Differential Game-Based Control for Nonlinear Human-Robot Interaction System With Unknown Desired Trajectory

Differential game is an effective technique to describe the negotiation between the humans and robots, which is widely used to realize the trajectory tracking tasks in the human-robot interaction (HRI). However, most existing works consider the control-affine HRI systems and assume the desired trajectory is available to both the human and the robot, which limit the scope of applications. To overcome these difficulties, this work focuses on the nonaffine HRI system and supposes that the desired trajectory is not available to the robot. A novel differential game framework encoding the desired trajectory estimator is proposed, where the desired trajectory is estimated via the Gaussian process regression (GPR) technique. To address the challenge arising from the nonlinearity of the HRI system, we equivalently transform the original problem into the one in a differentially flat space, and seek the equilibrium strategies for the transformed problem substitutionally. We further prove that the trajectory tracking error satisfies a probabilistic bound, whose confidence interval tightens as the decrease of noise variance during the interaction. Comparative simulation results show that our method outperforms the learning-based method in terms of robustness, parameters setting, and time consumption. Experiment results further show that the tracking error under the proposed human-robot cooperative algorithm is reduced by 55% compared to the human direct control.