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This research bridges generative AI and aerospace engineering by integrating diffusion models into indirect optimal control to solve fuel-optimal spacecraft trajectory problems with guaranteed optimality. The proposed method demonstrates superior convergence robustness compared to traditional random initialization techniques on complex Earth-Mars transfer scenarios, addressing a key limitation in current robotic control applications. By combining the exploration capabilities of deep learning with the rigorous mathematical foundations of indirect methods, this work advances the practical deployment of AI in high-stakes, long-horizon physical systems.
Diffusion-Based Multiple-Shooting Indirect Optimal Control for Fuel-Optimal Spacecraft Trajectory Generation
arXiv:2609.13990v1 Announce Type: cross Abstract: Diffusion-based generative models (DMs) have found applications in control problems, and in particular robotics, where the DMs enable exploration of possible control solutions. A critical shortcoming of these applications is that they have lacked optimality guarantees. This is a problem for their potential use in fuel-optimal spacecraft trajectories that are characterized with long time-horizons and bang-bang profiles. Alternatively, indirect optimal control methods ensure explicit satisfaction of necessary conditions, but are highly sensitive to the initial costate estimation needed to solve the resulting Hamiltonian boundary-value problems (HBVPs). To alleviate this sensitivity and enlarge the convergence domain of HBVPs, advanced indirect methods have been developed that use smoothing approaches and continuation. We propose a diffusion-based multiple shooting indirect control method that combines the exploration capability of DMs with indirect method to generate fuel-optimal spacecraft trajectories. We benchmark our method against an advanced indirect method on a fuel-optimal Earth-Mars low-thrust transfer problem, showing higher convergence robustness than the advanced indirect method that is based on random costate initialization. Code and visualizations are available at https://saeidtafazzol.github.io/Diffusion_Indirect_Control/.
Abstract:Diffusion-based generative models (DMs) have found applications in control problems, and in particular robotics, where the DMs enable exploration of possible control solutions. A critical shortcoming of these applications is that they have lacked optimality guarantees. This is a problem for their potential use in fuel-optimal spacecraft trajectories that are characterized with long time-horizons and bang-bang profiles. Alternatively, indirect optimal control methods ensure explicit satisfaction of necessary conditions, but are highly sensitive to the initial costate estimation needed to solve the resulting Hamiltonian boundary-value problems (HBVPs). To alleviate this sensitivity and enlarge the convergence domain of HBVPs, advanced indirect methods have been developed that use smoothing approaches and continuation. We propose a diffusion-based multiple shooting indirect control method that combines the exploration capability of DMs with indirect method to generate fuel-optimal spacecraft trajectories. We benchmark our method against an advanced indirect method on a fuel-optimal Earth-Mars low-thrust transfer problem, showing higher convergence robustness than the advanced indirect method that is based on random costate initialization. Code and visualizations are available at this https URL.
Systems and Control (eess.SY); Machine Learning (cs.LG)
arXiv:2609.13990 [eess.SY]
(or arXiv:2609.13990v1 [eess.SY] for this version)
https://doi.org/10.48550/arXiv.2609.13990 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 272 words
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