Robust, informative human-in-the-loop predictions via empirical reachable sets

In order to develop safe autonomous systems, accurate and precise models of human behavior must be developed. For intelligent vehicles, one can imagine the need for predicting driver behavior to develop minimally invasive active safety systems or to safely interact with human drivers on the road. We present an optimization-based method for approximating the stochastic reachable set for human-in-the-loop systems. This method identifies the most precise subset of states that a human driven vehicle may enter, given some data set of observed trajectories. We phrase this problem as a mixed integer linear program, solved via branch and bound methods. The resulting model uncovers the most representative set that encapsulates the likely trajectories, up to some probability threshold, by optimally rejecting outliers in the data set. This tool provides set predictions consisting of trajectories observed from the nonlinear dynamics and behaviors of the human driven car, and can account for modes of behavior, like the driver state or intent. This method is applied to predict lane changing behavior, achieving \sim90% accuracy over long time horizons. This flexible algorithm is to handle realistic complex human driving data and provide a robust and informative prediction of driver behavior.