Trajectory Optimization Applied to Air Races

Abstract

The paper describes a novel approach for the optimization of air race trajectories taking into account the highly non-linear nature of the dynamics of the participating aircraft. Therefore, no point-mass model is utilized for the optimization task but an enhanced, scalable multi-fidelity simulation model that is a sequential model extending the translation dynamics by different representations for the attitude and the rotational dynamics of the flight system. The inner loop can either contain linear transfer functions for the load factors and the roll rate, linear state-space models for the longitudinal and the lateral motion of the aircraft or fully non-linear rotational and attitude dynamics. Thus, the full dynamic order of the flight system considered is taken into account such that the resulting optimal race trajectory is actually achievable. Inversion controllers for the different loops are incorporated into the simulation model. With this sequential structure of the model, the complexity level of the rotational dynamics and thus the optimization time and quality can easily be switched to the required level. Furthermore, a procedure for generating robust and suitable initial guesses for the optimization with full, non-linear 6-degree of freedom simulation models is established. This novel approach allows for the solution of highly complex trajectory optimization problems where classical methods failed due to stiffness problems.