**3. Software for integrated haptic rendering**

This section deals with the Computer Haptics aspects of the integrated force and tactile feedback, addressing, from one side, the physical and geometrical model of interaction, from the other, the computational challenges of the integrated rendering. The first part of this section is dedicated to a review of the models of contact, taking into account friction, soft finger representation and multiple finger interaction, both for kinesthetic and tactile feedback. The second part deals with architectural configurations of simulation and haptic rendering engines taking into account multi-rate and multi-resolution techniques.

critical since there is no need of gravity compensation. Moreover the single finger

One finger device has a superior level of complexity since the weights of the display has to be compensated by the kinaesthetic device. There are various implemented solutions that

Wagner in (Wagner, 2005) proposed the integration of kinaesthetic feedback with a shape display. Kheddar introduced the concept of a multilevel device for the different spatial level

In the case of multi-finger interaction a major problem has to be considered. For allowing the simulation of grasping of reduced thickness the fingers have to be free to get close each other. This results in very though requirements for the thickness of the tactile display in the palmar area of the fingertip. The display has to be as flat as possible in order to allow the finger of user to get close together during grasps of small virtual objects. There are no experiments that exactly establish what is the exact tolerable thickness of a display for supporting multi-finger interaction, but simple tests can demonstrate that it must be kept in

One possible way to get around this issue is to employ an electro-tactile display that can reach a very flat shape like in (Sato et al.,2007). However, electro-tactile displays show several disadvantages like large variation of perceived stimulus from subject to subject, dependence from wetness of the finger surface, employment of high voltage etc. Those unwanted feature made them hardly usable in the context of a virtual reality simulation. Other attempts has been done for obtaining mechanical tactile displays with flat shape.

Benali-Khoudja in (Benali-Khoudja et al., 2003) developed a pin-array display based on a multilayer approach that has been conceived for integration with kinesthetic feedback. In the European Project HAPTEX a system composed by a desktop haptic device and a piezo-electric pin-array display have been adapted for the integration and tested (Fontana et al., 2007).

Recently a novel pin-array display based on a customized solenoid transducer has been purposely developed by authors for the integration with a hand exoskeleton (Salsedo et

This section deals with the Computer Haptics aspects of the integrated force and tactile feedback, addressing, from one side, the physical and geometrical model of interaction, from the other, the computational challenges of the integrated rendering. The first part of this section is dedicated to a review of the models of contact, taking into account friction, soft finger representation and multiple finger interaction, both for kinesthetic and tactile feedback. The second part deals with architectural configurations of simulation and haptic

rendering engines taking into account multi-rate and multi-resolution techniques.

interaction puts no strict limits to vertical encumbrance of the display.

differ from the type of tactile display that is employed.

**3. Software for integrated haptic rendering** 


of details (Kheddar, 2004). - Multiple Finger Spatial:

the range of few millimetres.

al.,2011).

The haptic rendering for object manipulation and exploration has the characteristic of combining the techniques from physics simulation with the principles of control and knowledge about human perception. Without losing generality haptic interaction scenarios can be represented by a physics simulation in which one or more virtual entities have the special role of exchanging haptic information with the user. These entities are called *proxies*. In some scenarios these virtual entities represent a user body part that directly interacts with other objects in the environment. A different type of representation is the one happening when the user interacts by means of a virtual tool as a stylus or a more complex tool. Examples of applications in the former type are exploration of surfaces, grasping, haptic rehabilitation and scenarios in which an avatar is employed. Examples of the latter type are drilling, simulation and even driving simulation. Clearly, the type of proxy depends on the type of haptic interface and the specific attachment to the user body part. For direct contact, like virtual finger exploration, the robotic endeffector applies forces on the fingers of the user using a rigid attachment to the user, or, following an encountered haptic approach. Instead devices in which the user holds a stylus or a handle are more suited for tool based proxies.

The type of proxy has effects, for the purpose of our discussion, in terms of the geometry and physical modeling of contact having to simulate, in one case, the contact between the finger or a body part with virtual objects, while in the other the contact of a virtual rigid object that transmits the contact to the user.

The general aim of the proxy is to be respectful of the physical properties of the virtual world, meaning that its behavior will avoid penetration with other objects. There is anyway a caveat. In real world the user moves the haptic interface end-effector specifying in this way a requested virtual position for the proxy. This requested position and orientation is a virtual entity called *haptic handle*. When the proxy touches an object like a virtual wall, the haptic interface produces a force to represent the opposition of the wall to penetration but this force is not always able to prevent the motion of the user in real space into the space where the virtual object is located. The discrepancy between proxy position and haptic handle position is a key element of haptic rendering. The common to rendering approach is to simulate the presence of a virtual spring between the proxy and the handle with a factor proportional to the stiffness of the object in contact. This approach is called penalty based because force is proportional to the penalty of entering with the handle into the object. This spring can introduce some instability and for this reason it can be replaced by a damped spring. Please note how, in this discussion, we have not taken into account the effect of the force produced by the spring on the proxy.

Moreover, we have not made distinctions between impedance and admittance interfaces. In the formers the low level controller receives forces to be applied to the user at the endeffector, and in most of the cases such force is computed on the side of the computer performing simulation and collision. In the latters the low level controller specifies a position to be held with a given stiffness, up to the maximal force of the device.
