In this paper, the efficient deployment and mobility of multiple unmanned aerial vehicles (UAVs), used as aerial base stations to collect data from ground Internet of Things (IoT) devices, is investigated. In particular, to enable reliable uplink communications for IoT devices with a minimum total transmit power, a novel framework is proposed for jointly optimizing the three-dimensional (3D) placement and mobility of the UAVs, device-UAV association, and uplink power control. First, given the locations of active IoT devices at each time instant, the optimal UAVs' locations and associations are determined. Next, to dynamically serve the IoT devices in a time-varying network, the optimal mobility patterns of the UAVs are analyzed. To this end, based on the activation process of the IoT devices, the time instances at which the UAVs must update their locations are derived. Moreover, the optimal 3D trajectory of each UAV is obtained in a way that the total energy used for the mobility of the UAVs is minimized while serving the IoT devices. Simulation results show that, using the proposed approach, the total transmit power of the IoT devices is reduced by 45% compared to a case in which stationary aerial base stations are deployed. In addition, the proposed approach can yield a maximum of 28% enhanced system reliability compared to the stationary case. The results also reveal an inherent tradeoff between the number of update times, the mobility of the UAVs, and the transmit power of the IoT devices. In essence, a higher number of updates can lead to lower transmit powers for the IoT devices at the cost of an increased mobility for the UAVs.