Computational Guidance and Control for Aerospace Systems

Abstract

The objective of this dissertation is to develop new techniques that advance the state of the art in optimization-based trajectory generation. Two complementary techniques are studied. First, explicit trajectory generation computes a single path that connects two boundary conditions. For a general optimal control problem, sequential convex programming is used to design iterative algorithms that solve challenging aerospace problems. The limited power available on a spacecraft has long been at odds with the computationally demanding algorithms required to solve such problems, and so specialized techniques for developing real-time capable implementations of these algorithms are presented. Runtime analysis offers initial evidence that it is possible to solve explicit trajectory optimization problems reliably and fast enough to be considered a viable technology. As an alternative approach, implicit trajectory generation computes a set of functions that implicitly define an entire set of trajectories. By carrying out more extensive offline computations, it is shown that a feasible trajectory can be obtained from a wide array of initial conditions by using numerical integration. Consequently, the required real-time computations are significantly reduced compared to explicit trajectory optimization algorithms. Implicit trajectory generation methods can also offer a stronger theoretical, and offline-certifiable, guarantee that a feasible trajectory will be available for a prescribed set of vehicle conditions. Examples in powered descent and satellite attitude control are used to demonstrate each method.