# Predicting Stochastic Human Forward Reachable Sets Based on Learned Human Behavior

## TL;DR

This paper introduces a novel framework combining Hamilton-Jacobi reachability with machine learning to predict human behavior in collision avoidance, enabling the creation of stochastic reachable sets with adjustable safety probabilities.

## Contribution

It integrates HJ reachability information into machine learning models and proposes a flexible stochastic reachable set generation method for safety-critical scenarios.

## Key findings

- Incorporating HJ reachability improves prediction accuracy.
- The stochastic reachable sets can represent trajectories with 75% to 100% probability.
- The framework generalizes to new scenarios effectively.

## Abstract

With the recent surge of interest in introducing autonomous vehicles to the everyday lives of people, developing accurate and generalizable algorithms for predicting human behavior becomes highly crucial. Moreover, many of these emerging applications occur in a safety-critical context, making it even more urgent to develop good prediction models for human-operated vehicles. This is fundamentally a challenging task as humans are often noisy in their decision processes. Hamilton-Jacobi (HJ) reachability is a useful tool in control theory that provides safety guarantees for collision avoidance. In this paper, we first demonstrate how to incorporate information derived from HJ reachability into a machine learning problem which predicts human behavior in a simulated collision avoidance context, and show that this yields a higher prediction accuracy than learning without this information. Then we propose a framework to generate stochastic forward reachable sets that flexibly provides different safety probabilities and generalizes to novel scenarios. We demonstrate that we can construct stochastic reachable sets that can capture the trajectories with probability from 0.75 to 1.