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

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.

Global Search of Optimal Spacecraft Trajectories using Amortization and Deep Generative Models

Preliminary spacecraft trajectory optimization is a parameter dependent global search problem that aims to provide a set of solutions that are of high quality and diverse. In the case of numerical solution, it is dependent on the original optimal control problem, the choice of a control transcription, and the behavior of a gradient based numerical solver. In this paper we formulate the parameterized global search problem as the task of sampling a conditional probability distribution with support on the neighborhoods of local basins of attraction to the high quality solutions. The conditional distribution is learned and represented using deep generative models that allow for prediction of how the local basins change as parameters vary. The approach is benchmarked on a low thrust spacecraft trajectory optimization problem in the circular restricted three-body problem, showing significant speed-up over a simple multi-start method and vanilla machine learning approaches. The paper also provides an in-depth analysis of the multi-modal funnel structure of a low-thrust spacecraft trajectory optimization problem.

Learning Optimal Control and Dynamical Structure of Global Trajectory Search Problems with Diffusion Models

Spacecraft trajectory design is a global search problem, where previous work has revealed specific solution structures that can be captured with data-driven methods. This paper explores two global search problems in the circular restricted three-body problem: hybrid cost function of minimum fuel/time-of-flight and transfers to energy-dependent invariant manifolds. These problems display a fundamental structure either in the optimal control profile or the use of dynamical structures. We build on our prior generative machine learning framework to apply diffusion models to learn the conditional probability distribution of the search problem and analyze the model's capability to capture these structures.

Constraint-Aware Diffusion Models for Trajectory Optimization

The diffusion model has shown success in generating high-quality and diverse solutions to trajectory optimization problems. However, diffusion models with neural networks inevitably make prediction errors, which leads to constraint violations such as unmet goals or collisions. This paper presents a novel constraint-aware diffusion model for trajectory optimization. We introduce a novel hybrid loss function for training that minimizes the constraint violation of diffusion samples compared to the groundtruth while recovering the original data distribution. Our model is demonstrated on tabletop manipulation and two-car reach-avoid problems, outperforming traditional diffusion models in minimizing constraint violations while generating samples close to locally optimal solutions.

Efficient and Guaranteed-Safe Non-Convex Trajectory Optimization with Constrained Diffusion Model

Trajectory optimization in robotics poses a challenging non-convex problem due to complex dynamics and environmental settings. Traditional numerical optimization methods are time-consuming in finding feasible solutions, whereas data-driven approaches lack safety guarantees for the output trajectories. In this paper, we introduce a general and fully parallelizable framework that combines diffusion models and numerical solvers for non-convex trajectory optimization, ensuring both computational efficiency and constraint satisfaction. A novel constrained diffusion model is proposed with an additional constraint violation loss for training. It aims to approximate the distribution of locally optimal solutions while minimizing constraint violations during sampling. The samples are then used as initial guesses for a numerical solver to refine and derive final solutions with formal verification of feasibility and optimality. Experimental evaluations on three tasks over different robotics domains verify the improved constraint satisfaction and computational efficiency with 4$\times$ to 22$\times$ acceleration using our proposed method, which generalizes across trajectory optimization problems and scales well with problem complexity.

Amortized Global Search for Efficient Preliminary Trajectory Design with Deep Generative Models

Preliminary trajectory design is a global search problem that seeks multiple qualitatively different solutions to a trajectory optimization problem. Due to its high dimensionality and non-convexity, and the frequent adjustment of problem parameters, the global search becomes computationally demanding. In this paper, we exploit the clustering structure in the solutions and propose an amortized global search (AmorGS) framework. We use deep generative models to predict trajectory solutions that share similar structures with previously solved problems, which accelerates the global search for unseen parameter values. Our method is evaluated using De Jong's 5th function and a low-thrust circular restricted three-body problem.