Trajectory prediction and planning are fundamental components for autonomous vehicles to navigate safely and efficiently in dynamic environments. Traditionally, these components have often been treated as separate modules, limiting the ability to perform interactive planning and leading to computational inefficiency in multi-agent scenarios. In this paper, we present a novel unified and data-driven framework that integrates prediction and planning with a single consistency model. Trained on real-world human driving datasets, our consistency model generates samples from high-dimensional, multimodal joint trajectory distributions of the ego and multiple surrounding agents, enabling end-to-end predictive planning. It effectively produces interactive behaviors, such as proactive nudging and yielding to ensure both safe and efficient interactions with other road users. To incorporate additional planning constraints on the ego vehicle, we propose an alternating direction method for multi-objective guidance in online guided sampling. Compared to diffusion models, our consistency model achieves better performance with fewer sampling steps, making it more suitable for real-time deployment. Experimental results on Waymo Open Motion Dataset (WOMD) demonstrate our method's superiority in trajectory quality, constraint satisfaction, and interactive behavior compared to various existing approaches.

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.

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.

The preliminary spacecraft trajectory design phase can be posed as a parameterized global search problem for optimal spacecraft trajectories. At each stage of the preliminary design, the mission objectives, requirements, and constraints may change, resulting in variations of the global search problem parameters. Parameters may also change to represent increased modeling fidelity. The aim at any stage of the preliminary design is to solve for a large set of high quality spacecraft trajectories with diverse, or similarly qualitatively different, features. High quality is naturally defined by the value of a solution's objective value relative to the best known. Examples of qualitatively different features may include trajectories that have a different number of revolutions around a central body, a different number or sequence of gravity assist flybys, solutions that avoid radiation belts or other hazards, or solutions that depart the original or target orbital planes. The benefit of having different qualitative solutions is that it allows mission designers to trade different priorities in their design and reflects the fact that not all relevant objectives and constraints can be incorporated into the optimal spacecraft trajectory problem so early or readily in the design phase (i.e., without prior knowledge of what is relevant and when designing at a quick cadence). In the simplest of cases, a mission designer's past experience may be sufficient to guide them in finding a high quality set of solutions.

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.

Motivated by the need to solve open-loop optimal control problems with computational efficiency and reliable constraint satisfaction, we introduce a general framework that combines diffusion models and numerical optimization solvers. Optimal control problems are rarely solvable in closed form, hence they are often transcribed into numerical trajectory optimization problems, which then require initial guesses. These initial guesses are supplied in our framework by diffusion models. To mitigate the effect of samples that violate the problem constraints, we develop a novel constrained diffusion model to approximate the true distribution of locally optimal solutions with an additional constraint violation loss in training. To further enhance the robustness, the diffusion samples as initial guesses are fed to the numerical solver to refine and derive final optimal (and hence feasible) solutions. Experimental evaluations on three tasks verify the improved constraint satisfaction and computational efficiency with 4$\times$ to 30$\times$ acceleration using our proposed framework, which generalizes across trajectory optimization problems and scales well with problem complexity.

For example, a grid-based search is a classical approach for spacecraft preliminary trajectory design. However, this technique is more suitable for impulsive trajectory since the search space is much smaller. Due to the curse of dimensionality, low-thrust trajectory design often needs a more intelligent global search algorithm. Evolutionary algorithms, including Differential Evolution (DE) [4], Genetic algorithm (GA) [5], Particle swarm optimization (PSO) [6], etc., have been widely used in global optimization problems in spacecraft trajectory design [7, 8, 9, 10]. These algorithms iteratively generate new solutions by introducing randomness to previously obtained solutions and downselecting the solutions based on specific quality metrics. In addition, researchers also combine stochastic search algorithms with local gradient-based optimizers to attempt to find the globally optimal solution. The multistart method samples the search space with a fixed distribution and feeds the samples into a local optimizer as starting points for local search [10]. Inspired by energy minimization principles in computational chemistry, Monotonic Basin Hopping (MBH) [11, 12] adds random perturbations during the local search to uncover multiple local optima solutions that are close to each other. MBH rapidly became popular in the sphere of spacecraft trajectory design [1, 13, 14] and has been established as the state-of-the-art algorithm in terms of efficiency and solution quality through various benchmarks [15, 9, 10].