Low-Thrust, Multiple Revolution, Guaranteed Convergence Keplerian Orbital Transfers Using a Lyapunov Function-based Control Law

Abstract

Calculating optimal low-thrust, multiple-revolution orbital transfers can be computationally intensive. Developing computationally efficient guidance algorithms that produce solutions to the low-thrust, multiple-revolution transfer problem that approach optimality can be useful, especially in the context of on-board guidance applications due to the limited computational power on spacecraft. The Q-law by Petropoulos is a candidate Lyapunov function based on the Keplerian orbital elements that offers flexible customization parameters for trajectory designers that enable adaptation to diverse orbital transfer scenarios to increase efficiency, but lacks mathematical proof of guaranteed convergence to the target orbit. The Chang-Chichka-Marsden (CCM) guidance law utilizes a true Lyapunov function (meaning it has guaranteed local neighborhood and path-independent global convergence to target orbits), but lacks the customizability that Q-law does. The local neighborhood portion of the proof was explored by Chang et al., but the global path-independent convergence portion has not yet been utilized experimentally to the author’s knowledge. This thesis proposes a new algorithm using the Chang-Chichka-Marsden Lyapunov function and control law utilizing the definition of intermediate target orbits to control the rate of convergence of individual orbital elements towards the final target orbit. This effectively combines the guaranteed convergence of the Chang-Chichka-Marsden algorithm with the trajectory customizability of the Q-law that enables it to adapt to varied orbital transfer scenarios.