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 con- trol, there is no longer a form of the second-order differential equa- tion (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 simulationiscarriedouttoshowthedifferencebetweentheclassical impedance control and the proposed impedance control. Experi- ments 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.