3D trajectory optimization of an acrobatic air race with direct collocation method and quaternion equations of motion

The main purpose of this thesis is to develop a software to optimize the 3D air race trajectory. Air race competitions such as Red Bull are becoming very popular around the world, but behind this eye catching competitions there are always engineers supporting every team to help their pilots to make the fastest lap time in order to win the competition. Nowadays, by the help of advanced computing systems and proficient optimization algorithm, engineers are able to model the trajectory of these air races and optimize them offline. These optimized trajectories are handed to the pilots before the competition, in order to help them train themselves in a simulator and then with a real aircraft. In this thesis the equations of motion (EOM) of point-mass model is used for optimization. The first approach was with the EOM based on Euler angles. As we know from flight dynamics, with the Euler angles we will have a singularity in our equations when the aircraft is experiencing the ±π/2 pitch angle. In order to avoid the singularity in the Euler case, we switch to EOM based on Quaternions. Although the quaternions are used for the optimization of the trajectory, we will also represent the results for Euler based EOM. The software used to develop the code for this optimization is MATLAB 2016b. Algorithm is proposed and implemented by the author. Build-in optimization function (FMINCON) is used to optimize the trajectory based on the proposed algorithm.