Game Development Reference
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V h
V e
Z h ( V )
Z e ( V )
F e
F h
Figure 9.1 Analogy between a haptic system and an electric network
The other possibility is a behaviour similar to admittance, by accepting forces and
returning movements (positions and/or speed). This is the case of approaches that
help to secure management of the contacts by constraints.
By using an analogy with an electric model, we can see the haptic interface as a dipole
that restores forces F h and F e and speeds V h and
V e to the two accessible terminals
(Figure 9.1). The negative sign on the speed is necessary to maintain the consistency
with the formalism per electric network.
In this chapter, we introduce intuitive haptic coupling before formally modelling it
in the following paragraph. If we use a device in impedance and an environment in
impedance, the simulation provides a force and the device measures amovement at each
time step. Using this data, the interface takes charge of restoring a force to the user and a
movement to the simulation. To obtain a transparent haptic feedback, it is necessary for
the speeds and forces between the human operator and the environment to be identical.
For this, the perfect haptic interface should be able to simulate the movement in free
space without any inertia or friction, as well as infinite stiffness for certain constraints.
Now, the interface itself has its own impedance due to its mechanics.
To explain the strategy of the coupling used in a simple way, we take the example
of a haptic device of one degree of freedom (Figure 9.2). This device is a cursor, which
only carries out a 1D translation movement. It has a mass m d , and the viscous friction
of this interface is noted as b d . It is motorised and instrumented (its precise position is
known), which allows the user to feel the force.
We want to link this interface to a virtual environment consisting of a virtual cube
that can move on a slide. This slide has stops that limit the cube in its movement. We
thus want the user to feel these stops when he moves the cube. We can thus think that
we only have to reduce the mass m d and the viscous friction b d to obtain perfect trans-
parency. However, we observe that when we sample the data, the stability test is not
always satisfactory (Adams & Hannaford, 1999). This does not mean that the system
will never be stable, but that certain impedance combinations of the environment and
reactions of the human operator can destabilise the system. In order to avoid this, we
set up a virtual mechanical coupling, which corresponds to the use of a damper spring
system between the movement measured on the device and the movement simulated
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