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
While thefirst-order derivatives of an objective function and constraints have often been analytically provided in the gradient-based optimization algorithms,the joint use of the secondorder derivatives can further im...While thefirst-order derivatives of an objective function and constraints have often been analytically provided in the gradient-based optimization algorithms,the joint use of the secondorder derivatives can further improve the computational efficiency and robustness.This paper implements thefirst-and second-order analytical derivatives in the direct multiple shootingbased,regularized method of minimizing the fuel expenditure for impulsive space trajectories.The high-order dynamical information expresses the Hessian matrix of the Lagrange function in the nonlinear programming problem.The result is an efficient tool for robustly computing fueloptimal,multi-impulse trajectories in the regularized framework of removing singularities associated with null thrust impulses from the derivatives of the objective function.The computational performance is compared for the cases of optimizing impulsive transfers between cislunar periodic orbits within the regularized framework implementing the analytical derivatives in different ways over various initial guess trajectories and computational conditions.The results indicate the superiority of adopting both thefirst-and second-order analytical derivatives in terms of the efficiency and robustness.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While thefirst-order derivatives of an objective function and constraints have often been analytically provided in the gradient-based optimization algorithms,the joint use of the secondorder derivatives can further improve the computational efficiency and robustness.This paper implements thefirst-and second-order analytical derivatives in the direct multiple shootingbased,regularized method of minimizing the fuel expenditure for impulsive space trajectories.The high-order dynamical information expresses the Hessian matrix of the Lagrange function in the nonlinear programming problem.The result is an efficient tool for robustly computing fueloptimal,multi-impulse trajectories in the regularized framework of removing singularities associated with null thrust impulses from the derivatives of the objective function.The computational performance is compared for the cases of optimizing impulsive transfers between cislunar periodic orbits within the regularized framework implementing the analytical derivatives in different ways over various initial guess trajectories and computational conditions.The results indicate the superiority of adopting both thefirst-and second-order analytical derivatives in terms of the efficiency and robustness.
