Airframe and trajectory pursuit modeling for simulation assisted air race planning

Aviation displays like air shows or air races are attracting a large audience, increasing the popularity and fascination of aerospace in the public beyond mere air travel. Whereas in the past, such events have taken place separately, attempts are made to establish a worldwide series of air races, as an aerospace pendant to the Formula One car race series. With the events taking place in many different countries on all continents, different regulations apply for certifying the events. Furthermore, the tracks need to be comparable, attractive to the public, challenging for the pilots and more than everything else provide a high level of safety. To make the planning and assessment process for the different races more objective and to put it on a scientific basis, a track planning and analysis tool has been developed. This publication presents the kinematic and dynamic aircraft simulation used for initial track generation and assessment together with the control algorithms required to follow the highly curved trajectories utilizing the full envelope of the aircraft at maximum bandwidth. A nonlinear point-mass model is used and a new approach is developed where the attitude and rotational dynamics of the full 6-DoF model are given with respect to the Kinematic Flight-Path Frame, thus allowing to switch between different depths of modeling for the rotational dynamics without the need to modify the nonlinear point-mass model. Three alternatives for modeling the attitude and rotational dynamics are presented, namely a full, non-linear 6-DoF model, a simplified, hybrid 6-DoF model and a simulation model with linear transfer functions for the commanded load factors. In order to guarantee perfect trajectory following of the simulation model, a control system is implemented based on the principle of dynamic inversion. Therefore, the given reference trajectory has to be at least four times differentiable. Reference values for the aircraft inputs are computed from derivatives of the trajectory to produce smooth command histories of the derivative order of the aircraft dynamics. Error feedback is used at all derivative levels to stabilize the aircraft on the trajectory and to compensate for nonlinear limitations in maneuvering capability. Re-alignment and aerobatic maneuvers are implemented as parameterized segments controlled by a finite-state machine. For that, different high-level controllers have been implemented as basis. The trajectory and the corresponding simulated aircraft state histories are used to compute and evaluate different static and dynamic safety criteria as well as to assess the track in terms of spectator attractiveness and pilot skill level.