Global Ascent Trajectory Optimization of a Space Plane

Abstract

The main goal of any launch vehicle is to bring as much payload to space as possible. Space planes have been studied for decades, as they are thought to be more cost effective for frequent access to space than traditional expendable launchers. This research aims at optimizing the payload capacity of a single stage to orbit (SSTO) horizontal take-off horizontal landing (HTHL) space plane, by flying a minimum fuel an heat load trajectory. Trajectory optimization of launch vehicles is traditionally performed with local optimization methods. The objective of this research is to find a good approach to optimize the ascent trajectory with a global optimizer. To achieve this goal, a simulation model is set up. This model propagates the ascent trajectory based on a guided angle of attack and throttle setting as a function of the normalized energy state of the vehicle. The guidance parameters are defined at a number of control nodes and are stored in a decision vector. This vector is randomly initialized and subsequently optimized. The performance of different optimization methods and problem settings is assessed based on the convergence of the optimized populations with respect to a set of evaluation objectives. Specifically multi-objective (MO) global optimizers were selected for this research. The performance of MOEA/D, NSGA-II and NSGA-II-tabu was compared. MOEA/D was found to give the most consistent result and fastest convergence. Different combinations of control parameters were used. The use of thrust-vector control improved the convergence and the quality of the results, as long as the problem dimension was not over-sized. Also various approaches for constraint and objective handling were evaluated. As the objectives and constraints were highly conflicting, a penalty function had to be included to reduce the sensitivity to premature convergence to no-flying solutions.
The resulting set up was not able to find a solution for the complete trajectory. The trajectory was therefore split in three phases: take-off, acceleration and pull-up. The first two stages were optimized successfully and resulted in similar payload capacities as found in the literature with traditional methods. The final pull-up stage needs to be further investigated. Although this research has shown that global optimizers can be used for the ascent trajectory optimization, further research is required before the methods can be applied effectively.