In order to analyze the complex interactive behaviors between the robot and two humans, this paper presents an adaptive optimal control framework for human-robot-human physical interaction. N-player linear quadratic differential game theory is used to describe the system under study. N-player differential game theory can not be used directly in actual scenerie, since the robot cannot know humans' control objectives in advance. In order to let the robot know humans' control objectives, the paper presents an online estimation method to identify unknown humans' control objectives based on the recursive least squares algorithm. The Nash equilibrium solution of human-robot-human interaction is obtained by solving the coupled Riccati equation. Adaptive optimal control can be achieved during the human-robot-human physical interaction. The effectiveness of the proposed method is demonstrated by rigorous theoretical analysis and simulations. The simulation results show that the proposed controller can achieve adaptive optimal control during the interaction between the robot and two humans. Compared with the LQR controller, the proposed controller has more superior performance.
Keywords: adaptive optimal control; game theory; physical human-robot interaction; robot control.