Accurate trajectory tracking is a critical property of unmanned aerial vehicles (UAVs) due to system nonlinearities, under-actuated properties and constraints. Specifically, the use of unmanned rotorcrafts with accuracy trajectory tracking controllers in dynamic environments has the potential to improve the fields of environment monitoring, safety, search and rescue, border surveillance, geology and mining, agriculture industry, and traffic control. Monitoring operations in dynamic environments produce significant complications with respect to accuracy and obstacles in the surrounding environment and, in many cases, it is difficult to perform even with state-of-the-art controllers. This work presents a nonlinear model predictive control (NMPC) with collision avoidance for hexacopters’ trajectory tracking in dynamic environments, as well as shows a comparative study between the accuracies of the Euler–Lagrange formulation and the dynamic mode decomposition (DMD) models in order to find the precise representation of the system dynamics. The proposed controller includes limits on the maneuverability velocities, system dynamics, obstacles and the tracking error in the optimization control problem (OCP). In order to show the good performance of this control proposal, computational simulations and real experiments were carried out using a six rotary-wind unmanned aerial vehicle (hexacopter—DJI MATRICE 600). The experimental results prove the good performance of the predictive scheme and its ability to regenerate the optimal control policy. Simulation results expand the proposed controller in simulating highly dynamic environments that showing the scalability of the controller.