Regularizing fuel-optimal, multi-impulse trajectories

Abstract

The regularization theory has successfully enabled the removal of gravitational singularities associated with celestial bodies. This paper merges regularizing techniques into a multi-impulse trajectory design framework that requires delicate computations specifically in a fuel minimization problem. Regularized variables based on the Levi-Civita or Kustaanheimo-Stiefel transformation express instantaneous velocity changes in a gradient-based direct optimization method. The formulation removes the notorious singularities associated with null thrust impulses from derivatives of an objective function in the fuel minimization problem. The favorite singularity-free property enables accurate reductions of unnecessary impulses and additions 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.