Robust Trajectory Optimization of Constrained Re-entry Flight

This paper aims to explore the trade-off between performance and robustness in the context of robust optimal trajectories for constrained re-entry flight with prescribed endpoint regions for Terminal Area Energy Management. A computational framework is developed to generate state-constrained trajectories that account for uncertainty, using non-intrusive Uncertainty Quantification methods and ensemble optimal control with pseudospectral transcription. The optimality of the results is proven by deriving the optimality conditions and Hamiltonian for the ensemble optimal control problem. Scaling the nominal controls and objective function with the number of ensembles was essential for the convergence in high-dimensional uncertainty scenarios. Simulation results for optimal ensemble controls, constraints, costates, and Hamiltonian shows excellent agreement with necessary optimality conditions.