Regularizing fuel-optimal multi-impulse trajectories

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.