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

The global search for optimal long time-duration, low-thrust spacecraft trajectories is a computationally expensive problem, that is characterized by clustering patterns in locally optimal solutions. During preliminary mission design, mission parameters have not been fully defined yet, necessitating that trajectory designers efficiently generate high-quality control solutions across a wide range of different scenarios. Generative machine learning models can be trained to learn how the solution structure varies with respect to an evolving mission parameter, thereby accelerating the global search for a large number of missions with varying parameters. In this work, state-of-the-art diffusion models are integrated with the indirect approach for trajectory optimization within a global search framework. The main difficulty with the indirect method lies in generating good initial guesses for the non-intuitive costate variables, which are crucial for solver convergence. By training a diffusion model to learn the structure of high-quality solutions in costate space, it can generate initial costate guesses for new mission parameters. 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 predicts how the costate solution structure changes, based on the maximum spacecraft thrust magnitude. We warm-start a numerical solver with initial costates sampled from the diffusion model for problems with unseen thrust magnitudes and compare the number of solutions generated per minute to samples from a uniform distribution and from an adjoint control transformation. Results show that the diffusion model accelerates the global search process by one to two orders of magnitude, allowing for rapid generation of high-quality solutions.