Abstract

The density of the reachable states can help understand the risk of safety-critical systems, especially in situations when worst-case reachability is too conservative. In this work, we propose a data-driven method to compute the density distribution of reachable states for nonlinear and even black-box systems. Our semi-supervised approach learns system dynamics and the state density jointly from trajectory data, guided by the fact that the state density evolution follows the Liouville partial differential equation. With the help of neural network reachability tools, our approach can estimate the set of all possible future states as well as their density. Moreover, we could perform online safety verification with probability ranges for unsafe behaviors to occur. We use an extensive set of experiments to show that our learned solution can produce a much more accurate estimate of density distribution, and can quantify risks less conservatively and flexibly compared with worst-case analysis. We also study the use of such an approach in combination with model predictive control for verifiable safe path planning under uncertainties.

State density estimation

Our approach (NN) achieves 99% reduction in KL divergence!

Compute probabilistic bound for reachable sets

Visualization for density / reachability

Safety & feasibility comparison in motion planning

Under the same level of safety, our method achieves the highest feasibility.

Paper and Code

	Yue Meng, Dawei Sun, Zeng Qiu, Md T.B. Waez, and Chuchu Fan. Learning Density Distribution of Reachable States for Autonomous Systems Conference on Robot Learning (CoRL), 2021 [PDF][Code][Poster]
	Yue Meng, Zeng Qiu, Md T.B. Waez, and Chuchu Fan. Case Studies for Computing Density of Reachable States for Safe Autonomous Motion Plannings The 14th NASA Formal Methods Symposium (NFM), 2022 [PDF][Code]

This work is from REALM lab