Trajectory planning is an essential element in robotics applications. The quality of the planned trajectory strongly influences the robot behaviour, particularly when the autonomous robot operates in complex and structured environments. This thesis focuses on the study, deployment and testing of a trajectory planning algorithm for autonomous UAVs, exploiting the Model Predictive Control theory and the Rapidly-exploring Random Tree "star" (RRT*) algorithm. The developed logic makes use of the RRT* algorithm to explore the search space and, then, constructing an incremental optimal tree to connect a given start and a goal pose in the search space. During the exploration phase, whenever two states are attempted to be connected, the deployed Model Predictive Control logic computes a "cost-to-go" cost of moving between two adjacent states in the graph by predicting the motion of the UAV, exploiting its dynamic model.