  Robots such as autonomous vehicles and assistive manipulators are
increasingly operating in dynamic environments and close physical proximity to
people. In such scenarios, the robot can leverage a human motion predictor to
predict their future states and plan safe and efficient trajectories. However,
no model is ever perfect -- when the observed human behavior deviates from the
model predictions, the robot might plan unsafe maneuvers. Recent works have
explored maintaining a confidence parameter in the human model to overcome this
challenge, wherein the predicted human actions are tempered online based on the
likelihood of the observed human action under the prediction model. This has
opened up a new research challenge, i.e., \textit{how to compute the future
human states online as the confidence parameter changes?} In this work, we
propose a Hamilton-Jacobi (HJ) reachability-based approach to overcome this
challenge. Treating the confidence parameter as a virtual state in the system,
we compute a parameter-conditioned forward reachable tube (FRT) that provides
the future human states as a function of the confidence parameter. Online, as
the confidence parameter changes, we can simply query the corresponding FRT,
and use it to update the robot plan. Computing parameter-conditioned FRT
corresponds to an (offline) high-dimensional reachability problem, which we
solve by leveraging recent advances in data-driven reachability analysis.
Overall, our framework enables online maintenance and updates of safety
assurances in human-robot interaction scenarios, even when the human prediction
model is incorrect. We demonstrate our approach in several safety-critical
autonomous driving scenarios, involving a state-of-the-art deep learning-based
prediction model.
