For robot interaction control, the interaction force between the robot and the manipulated object or environment should be monitored. Impedance control is a type of interaction control. Specifically, in impedance control, the dynamic relationship between the interaction force and the resulting motion is controlled. In order to control the impedance of a mechanical system, typically, the interaction force has to be sensed. Due to the inherent limitations of direct force sensing at the interaction site, in the present work, the interaction force is observed using robust observers. In particular, to enhance the accuracy of impedance control, a first order sliding mode impedance controller is designed and incorporated in the present paper. Its advantage over position-based interaction control algorithms is demonstrated through experimentation. Experimental results are given to show the effectiveness of the proposed algorithms.