Regularizing fuel-optimal multi-impulse trajectories

Abstract

The regularization theory has successfully enabled the removal of gravitational singularities associated with celestial bodies. In this study, regularizing techniques are merged into a multi-impulse trajectory design framework that requires delicate computations, particularly for a fuel minimization problem. Regularized variables based on the Levi–Civita or Kustaanheimo–Stiefel transformations express instantaneous velocity changes in a gradient-based direct optimization method. The formulation removes the adverse singularities associated with the null thrust impulses from the derivatives of an objective function in the fuel minimization problem. The favorite singularity-free property enables the accurate reduction of unnecessary impulses and the generation of necessary impulses for local optimal solutions in an automatic manner. Examples of fuel-optimal multi-impulse trajectories are presented, including novel transfer solutions between a near-rectilinear halo orbit and a distant retrograde orbit.