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Figure 16.5 Calculation of haptic rendering by penalty (a) and by virtual proxy (b)
In practice, this means that the simulation provides a position that the device is sup-
posed to take. If this is the case ( e
0), no force is returned to the operator. Otherwise,
the two positions are separate and the forces are created on the basis of the difference
measured. On one hand, the forces sent to the device try to reach the position desired
by the simulation. Figure 16.5 illustrates the difference of haptic calculation strategy
between direct interfacing by penalty and approach by virtual proxy. In the first case,
the force is calculated on the basis of an interpenetration measurement, whereas in the
second case, the force comes from a difference in position.
The readers may legitimately think that the operator realises that the movement
of the device that he controls does not exactly correspond to the movement displayed by
the simulation during a contact. However, the difference between the two positions is
not visible in reality. On the contrary, it is rather perceived as hardness, i.e. impossibility
to penetrate an obstacle. The operator is in fact more receptive in terms of the effort
he puts in rather than the position he maintains. 3
= Implementation
Implementation of admittance control was first suggested by Zilles and Salisbury
(1995), and then extended by Ruspini et al. (1997). In these works, the avatar is
assumed to be point-based and is called god-object or virtual proxy . It is first assumed
that the proxy moves to the position indicated by the operator. If no collision is
detected, this position is maintained and no force is returned. On the other hand,
if a collision is detected, the position of the proxy is calculated in order to respect
various constraints of the environment, expressed in the form of various plane equa-
tions, as shown in figure 16.6. As the proxy has to remain on the positive side of these
planes, we face a classic problem of minimisation (of distance between the proxy and
the position of the device) under constraints. We restrict the movement if the position
is too far from the previous position. Various methods have been suggested to cal-
culate this position (Zilles & Salisbury, 1995; Ruspini et al., 1997; Balaniuk, 1999;
3 This property of the human brain is used for pseudo-haptic feedback (Lécuyer et al., 2000).
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