Sampled- and continuous-time passivity and stability of virtual environments

We propose a new time-domain passivity observer (PO) and passivity controller (PC) which removes the constant-velocity assumption during one sample time, which was used in our previous PO/PC approach. A new sampled-time definition of passivity is introduced, and this new definition is compared with the previous sampled-time definition of passivity. Through this comparison, we propose the more accurate PO/PC approach. The proposed new PO/PC approach is applied to the "Excalibur" haptic interface system with very high stiffness (K = 120 kN·m) virtual environment, and stable contact is demonstrated.