In this paper, we propose an unmanned aerial vehicle (UAV)-assisted federated learning (FL) framework that jointly optimizes UAV trajectory, user participation, power allocation, and data volume control to minimize overall system energy consumption. We begin by deriving the convergence accuracy of the FL model under multiple local updates, enabling a theoretical understanding of how user participation and data volume affect FL learning performance. The resulting joint optimization problem is non-convex; to address this, we employ alternating optimization (AO) and successive convex approximation (SCA) techniques to convexify the non-convex constraints, leading to the design of an iterative energy consumption optimization (ECO) algorithm. Simulation results confirm that ECO consistently outperform existing baseline schemes.