Decision boundary learning for safe vision-based navigation via Hamilton-Jacobi reachability analysis and Support Vector Machine

We develop a self-supervised learning method that can predict the decision boundary between safe and unsafe high-level waypoints for robot navigation given the first-person view in the form of an RGB image, and the current speed of the robot, without knowledge of the map of the environment. To provide the theoretical basis for such predictions, we use Hamilton-Jacobi reachability analysis, a formal verification method, as the oracle for labeling training datasets. Given the labeled data, our neural network learns the coefficients of a decision boundary via a soft-margin Support Vector Machine loss function to classify safe and unsafe system states. We experimentally show that our method is generalizable to the real world and generates safety decision boundaries in unseen indoor environments. Our method's advantages are its explainability, robustness, data efficiency, and accurate safety prediction. Finally, we demonstrate our method via real-world experiments