Q-Law Aided Direct Trajectory Optimization of Many-Revolution Low-Thrust Transfers

Abstract

Low-thrust spacecraft trajectory optimization for the many-revolution orbital transfer problem is especially challenging due to the high problem dimension and perturbing accelerations that prevent or complicate accurate analytical solutions. This analysis seeks to simplify the calculation of the nonaveraged spiral trajectory through the use of the well-known Q-Law guidance algorithm. Here, Q-Law is used to seed phases of the direct trajectory optimization problem. We explore the trade space between the fast calculation speed of Q-Law and the time or mass optimality of the full optimization problem using the common example of a geostationary transfer orbit to geostationary transfer. We find that a computationally efficient, near-optimal solution can be achieved by using Q-Law for an initial fraction of a spiral trajectory and direct optimization for the remainder of the trajectory. This reduces the direct optimization problem to a lower dimension and enables the spacecraft to reach a specific final state. Q-Law is particularly effective for portions of the trajectory where there are many eclipses, which can challenge direct optimization methods.