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Federated learning is a distributed machine learning approach that enables a large number of edge/end devices to perform on-device training for a single machine learning model, without having to share their own raw data. We consider in this paper a federated learning scenario wherein the local training is carried out on IoT devices and the global aggregation is done at the level of an edge server. One essential challenge in this emerging approach is IoT devices selection (also called scheduling), i.e., how to select the IoT devices to participate in the distributed training process. The existing approaches suggest to base the scheduling decision on the resource characteristics of the devices to guarantee that the selected devices would have enough resources to carry out the training. In this work, we argue that trust should be an integral part of the decision-making process and therefore design a trust establishment mechanism between the edge server and IoT devices. The trust mechanism aims to detect those IoT devices that over-utilize or under-utilize their resources during the local training. Thereafter, we introduce DDQN-Trust, a double deep Q learning-based selection algorithm that takes into account the trust scores and energy levels of the IoT devices to make appropriate scheduling decisions. Finally, we integrate our solution into four federated learning aggregation approaches, namely, FedAvg, FedProx, FedShare and FedSGD. Experiments conducted using a real-world dataset show that our DDQN-Trust solution always achieves better performance compared to two main benchmarks: the DQN and random scheduling algorithms. The results also reveal that FedProx outperforms the competitor aggregation models in terms of accuracy when integrated into our DDQN-Trust solution. [ABSTRACT FROM AUTHOR]