Direct Head Tracking - Robotized Transcranial Magnetic Stimulation - page 132

In this way, the calibration phantom acts like a marker for a standard tracking
system (e.g. a Polaris System) for the robot calibration. For a standard track-
ing system, a marker is measured and results in a transform matrix from the
tracking system to the specific marker coordinate system. With a 3D laser scanner,
we cannot measure such a transform matrix directly as the laser scanning system
does not directly provide the pose matrix of the tool. To determine its pose, we
require a reference image M ref of the calibration tool. Then the pose matrix
M ref T M , relating the reference image to the actual position and orientation of the
scanned tool, can be computed with, e.g., the Iterative Closest Point (ICP) algo-
rithm [ 3 , 5 ]. As described above, this indirect approach is necessary since the laser
scanning system only provides a point cloud of the measured surface. Figure 8.2
shows the MATLAB GUI used for landmark-based preregistration and ICP reg-
istration as well as a typical result.
With this setup, we can calculate the transform from the robot to the reference
image of the calibration phantom using a hand-eye calibration method (see Sect. 4.1 ) .
In the presented case of a laser scanner, the ICP method results in additional dis-
tortion for the tracked data. We are therefore using the QR24 calibration algorithm as
it allows for non-orthonormal calibration matrices. Subsequently, we use the general
relation

R T E E T M ¼ R T M ref M ref T M

ð 8 : 1 Þ

for calibration which is also illustrated in Fig. 8.3 a.
Here, the matrices E T M , the transform from the robot's end effector E to the
calibration phantom M, and R T M ref , the transform from the robot's base R to the
reference image M ref , are unknown.
As we measure the head position in laser scanner coordinates, we are interested
in the calibration of the robot to the laser scanner R T L instead of the calibration of
robot to reference image R T M ref .
When we transform the reference image to the origin of the laser scanner
coordinate frame, the application of the ICP method for a scan of the phantom will
result in a transformation matrix of the phantom to the laser scanner. In this way,
the laser scanner acts like a standard tracking system that is used for hand-eye
calibration. Hence, the presented method results in the needed transform R T L
which is illustrated in Fig. 8.3 b. Therefore, we define the origin and axes manually
in the reference image by selecting three points (origin, x-axis, y-axis) that span
the coordinate system.

8.3.1.2 Coil Registration

The registration of the coil C has to be done the same way as presented above. For
the TMS coil different ways to obtain a high quality reference image exist. A CT or