Safe and Adaptive Trajectory Reshaping of Constrained Re-entry Flight: Recovery Ensemble Control

A novel computational framework, called the Recovery Ensemble Control (REC), has been proposed to develop constrained trajectory reshaping strategies for aerospace missions. The framework simplifies the uncertainty space by exploiting Sparse Grid methods, one of which is the Conjugate Unscented Transformation (CUT). Subsequently, the uncertainty-aware optimal control problem (OCP) is rewritten as a computationally tractable Ensemble Optimal Control problem where each sample is commanded with a nominal and a recovery control term. The problem is solved by means of Pseudo-spectral Optimal Control Methodology and Nonlinear Programming, whereby the recovery control and the expected value of the original objective term are minimized. Recovery control terms are shown to be a function of both nominal control and costates, which can be either generated via an offline database or computed via a traditional optimization procedure in real-time, without incurring any computationally expensive robust trajectory optimization. Instead of re-optimizing a deterministic trajectory in real-time under uncertainties or producing conservative robust trajectories with structured feedback controllers, minimization of the recovery control lends itself to a more optimal and adaptable trajectory reshaping strategy by reducing the required control effort for switching from one to another in high-dimensional uncertainties. Furthermore, REC framework has been applied to a strictly constrained benchmark re-entry problem. In this problem, a re-entry vehicle is commanded to maneuver from an Entry Interface with uncertainties towards a Terminal Area Energy Management (TAEM) under angle-of-attack limits, dynamic load, and heat flux constraints while maximizing the cross-range. The problem has been solved for various recovery weights and computational strategies, under both parametric and navigational uncertainties, so as to scrutinize their effects on the optimality. The resulting framework is shown to allow for the computation of ensemble controls offline for navigational and parametric uncertainties, thereby ensuring maximum safety and minimal extra control effort for adaptive trajectory reshaping.