Comparison of Numerical Methods for Low-Thrust Spacecraft Trajectory Optimization

Low-thrust spacecraft propulsion systems enable fuel-efficient trajectories through space but the resulting trajectory optimization problems can be challenging. In this work, various numerical approaches for designing such low-thrust trajectories have been analyzed and compared. First, the Hermite-Legendre-Gauss-Lobatto (HLGL) and the Legendre-Gauss pseudospectral (PS) direct collocation methods, which are used for transcribing an optimal control problem into a nonlinear programming problem, have been compared for a minimum-time low-thrust Earth-to-Mars transfer problem. Next, a novel control law, the RQ-Law, is presented for generating low-thrust three-dimensional multi-revolution coasting-enabled rendezvous trajectories with a moving target, based on modified equinoctial elements. It builds upon the Q-Law, which is a Lyapunov feedback control law for orbital transfers. The RQ-Law offers an alternate method of determining the Lyapunov-optimal thrust angles used for both orbital transfer and phasing. It also provides a new target semimajor axis augmentation scheme that is demonstrated to perform phasing in a wide range of eccentric orbits. Compared with existing low-thrust Lyapunov rendezvous methods, the RQ-Law can include coasting arcs in the trajectory to save fuel as well as account for a minimum periapsis radius constraint. Alongside a thorough qualitative comparison of the RQ-Law, the performance of this law is evaluated numerically by using it to generate a rendezvous trajectory involving large changes in all six orbital elements. This performance was compared with a hybrid control law composed of an existing modified equinoctial Q-Law and a spiral phasing law. Three trade studies were performed that studied, respectively, the effects of the chaser departure point, the point at which low-thrust phasing is initiated, and the target orbit eccentricity, on the RQ-Law performance. Finally, to investigate the use of the RQ-Law to help mitigate the problem of space debris, we develop a low-thrust multiple-rendezvous trajectory to traverse a predetermined sequence of targets. The RQ-Law advances the state-of-the-art of the Q-Law and provides an integrated design tool for preliminary low-thrust rendezvous trajectory generation without needing an initial guess. The contributions of this thesis can be used for a variety of planetocentric and interplanetary space missions that use low-thrust electric propulsion.

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