Sampled- and Continuous-Time Passivity and Stability of Virtual Environments

Abstract

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 ( = 120 kN m) virtual environment, and stable contact is demonstrated. Index Terms-Haptic interface, passivity controller (PC), passivity observer (PO), time-domain passivity.

Design of Networked Control Systems Using Passivity

“…We refer to both IPES and ZOH devices as IPESH. We present a noncausal version of the IPESH which is based on the causal version of the IPESH presented in [16], [43,Definition 4] and earlier work in [12] and [44].…”

Multi-rate networked control of conic (dissipative) systems

“…Additionally, we present a corollary for transforming a continuous-time conic single-input, single-output (SISO) linear time-invariant (LTI) system into a discretetime conic SISO LTI system using the IPESH-Transform. We begin by recalling the definition for the IPESH which is based on the earlier work of [25], [26].…”

Passive set-position modulation approach for haptics with slow, variable, and asynchronous update

“…[6]) is extendable here, particularly, to the case of variable/asynchronousrate haptics. Other well-known and related approach is the timedomain passivity approach (or PO/PC) [7,8,9], which however may not be applicable for slow-rate haptics, since the PC/PO has been proved only to enforce stability, not passivity, when continuous dynamics is not negligible [9]. Another related approach is the energy bounding algorithm (EBA) [10], which modulates control force rather than the set-position signal as done here.…”

“…continuous x(t) and discrete y(k)), yet, most of other works (e.g. [7,8,9,11,12,13]) usually neglects it or considers it as something necessarily detrimental.…”