End-to-End Ascent-Entry Mission Performance Optimization Using Gaussian Quadrature Collocation

TL;DR

This paper presents a systematic method for optimizing ascent-entry trajectories of a rocket vehicle using Gaussian quadrature collocation, improving control margins and reducing effort during atmospheric entry under thermal constraints.

Contribution

It introduces an end-to-end trajectory optimization approach for ascent and entry phases using an adaptive Gaussian quadrature collocation method, accounting for thermal constraints and control effort.

Findings

Optimized trajectories can reduce control effort during entry within certain thermal limits.

Small ascent adjustments can improve entry control margins.

Control effort increases and saturates outside specific thermal constraint ranges.

Abstract

The performance optimization for a combined ascent-entry mission subject to constraints on heating rate and heating load is studied. The ascent vehicle is modeled as a three-stage rocket that places the vehicle onto a suborbital exo-atmopheric trajectory after which the vehicle undergoes an unpowered entry and descent to a vertically downward terminal condition. The entry vehicle is modeled as a high lift-to-drag ratio vehicle that is capable of withstanding high levels of thermal and structural loads. A performance index is designed to improve control margin while attenuating phugoid oscillations during atmospheric entry. Furthermore, a mission corresponding to a prototype launch and target point is used in this study. The trajectory optimization problem is formulated as a multiple-phase optimal control problem, and the optimal control problem is solved using an adaptive Gaussian quadrature collocation method. A key aspect of the optimized trajectories is that, for particular ranges of maximum allowable heating rate and heating load during entry, relatively small adjustments made during ascent can potentially decrease the control effort required during atmospheric entry. Outside of these ranges for maximum allowable heating rate and heating load, however, it is found that the required control effort increases and eventually saturates the commanded angle of attack upon initial descent. The key features of the optimized trajectories and controls are identified, and the approach developed in this paper provides a systematic method for end-to-end ascent-entry trajectory optimization.