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.

Predicting Long-Term Human Behaviors in Discrete Representations via Physics-Guided Diffusion

Long-term human trajectory prediction is a challenging yet critical task in robotics and autonomous systems. Prior work that studied how to predict accurate short-term human trajectories with only unimodal features often failed in long-term prediction. Reinforcement learning provides a good solution for learning human long-term behaviors but can suffer from challenges in data efficiency and optimization. In this work, we propose a long-term human trajectory forecasting framework that leverages a guided diffusion model to generate diverse long-term human behaviors in a high-level latent action space, obtained via a hierarchical action quantization scheme using a VQ-VAE to discretize continuous trajectories and the available context. The latent actions are predicted by our guided diffusion model, which uses physics-inspired guidance at test time to constrain generated multimodal action distributions. Specifically, we use reachability analysis during the reverse denoising process to guide the diffusion steps toward physically feasible latent actions. We evaluate our framework on two publicly available human trajectory forecasting datasets: SFU-Store-Nav and JRDB, and extensive experimental results show that our framework achieves superior performance in long-term human trajectory forecasting.

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.

Negotiation-Aware Reachability-Based Safety Verification for AutonomousDriving in Interactive Scenarios

Safety assurance is a critical yet challenging aspect when developing self-driving technologies. Hamilton-Jacobi backward-reachability analysis is a formal verification tool for verifying the safety of dynamic systems in the presence of disturbances. However, the standard approach is too conservative to be applied to self-driving applications due to its worst-case assumption on humans' behaviors (i.e., guard against worst-case outcomes). In this work, we integrate a learning-based prediction algorithm and a game-theoretic human behavioral model to online update the conservativeness of backward-reachability analysis. We evaluate our approach using real driving data. The results show that, with reasonable assumptions on human behaviors, our approach can effectively reduce the conservativeness of the standard approach without sacrificing its safety verification ability.

Prediction-Based Reachability for Collision Avoidance in Autonomous Driving

Safety is an important topic in autonomous driving since any collision may cause serious damage to people and the environment. Hamilton-Jacobi (HJ) Reachability is a formal method that verifies safety in multi-agent interaction and provides a safety controller for collision avoidance. However, due to the worst-case assumption on the car's future actions, reachability might result in too much conservatism such that the normal operation of the vehicle is largely hindered. In this paper, we leverage the power of trajectory prediction, and propose a prediction-based reachability framework for the safety controller. Instead of always assuming for the worst-case, we first cluster the car's behaviors into multiple driving modes, e.g. left turn or right turn. Under each mode, a reachability-based safety controller is designed based on a less conservative action set. For online purpose, we first utilize the trajectory prediction and our proposed mode classifier to predict the possible modes, and then deploy the corresponding safety controller. Through simulations in a T-intersection and an 8-way roundabout, we demonstrate that our prediction-based reachability method largely avoids collision between two interacting cars and reduces the conservatism that the safety controller brings to the car's original operations.

Generating Robust Supervision for Learning-Based Visual Navigation Using Hamilton-Jacobi Reachability

In Bansal et al. (2019), a novel visual navigation framework that combines learning-based and model-based approaches has been proposed. Specifically, a Convolutional Neural Network (CNN) predicts a waypoint that is used by the dynamics model for planning and tracking a trajectory to the waypoint. However, the CNN inevitably makes prediction errors, ultimately leading to collisions, especially when the robot is navigating through cluttered and tight spaces. In this paper, we present a novel Hamilton-Jacobi (HJ) reachability-based method to generate supervision for the CNN for waypoint prediction. By modeling the prediction error of the CNN as disturbances in dynamics, the proposed method generates waypoints that are robust to these disturbances, and consequently to the prediction errors. Moreover, using globally optimal HJ reachability analysis leads to predicting waypoints that are time-efficient and do not exhibit greedy behavior. Through simulations and experiments on a hardware testbed, we demonstrate the advantages of the proposed approach for navigation tasks where the robot needs to navigate through cluttered, narrow indoor environments.