Optimization study of a trans-Atlantic abort for the U.S. space shuttle using a pseudospectral Legendre method

Abstract

The problem of performance optimization for a trans-Atlantic shuttle abort is considered. At five points during the second stage of ascent, a failure of a main engine occurs, which necessitates an abort from the nominal mission. The abort trajectories generated initiate from the current state at the time of abort and terminate at the TAEM interface for a landing site. The abort trajectories consist of three regimes, or phases of flight, and each phase has a different dynamic model governing the motion of the vehicle. To ensure a solution is obtained for each abort, additional constraints on the vehicle are formulated as soft constraints in the penalty function. In particular, the third phase cost functional consists of a weighted combination of heating rate, dynamic pressure and sensed acceleration. Thus, the problem formulation is one of a multiple phase optimal control problem. A Pseudospectral Legendre Method is used to discretized the optimal control problem into a nonlinear programming problem, which is then solved using a sparse nonlinear optimizer. The first study conducted compares the trajectories generated to each landing site for various combinations of third phase cost functional weighting factors. A cost calculation is developed to compare each optimized abort trajectory. The second study evaluates the significance of the improvements due to the chosen weighting factor combination with that of an entry aerodynamic model uncertainty.