Stable haptic display of 1-DOF grasping with coupling impedance for internal and external forces

We discuss a haptic display for 1-DOF grasping of a virtual object by two fingers. Much research has been done on fundamental analysis for stability of haptic displays. But it is difficult to apply the results immediately to grasping situations by two fingers, since the studies deal with a single device and a single object. This is because the fingertip force in grasping situations has two components, internal and external force. The conventional methods, which calculate the coupling impedance at each contact point separately, have no other alternative but to calculate the impedance for the sum of the internal and external force components. So even if only the impedance for external force should be changed, the impedance for internal force is also changed at the same time. We propose a method, in which the coupling impedance is calculated separately for internal and external forces. Second, we discuss the stability of the proposed method and compare it with the conventional method. Finally, we perform some experiments to confirm the effects of the proposed method.