Global Search for Optimal Low Thrust Spacecraft Trajectories using Diffusion Models and the Indirect Method

TL;DR

The paper tackles the computational bottleneck of globally searching long-duration, low-thrust spacecraft trajectories by marrying diffusion-based generative modeling with an indirect optimal-control framework. By conditioning a diffusion model on the thrust bound, the method learns the costate structure that underpins locally optimal solutions, enabling rapid warm-starts for the indirect solver and dramatically increasing feasible solution generation rates. Two CR3BP transfers, Europa DRO and GTO halo, demonstrate that the diffusion-informed approach outperforms baseline sampling and adjoint-based initialization in both feasibility and throughput while preserving Pareto-relevant quality. The work underscores the value and limitations of data-intensive learning for mission design, and points to future extensions including tighter tolerances, multi-parameter conditioning, and higher-fidelity dynamics to enable on-board applicability.

Abstract

Long time-duration low-thrust nonlinear optimal spacecraft trajectory global search is a computationally and time expensive problem characterized by clustering patterns in locally optimal solutions. During preliminary mission design, mission parameters are subject to frequent changes, necessitating that trajectory designers efficiently generate high-quality control solutions for these new scenarios. Generative machine learning models can be trained to learn how the solution structure varies with respect to a conditional parameter, thereby accelerating the global search for missions with updated parameters. In this work, state-of-the-art diffusion models are integrated with the indirect approach for trajectory optimization within a global search framework. This framework is tested on two low-thrust transfers of different complexity in the circular restricted three-body problem. By generating and analyzing a training data set, we develop mathematical relations and techniques to understand the complex structures in the costate domain of locally optimal solutions for these problems. A diffusion model is trained on this data and successfully accelerates the global search for both problems. The model predicts how the costate solution structure changes, based on the maximum spacecraft thrust magnitude. Warm-starting a numerical solver with diffusion model samples for the costates at the initial time increases the number of solutions generated per minute for problems with unseen thrust magnitudes by one to two orders of magnitude in comparison to samples from a uniform distribution and from an adjoint control transformation.

Figures (20)

• Figure 1:
• Figure 2: Visualization of the global search strategy used for data generation. Two different approaches are shown: the lower path, where the preliminary screening approach is directly used to generate feasible solutions, and the upper path where it is combined with SNOPT.
• Figure 3: Preliminary screening algorithm.
• Figure 4: Visualization of the workflow used to train the diffusion model with fixed conditional parameters $\alpha$ and to test it on unseen $\alpha$-values.
• Figure 5: Illustration of the application of diffusion models, in the context of indirect low-thrust trajectory optimization. The trajectories resulting from a selected costate vector (red) from the distribution are shown at three diffusion steps.