Artificial Intelligence (AI) based models are increasingly deployed in the Internet of Things (IoT), paving the evolution of the IoT into the AI of things (AIoT). Currently, the predominant approach for AI model training is cloud-centric and involves the sharing of data with external parties. To preserve privacy while enabling collaborative model training across distributed IoT devices, the machine learning paradigm called Federated Learning (FL) has been proposed. The future FL network is envisioned to involve up to millions of distributed IoT devices involved in collaborative learning. However, communication failures and dropouts by nodes can lead to inefficient FL. Inspired by the UAV-assisted communications in 5G heterogeneous networks (HetNet), we propose the UAV-assisted FL in this article. The FL model owner may employ UAVs to provide the intermediate model aggregation in the sky and mobile relay of the updated model parameters from data owners to the model owner. This therefore increases the reach of FL to data owners that face uncertain network conditions and improves the communication efficiency. To incentivize the UAV service providers, we adopt the multi-dimensional contract incentive design as a case study. The incentive compatibility of the contract ensures that the UAVs only choose an incentive package corresponding to its type, for example, traveling cost. The simulation results show that the UAV-assisted FL achieves significant improvement in communication efficiency and validates the incentive compatibility of our contract design.