Figure 1: The longitudinal mode.
of sensation to close the description of the simulator
objective.
Remark: The results presented here are done for
the longitudinal mode. However, they could be ex-
tended for the other space directions. The longitudi-
nal mode is composed of the surge and pitch motions
as depicted in figure 1.
2 MOTION PERCEPTION
Even in the absence of visual information (closed-eye
subject), humans detect motion thanks to their inertial
receptor: the vestibular system. Located in the inner
ear, this biological apparatus measures both linear and
angular motion of the head (a thorough description is
given in (Elloumi, 2006; Telban et al., 2000; Ange-
laki and Dickman, 2004)) if they are beyond detection
thresholds (on acceleration and speed respectively).
The motion sensation is built at the level of the
brain not only from the vestibular system informa-
tion but also from all the perception receptors (most
particularly: the eyes) cues. In this paper, as com-
monly done in driving simulation, we consider that
apart from the vestibular system, all the other sensors
receive coherent and well adapted cues. As a conse-
quence, in this paper the motion sensation will be con-
sidered as the interpretation of head displacements by
the inertial receptor.
One remarkable gain of working with motion sen-
sations instead of real trajectories (accelerations) is il-
lustrated by the tilt coordination. In driving (or flight)
simulation, a simultaneous rotation of the driver’s
head and the visual scene at a very slow rate happens
to create an illusion of linear acceleration: ”When a
visual scene representing an accelerated translation
is presented to the driver while the simulation cockpit
is tilted at an undetectable rate, the relative variation
of the gravity vector will be partly interpreted as an
actual linear acceleration” (Reymond et al., 2002).
Thus from a control point of view, the tilt coordination
leads to a low-frequency motion sensation through a
very small variation of the jacks’ displacement as we
shall see in the next section.
Scaling Saturation
High Frequency
Filtering
real
acceleration
treated
acceleration
Scaling Saturation
High Frequency
Filtering
real
acceleration
treated
acceleration
Figure 2: Preliminary treatments for the classical MCA.
3 CLASSICAL MOTION CUEING
ALGORITHM
This scheme was developed in 1970 by (Parrish et al.,
1975). Despite its simplicity, this algorithm displays
the importance of tilt coordination to restitute longitu-
dinal accelerations. This scheme is based on the sim-
ple observation that the simulator translation is very
limited so that only fast (onset) accelerations could be
tracked. Consequently, the principle of this method is
to use filtering to extract from the real car accelera-
tion the high frequency component and address it to
the robot translation. Hopefully, the tilt coordination
enables the reproduction of slow (sustained) accelera-
tions. Filtering (low frequencies) is performed to sup-
ply the tilt rotation as well. As for the restitution of
the rotation speed, high pass filtering is performed to
deal with angular limits.
The classical MCA is a linear approach which is
commonly preceded by some preliminary treatments
of the real accelerations to cope with robot motion
limits (see figure 2).
4 THE REDUNDANCY PROBLEM
Restituting longitudinal acceleration on redundant
simulators could be done thanks to three degrees of
freedom (dof) as depicted in Fig.3: the base transla-
tion (X) (performed by the rails), the hexapod trans-
lation (x) and the tilt coordination (θ : tilt angle)
(both performed by the jacks). As shown in (Elloumi,
2006), the behavior of the last dof is independent from
the first two as the rotation due to the tilting is limited
by a very low detection threshold.
As a consequence, in order to improve the qual-
ity of motion cueing only the translations behaviors
should be considered. The considered linear acceler-
ation
1
provided to the driver by the simulation robot
is then:
¨
X + ¨x .
Besides as the rails and jacks bandwidths are over-
lapping in the high frequencies domain, these two dof
could be considered as equivalent. How could we
1
The tilt coordination contribution gθ (where g is the
gravity magnitude) is omitted from the hybrid algorithms
that we shall present (but could be added outside these al-
gorithms).
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