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 fr...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.展开更多
The Modified Picard-Chebyshev Method(MPCM)is implemented as an orbit propagation solver for a numerical optimization method that determines minimum time orbit transfer trajectory of a satellite using a series of multi...The Modified Picard-Chebyshev Method(MPCM)is implemented as an orbit propagation solver for a numerical optimization method that determines minimum time orbit transfer trajectory of a satellite using a series of multiple impulses at intermediate waypoints.The waypoints correspond to instantaneous impulses that are determined using a nonlinear constrained optimization routine,SNOPT with numerical force models for both Two-Body and J2 perturbations.It is found that using the MPCM increases run-time performance of the discretized lowthrust optimization method when compared to other sequential numerical solvers,such as Adams-Bashforth-Moulton and Gauss-Jackson 8th order methods.展开更多
文摘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.
文摘The Modified Picard-Chebyshev Method(MPCM)is implemented as an orbit propagation solver for a numerical optimization method that determines minimum time orbit transfer trajectory of a satellite using a series of multiple impulses at intermediate waypoints.The waypoints correspond to instantaneous impulses that are determined using a nonlinear constrained optimization routine,SNOPT with numerical force models for both Two-Body and J2 perturbations.It is found that using the MPCM increases run-time performance of the discretized lowthrust optimization method when compared to other sequential numerical solvers,such as Adams-Bashforth-Moulton and Gauss-Jackson 8th order methods.
