A Constrained Inverse Modeling Approach for Trajectory Optimization

Kurzfassung

In aircraft trajectory optimization, modeling almost always relies on the usage of standard (forward) three- or more degrees of freedom equations of motion for the aircraft. The usual practice for simulating the trajectories is either to continuously trim the aircraft along the desired flight path and speed profile, and/or to use reduced point mass models that are defined in the vertical plane only. Alternative approaches became prominent in recent years, whereas in this paper the inverse modeling technique and an important extension to it is considered. First, inverse models have several advantages for trajectory optimization, the most important ones being the faster computation time and easy generation of start solutions, compared to standard forward models. In this work it is combined with speed- and flightpath- control loops to cancel the position error introduced during model integration. Still, an important problem remains: saturation limits and dynamics of the control systems used in the actual forward model are normally not considered when inverting the model equations, therefore losing the information of the limitations of the aircraft. In the presented case, the inversion becomes invalid, when the aircraft thrust is outside of the limits due to the commands of the inverse model inputs. This problem is addressed in the model by a pseudo-control-hedging (PCH) approach for altitude and velocity commands. By this means the inverse model inputs are automatically altered depending on the error between commanded and available thrust and the generated trajectory is rendered flyable.