Nonlinear model reference adaptive impedance control for human–robot interactions

• Four nonlinear MRAI controllers are presented, tested, and compared.
• The closed-loop dynamics of the robot is made similar to the reference model.
• The stability is proved using Lyapunov theorem.
• The effectiveness is investigated using a two-DOFs robot.

Four nonlinear Model Reference Adaptive Impedance Controllers are introduced, tested, and compared for the control of the robot impedance with uncertainties in model parameters. The intended application area is human–robot interactions (HRI), particularly rehabilitation robots and haptic interfaces. All of the controllers make the closed-loop dynamics of the robot similar to the reference impedance model besides providing asymptotic tracking of the impedance model for the robot end-effector in Cartesian coordinates. The tracking and global stability are proved using Lyapunov stability theorem. Based on the simulations and experiments on a two-DOFs robot, the effectiveness of the proposed controllers is investigated.