Robust Real-Time Robot/Camera Calibration - Robotized Transcranial Magnetic Stimulation - page 67

points in between. At each interpolation point, the headband position is checked,
and the trajectory is updated in case the head has moved. Furthermore, the cali-
bration is checked with the online calibration approach before the robot moves to
the next interpolation point. If a calibration error occurs during the robot move-
ment, the program stops the robot movement, and asks the user to check the
calibration (confirming the new calibration matrix). We refrain from automatically
updating the new calibration as computation or measurement errors could affect the
calibration which might lead to mis-positioning. Subsequently, the user can select
the target again and let the robot move to this point. When the target is reached, the
motion compensation module starts automatically to keep the coil pose constant
relative to the head during head motion (see Sect. 1.3.2.3 ) . During the motion
compensation loop the calibration is checked again, currently once every minute
(roughly 0.017 Hz). As the robot is moving continuously during motion compen-
sation, recording of the marker at link three and computation of the forward cal-
culation must be synchronized. Therefore, we interrupt the motion compensation
cycle for the marker recording, which is typically in the range of 50 ms. This is a
result of a tracking delay of roughly 10 ms, a tracking frequency of 30 Hz and a
short computation time of approximately 10 ms [ 18 ]. If a calibration error occurs,
the user can confirm the new calibration (we can assume that the user can determine
if the tracking system and/or robot were moved) or the motion compensation stops.
In the unlikely case the marker at link three shifts unrecognized, the software
detects a discrepancy between the current calibration and the computed online
calibration. Thus, the user will be informed and can stop the system for patient's
safety. Subsequently, the marker must be re-calibrated before using the online
calibration again. To proceed with the stimulation, however, the user is able to
revert to the QR24 method for hand-eye calibration to perform the calibration
between robot and tracking system. Note that a shift of the marker can not be
detected by the software when using the online calibration method for an auto-
matic calibration without comparison to an existing calibration.
4.2.4 Translational Error Estimation for Marker Calibration
An accurate and sophisticated marker calibration, i.e. computation of the transform
between marker and link three, is mandatory for the robust real-time robot/camera
calibration. To estimate the error of the marker calibration no ground truth is
available for comparison. Nevertheless, we can use another geometric relationship,
as illustrated in Fig. 4.6 , to partially verify the marker calibration:
Hence, we calculate the distance r from the marker M to the axis of rotation of
S 2 (coordinate system in joint 3), when we rotate joint three, and track the marker
during rotation. To do this, joint three is rotated with constant speed by more than
90 , while the other joints are set to 0 . By least-mean-squares fitting of the tracked
marker positions to a circle [ 23 ], r is estimated as the radius of this circle.