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

Abstract

We consider the following problem in haptics: information update from the virtual world is slow w.r.t. the local servo-loop rate of the haptic device, and the information transmission/update between the haptic device and the virtual world is of variable rate and/or asynchronous. For this, we propose a novel control framework, that, by relying on our recently proposed passive set-position modulation (PSPM) and discrete-time passive non-iterative integrators, enables us to enforce two-port hybrid (i.e. continuous-discrete) passivity for such slow and variable/asynchronous haptics as well as to separate the virtual world simulation design from the device's servo-loop tuning. Relevant experimental results are also presented.

Extension of colgate's passivity condition for variable-rate haptics

“…uniform-rate), these conditions become exactly the same as the Colgate's passivity condition (1). In this paper, we will also show that, under a condition similar to the new passivity condition (2), the recently proposed passive set-position modulation (PSPM) [5], [6], [9] can achieve passive haptic rendering while relaxing its assumption that the local device servo-loop should be much faster than the data update from the virtual environment. By doing so, this PSPM framework, together with non-iterative discrete-time passive integrator [10], can then achieve 1) passive haptic interaction even if communication is imperfect (e.g.…”

“…Then, we want this variable-rate virtual coupling (3)-(4) to possess the following two-port hybrid (i.e. continuousdiscrete) passivity [5]:…”

“…2, the virtual coupling (3)-(4) is a hybrid system, residing between the continuous-time haptic device and the discretetime virtual environment and containing both discrete and continuous terms. Here, note that the term ∑ This condition (5) implies that the maximum energy extractable from the virtual coupling by the human operator and the virtual world is bounded. If the (open-loop) haptic device is continuous-time passive (e.g.…”

“…Of course, here, we have this inequality (9) witht = t N+1 , rather than ∀t ∈ T N = [t N ,t N+1 ) as required for (5). Yet, note that this inter-sample passivity (i.e.…”

“…T k = T for all k ≥ 0). To this we may probably ascribe the fact that, in contrast to the uniform-rate haptics where the passivity condition (1) is readily applicable, most (or, to our knowledge, all, except [5], [6]) of the variable-rate haptics results (e.g. [7], [8]) do not enforce passivity, although this passivity is desirable in haptics in its capacity to ensure haptic interaction stability with a wide range of human-users, grips, etc.…”