  Reachability analysis is a widely used method to analyze the safety of a
Human-in-the-Loop Cyber Physical System (HiLCPS). This strategy allows the
HiLCPS to respond against an imminent threat in advance by predicting reachable
states of the system. However, it could lead to an unnecessarily conservative
reachable set if the prediction only relies on the system dynamics without
explicitly considering human behavior, and thus the risk might be
overestimated. To reduce the conservativeness of the reachability analysis, we
present a state prediction method which takes into account a stochastic human
behavior model represented as a Gaussian Mixture Model (GMM). In this paper, we
focus on the multi-rotor in a near-collision situation. The stochastic human
behavior model is trained using experimental data to represent human operators'
evasive maneuver. Then, we can retrieve a human control input probability
distribution from the trained stochastic human behavior model using the
Gaussian Mixture Regression (GMR). The proposed algorithm predicts the
probability distribution of the multi-rotor's future state based on the given
dynamics and the retrieved human control input probability distribution.
Besides, the proposed state prediction method considers the uncertainty of the
initial state modeled as a GMM, which yields more robust performance. Human
subject experiment results are provided to demonstrate the effectiveness of the
proposed algorithm.
