**3.1.3 Deformable objects**

The interaction with deformable objects raises the computational requirements of haptic rendering and it requires adapting the deformable representations coming from other domains (Nealen, M"uller, Keiser, Boxerman, & Carlson, 2006) to the specific characteristics of haptics. The fact that the object is deformable means that it has smaller stiffness, reducing the required update rate. Several models have been explored in literature mostly based on Finite Element Models (FEM) depending on the linearization approach and the entity of supported deformations.

The key point of deformable haptics is the management of the potential collision. When the collision between the proxy and the object is identified at a given point in space and time, it is being handled by the collision response. The first stage of the response deals with handling the spatial overlapping that is typically managed by moving the deformable surface outside the proxy, as an extension of the impulsive phase discussed above. The second stage has the role of preventing future penetration and it can be solved using the general methods discussed above: penalty or motion constraints. In cloth simulation, for

On the Integration of Tactile and Force Feedback 59

a method for computing the soft finger contacts based on local geometries and object

The position control approach for rendering first contact is not able to represent high frequency transients that characterize stiff materials. A possible solution to this problem has been addressed by event-based haptics (Kuchenbecker, Fiene, & Niemeyer, 2005) in which the first instants of contact are performed in open loop by superimposing a previously

The above contact models and contact resolution techniques have to be implemented in a framework that manages the interfaces with the haptic interface control module under the limitations of computational resources. Each module has a different target rate connected to the perceptual field namely: 1 kHz for kinesthetic, 300Hz for tactile and 60Hz for visual. The computational resources pose strong limitations to the achievable update rates. Modularization allows not only to manage correctly different rates but also to keep the software flexible against changes, for design exploration and management. The result of such modularization is a multi-rate architecture (F Barbagli, Prattichizzo, & K Salisbury, 2005) in which modules at different rates exchange data at synchronization points. In

 Simulation: performs a relatively slow simulation of the object in the environment. Depending on the contact model it consider the proxy object as part of the

Collision detection: evaluates the collision between entities in the environment, and in

Haptic Rendering: transforms the state and forces acting on the proxy into commands

The collision detection module is typically the slowest part because it has to take into account the overall geometry of the virtual objects, although some techniques can be applied to limit the area of search based on speed and space boundaries. In addition, some GPU techniques can improve the rate, although it is difficult to reach the rate of the other components, in particular the haptic one. The connection between the collision detection and the simulation models is based on the notification of the contacts that are then used in the simulation block. Depending on the quality of the simulation in some cases it is worth clustering the contacts aggregating them based on their distance as performed by Otaduy

An additional technique that can be employed for guaranteeing haptic rates in the simulation is the adoption of a multi level approach in the simulation, in particular when dealing with deformable models. A coarse representation of the objects is used in a slow simulation, slow in the sense that the time step of the simulation advances at large steps,

Tactile Rendering: transforms the proxy into information for the tactile part

curvatures.

**3.1.6 High frequency contact** 

**3.2 Haptic rendering architecture** 

particular we can identify several elements:

for the control of the kinesthetic part

recorded force profile.

simulation

particular the proxy

(Miguel A. Otaduy, 2005).

example, the constraint model is applied using filtering of the motion inside a Conjugate Gradient method (Baraff & Witkin, 1998). Duriez et al. (Duriez, Andriot, & Kheddar, 2004), instead, adopted a contact model that employs Signorini's law for quite convincing FEM model supporting contacts between deformable objects. In particular the contact is resolved by equating the gap with a combination of a post contact gap and the projection of the two displacements along the contact normal. This equation is then expressed in terms of the exchanged contact forces and resolved in the general deformable FEM framework.
