Case Studies for Computing Density of Reachable States for Safe Autonomous Motion Planning

TL;DR

This paper presents a data-driven method combining density estimation and model predictive control to ensure safe autonomous motion planning under uncertainties, achieving high success rates with minimal training data.

Contribution

It introduces a novel approach that uses learned density distributions for risk assessment and path planning without requiring explicit system dynamics models.

Findings

Density estimation matches Monte-Carlo accuracy with fewer samples.

Achieves success rate above 99% in safe goal reaching.

Handles complex dynamics and uncertainties effectively.

Abstract

Density of the reachable states can help understand the risk of safety-critical systems, especially in situations when worst-case reachability is too conservative. Recent work provides a data-driven approach to compute the density distribution of autonomous systems' forward reachable states online. In this paper, we study the use of such approach in combination with model predictive control for verifiable safe path planning under uncertainties. We first use the learned density distribution to compute the risk of collision online. If such risk exceeds the acceptable threshold, our method will plan for a new path around the previous trajectory, with the risk of collision below the threshold. Our method is well-suited to handle systems with uncertainties and complicated dynamics as our data-driven approach does not need an analytical form of the systems' dynamics and can estimate forward state density with an arbitrary initial distribution of uncertainties. We design two challenging scenarios (autonomous driving and hovercraft control) for safe motion planning in environments with obstacles under system uncertainties. We first show that our density estimation approach can reach a similar accuracy as the Monte-Carlo-based method while using only 0.01X training samples. By leveraging the estimated risk, our algorithm achieves the highest success rate in goal reaching when enforcing the safety rate above 0.99.