A novel solution to control an hydraulic excavator during grading tasks is proposed, featuring a Model Predictive Controller designed using Local Model Networks (LMNs), i.e. linear time-invariant dynamic models averaged by nonlinear static functions. The Local Linear Models Tree (LoLiMoT) algorithm is employed to derive an LMN from experimental data of a real excavator. Then, a nonlinear MPC law is designed and implemented on the excavator's embedded control system. To further improve the computational efficiency, a time-varying MPC law is designed as well, where the LMN is linearized in real-time around the current operating point. Experimental results, conducted with the excavator in real-world conditions, show the effectiveness of both approaches in achieving performance comparable to state-of-the-art solutions, while utilizing a more compact dataset and without the need of the hydraulic cylinders' pressure measurement.