Optimization of Path-Constrained Systems using Pseudospectral Methods applied to Aircraft Trajectory Planning∗

Numerical optimal control techniques play an increasingly relevant role in trajectory planning for aerial vehicles. In the last decade, pseudospectral methods have been identified as a powerful alternative to other direct methods in numerical optimal control. We study the applicability and performance of pseudospectral methods when applied to problems involving systems with inequality path constraints such as aircraft trajectory optimization problems. We show that activation or deactivation of path constraints introduce non-smooth features in the solution that degrade the properties of pseudospectral methods, but proper reformulation of the problem as a multiphase problem preserves them. We finally propose an adaptive algorithm that automatically designs an appropiate multiphase reformulation of an optimal control problem. The results show that our method improves the accuracy of the numerical solution compared to direct application of the pseudospectral method.