6.2 Device and the signal data
6.2.1 Position data and calibration
It is clear that the position data are represented by the 3-dimensional signals from x, y and z axes with respect to the base unit. However, from both gaming and modelling points of view, the absolute distances from the base unit are not convenient to use, since they are
effected by not only the movements of the hands, but also many other factors. Therefore,
calibration and normalization are necessary before any game or data pretreatment for modelling.
Calibration is done by a set of the most basic postures. The postures include the closest and furthest reach when patients put the hands up, front and down. Figure 6.2 shows the ideal standing of the patients with respect to the base unit. Ideally, the player should stand
on the z axis one arm length away from the base unit, with the torso (segment between two controllers) parallel to the x axis.
●
Ideal case: Top view
● ● ● ● Screen ● Base Unit ● ● Head
left controller right controller
X
Z
Figure 6.2: Top view of the ideal standing position. The coordinate system is centred at base unit. Dashed line is the x axis and z axis.
However, it is not possible to guarantee such standing practically. Patients may stand with
a different angle and position, as shown in Figure 6.3a and Figure 6.3b. People may also
move during the game. In addition, patients have different arm lengths. Thus, any model
based on such data directly will lead to unreliable result. To solve these problems, we need to carry out the following steps to normalize the data: centring, standardizing and rotating.
Centring
By using the base unit as the reference point, the trajectories of the hands would be very complicated. One patient may also change their standing position during the one as- sessment game. However, if the reference becomes the shoulders, the movement will be constrained in a sphere of radius one arm length. Therefore, the first step is to change the reference point from base unit to the shoulders. This step will not change the shape of the trajectories, however, because there are no sensors on the shoulder, the position of the shoulders must be estimated.
We first transfer the reference point to the middle controller on the belt around patients
●
Stand at the left: Top view
● ● ● ● Screen ● Base Unit ● ● Head
left controller right controller
X
Z
(a) One possible standing position
●
Stand at the right: Top view
● ● ● ● Screen ● Base Unit ● ● Head left controller right controller X Z
(b) Another possible standing position Figure 6.3: Possible standings of the players.
tracting the positions of the third controller from the positions of other two controllers:
(xc1(t), yc1(t), zc1(t))= (x1(t) − x3(t), y1(t) − y3(t), z1(t) − z3(t))
(xc2(t), yc2(t), zc2(t))= (x2(t) − x3(t), y2(t) − y3(t), z2(t) − z3(t))
where x, y, z are readings of the 3-D positions of the controllers. Subscripts are the indices
of the controllers and the superscriptcmeans the centred signals.
The calibration data give us the information to estimate the shoulder positions. When patients put their arms down to the lowest positions, we can have the x and z coordinates for the shoulders. The y coordinate can be obtained by the arm length, which is given in the clinical information of the patients. This posture is chosen because it is the easiest posture, and thus the most reliable posture for us to calculate the shoulder position. By some simple calculations, the shoulder positions can be obtained from this information. The hand positions can therefore be transferred to the sphere, with radius one arm length for further analysis.
These two transformations only shift the signals. Figure 6.4a and Figure 6.4b show the coordinate system before and after two transformations respectively. The arrows are the positive direction of each axis, the blue boxes are the controllers, the purple box is the base unit.
(a) Before transformation (b) After transformation
Figure 6.4: Three dashed lines and three gray arrows represent the coordinating system before any transformation. The purple box represents the base unit and the three blue boxes are the positions of the controllers. There are three smaller coordinating systems on two shoulders and the waist.
Standardizing
To make the position data more comparable, the values of the signals are standardized by dividing the arm length of the corresponding patient. The unit of the values are standard- ized to the number of arm lengths, and all the position data should be in the range from -1 to 1.
Rotating
As shown in Figure 6.3a and Figure 6.3b, the simple shifting in the 3-D space is not
enough to make movements comparable across different samples. Rotation is also re-
quired. As an illustrative example, Figure 6.5 shows how to rotate the red coordinate to the green coordinate. The rotation happens on the x-z plane, so we look at the two dimen- sional plot here. For example, if the coordinate is rotated 30 degrees anti-clockwise, as shown in red, it should be rotated back to the green coordinate. In other words, all of the position data need to be rotated 30 degrees clockwise. We define this angle by using the furthest position that the patient can reach on their left and right sides. These positions can be found in the calibration movement and in some assessment movements.
−1.0 −0.5 0.0 0.5 1.0 −1.0 −0.5 0.0 0.5 1.0 x z
Figure 6.5: Rotation from the red triangle to the green triangle