number of IoT devices, and highlight the dominant impact of the UAV
hovering height when serving wider areas. Our proposed algorithm outperforms
other optimization benchmarks in terms of minimizing the average energy
consumption at the most energy-demanding IoT device, and convergence time.
