Trajectory optimisation of an aerobatic air race

This paper deals with the synthesis of optimal trajectories for aerobatic air races. A typical example of an air race event is the Red Bull Air Race World Series, where high-performance aerobatic aircraft fly a prescribed slalom course consisting of specially designed inflatable pylons, known as ‘air gates’, in the fastest possible time. The trajectory that we seek to optimise is based on such a course. The air race problem is formulated as a minimum-time optimal control problem and solved in open-loop form using a direct numerical multi-phase trajectory optimisation approach based on collocation and non-linear programming. The multiphase feature of the employed collocation algorithm is used to enable a Receding-Horizon optimisation approach, in which only a limited number of manoeuvres in sequence is considered. It is shown that the Receding-Horizon control approach provides a near-optimal solution at a significantly reduced computational cost relative to trajectory optimisation over the entire course. To avoid the path inclination singularity in the equations of motion based on Euler angles, a point-mass model formulation is used that is based on quaternions. Numerical results are presented for an Extra 300S, a purpose-designed aerobatic aircraft.