High-Order Guidance for Time-Optimal Low-Thrust Trajectories with Accuracy Control

Abstract

This paper develops a high-order guidance scheme based on the expansion of the solution to a time-optimal low-thrust optimal control problem by using differential algebraic techniques. The result allows new optimal trajectories to be autonomously computed from the simple evaluation of polynomials, including updated times of flight. Furthermore, a differential algebraic technique known as automatic domain splitting is implemented to improve the guidance scheme by adaptively and automatically splitting the uncertainty domain into smaller subdomains, in which new guidance polynomials are then generated which are better equipped to handle deviations in their respective subdomains. The result is not only a more effective handling of deviations in the trajectory compared to previous algorithms which use just a single set of polynomials but one that can provide the control and time-of-flight updates to a desired accuracy across the entire domain. Combined with its high-order nature, the guidance scheme is capable of dealing with nonlinearity and large deviations with respect to the reference trajectory, thus being robust to mismodeling and unplanned events. The guidance scheme is evaluated in three scenarios: simplified rendezvous using Clohessy–Wiltshire equations to demonstrate automatic domain splitting in the guidance problem, an Earth–Mars transfer, and an asteroid landing trajectory. The results show the ability of the differential algebraic-based guidance to provide optimal control and time-of-flight updates and improvements of several orders of magnitude over previous differential algebraic-based schemes in handling large uncertainty experienced in spaceflight by leveraging automatic domain splitting.