Graebner & Beeson's diffusion model yields 40% more feasible spacecraft trajectories

Graebner and Beeson (affiliated with Princeton University, based on prior work) tackle a core challenge in preliminary spacecraft mission design: generating high-quality low-thrust trajectories across varying mission parameters quickly. Traditional indirect optimal control methods suffer from many local minima and expensive global searches. The authors propose a transfer learning framework that uses homotopy (smoothly varying a mission parameter, here the system mass) combined with Markov chain Monte Carlo (MCMC) to efficiently sample costate distributions. They compare three MCMC algorithms—random-walk Metropolis-Hastings, Hamiltonian Monte Carlo, and the No-U-Turn Sampler (NUTS)—on a planar multi-revolution transfer in the circular restricted three-body problem.

The results show gradient-based MCMC variants achieve the best balance between sample quality and computational cost. The MCMC-generated samples are then used to fine-tune a diffusion model conditioned on the mass parameter, enabling it to learn a global representation of the solution distribution and generate new solutions without further optimization. This approach yields 40% more feasible trajectories and a Pareto front that dominates the state-of-the-art adjoint control transformation method. The work establishes a practical, data-efficient method for solving families of indirect trajectory optimization problems, which is critical for accelerating iterative mission design loops.