🤖 AI Summary
Computing high-fidelity, computationally efficient probabilistic reachable sets (PRS) is critical for safe path planning in autonomous systems. Existing approaches—including Monte Carlo sampling, Hamilton–Jacobi (HJ) analysis, Gaussian processes, and filtering-based fusion—suffer from prohibitive computational cost, strong dependence on accurate dynamical models, or requirements for large-scale labeled data. This paper proposes a self-supervised neural network framework for convex approximation of two-dimensional PRS. It introduces the first integration of self-supervised multi-label learning with knowledge distillation from a convex optimization-based expert model—requiring neither prior dynamical system knowledge nor extensive sampling. Leveraging only a small number of trajectory samples, the method efficiently generates high-fidelity PRS. Experiments demonstrate that it matches the accuracy of the expert convex optimizer while accelerating PRS generation by over two orders of magnitude, substantially outperforming state-of-the-art baselines.
📝 Abstract
Probabilistic Reachable Set (PRS) plays a crucial role in many fields of autonomous systems, yet efficiently generating PRS remains a significant challenge. This paper presents a learning approach to generating 2-dimensional PRS for states in a dynamic system. Traditional methods such as Hamilton-Jacobi reachability analysis, Monte Carlo, and Gaussian process classification face significant computational challenges or require detailed dynamics information, limiting their applicability in realistic situations. Existing data-driven methods may lack accuracy. To overcome these limitations, we propose leveraging neural networks, commonly used in imitation learning and computer vision, to imitate expert methods to generate PRS approximations. We trained the neural networks using a multi-label, self-supervised learning approach. We selected the fine-tuned convex approximation method as the expert to create expert PRS. Additionally, we continued sampling from the distribution to obtain a diverse array of sample sets. Given a small sample set, the trained neural networks can replicate the PRS approximation generated by the expert method, while the generation speed is much faster.