(Georgia Institute of Technology, 2016-07-20)
Steffens, Michael J.
Trajectory optimization is an important part of launch vehicle conceptual design. Current methods for trajectory optimization involve numerical analysis, are computationally expensive and require trajectory experts in the loop, thus limiting efforts for design space exploration. A simplified performance analysis, like the rocket equation, is much better suited to the types of studies desired in conceptual design, where thousands of vehicles can be considered and compared. Unfortunately, the rocket equation does not take into account trajectory losses and therefore does not provide an accurate measure of performance. The lack of a fast and accurate method to evaluate launch vehicle performance represents a gap in the current capability that will be addressed in this thesis. The goal of this research is to formulate and implement a performance analysis method in the form of the rocket equation (i.e. closed-form) that takes into account the trajectory losses considered in a numerical trajectory analysis method. This goal is achieved by generating a surrogate model of launch vehicle trajectory data. Several challenges arise when generating this data in an automated fashion. For this reason, extreme value theory is used in conjunction with an industry standard optimization method. The trajectory problem is statistically posed finding the extreme value of a distribution representing the performance of all possible trajectories. The process of generating a surrogate model is formulated into a method named RAPTOR (Rapid Trajectory Optimization Routine). The method is successfully implemented on the Delta IV Heavy launch vehicle. Implementation of the RAPTOR method results in a capability that enables rapid and accurate performance evaluation of launch vehicles.
(Georgia Institute of Technology, 2014-04-09)
Steffens, Michael J.
Trajectory optimization is an important part of launch vehicle design and operation. With the high costs of launching payload into orbit, every pound that can be saved increases affordability. One way to save weight in launch vehicle design and operation is by optimizing the ascent trajectory. Launch vehicle trajectory optimization is a field that has been studied since the 1950’s. Originally, analytic solutions were sought because computers were slow and inefficient. With the advent of computers, however, different algorithms were developed for the purpose of trajectory optimization. Computer resources were still limited, and as such the algorithms were limited to local optimization methods, which can get stuck in specific regions of the design space. Local methods for trajectory optimization have been well studied and developed. Computer technology continues to advance, and in recent years global optimization has become available for application to a wide variety of problems, including trajectory optimization. The aim of this thesis is to create a methodology that applies global optimization to the trajectory optimization problem. Using information from a global search, the optimization design space can be reduced and a much smaller design space can be analyzed using already existing local methods. This allows for areas of interest in the design space to be identified and further studied and helps overcome the fact that many local methods can get stuck in local optima. The design space included in trajectory optimization is also considered in this thesis. The typical optimization variables are initial conditions and flight control variables. For direct optimization methods, the trajectory phase structure is currently chosen a priori. Including trajectory phase structure variables in the optimization process can yield better solutions. The methodology and phase structure optimization is demonstrated using an earth-to-orbit trajectory of a Delta IV Medium launch vehicle. Different methods of performing the global search and reducing the design space are compared. Local optimization is performed using the industry standard trajectory optimization tool POST. Finally, methods for varying the trajectory phase structure are presented and the results are compared.