Unconstrained Direct Optimization of Spacecraft Trajectories Using Many Embedded Lambert Problems

Ottesen, David; Russell, Ryan P.

doi:10.1007/s10957-021-01884-1

Cited by 10 publications

(3 citation statements)

References 80 publications

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“…1, for reducing the sensitivity. Note that this is a simplified one-sided shooting technique [8]. To further improve the convergence, the multiple forward-and backward-shooting procedure [7,14,15] would be more suitable.…”

Section: Multiple Shootingmentioning

confidence: 99%

“…The third condition suggests that |p| = 1 at impulses. When a converged solution does not satisfy the necessary conditions for optimality, the author's experience recommends that firstly add nodes to increase the resolution of states and controls [8] and in case the failure continues, increase γ 0 to explore the search space in a more distributed manner.…”

Section: Post Processingmentioning

confidence: 99%

“…However, the tolerance is a problem dependent parameter and the difficulty in generating new impulses that are not initially included would be a drawback. Another way is to introduce a fictitious expression for the impulsive thrust magnitude via a small constant parameter that makes the fictitious thrust magnitude always positive [8]. Again, it requires a problem dependent parameter and sacrifies the optimality due to the approximate nature.…”

Section: Introductionmentioning

confidence: 99%

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Regularizing fuel-optimal multi-impulse trajectories

Oshima

2024

Astrodyn

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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 generations 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.

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