Simple-Rotation Angle/Axis Representations Based Second-Order Impedance Control

Since the difference in angular velocity is used as the derivative of the orientation error in the classical impedance control, there is no longer a form of the second-order differential equation (SODE), and there is non-linearity in the classical impedance control, which limits applications. To address this problem, this article uses simple-rotation angle/axis representations (SRAAR), as well as their derivatives, to describe the end-effector's orientation displacement and its derivatives in impedance control. As a result, an SRAAR-based second-order impedance control, whose dynamic relationship has the form of SODE, is proposed. Furthermore, as a direct application of the proposed SRAAR-based second-order impedance control, an adaptive control method is also proposed to deal with the problem of uncertain dynamic parameters so that the desired dynamic relationship can be accurately realized. A simulation is carried out to show the difference between the classical impedance control and the proposed impedance control. Experiments on the Franka Emika Panda have been conducted, and the results validate the effectiveness of the proposed adaptive control, which also verifies the correctness of the proposed SRAAR-based second-order impedance control.