Safe Human-Machine Cooperative Game with Level-k Rationality Modeled Human Impact

This paper considers the problem of bounded rational human behavior in the cooperative human-machine game. The cooperation between human and machine is a raising topic for emergency handling, and it is critical to ensure the safety of human. First, a barrier-function-based state transformation is developed to ensure the safety constraints of the human-machine system state. A level-k rationality structure is then exploited by cognitive hierarchy to learn human behavior, and the bounded rational behavior is obtained by using Adaptive Dynamic Programming (ADP). Inspired by behavior modeling from sociology, a softmax probabilistic decision distribution is utilized to model human behavior, which imitates the true impact of human in the cooperative game. Finally, a simulation is implemented to test the effectiveness of the proposed behavior, which demonstrates that the full state constraints and stabilization are guaranteed.