FT-Control - Robotized Transcranial Magnetic Stimulation - page 83

from the robot's end effector to the FT sensor's coordinate frame must be known.
Second, due to gravity, any mounted tool biases the force and torque recordings.
This impact depends on the spatial orientation. To solve these problems, a cali-
bration must be performed. A sensor calibration calculates the transform to the end
effector and a tool calibration estimates the individual tool parameters, which are
the tool's weight and the tool's centroid. At rest, the tool's weight acts in the
centroid which therefore corresponds to the lever arm. Subsequently, this results in
occurrent torques. As long as the sensor is rigidly mounted to the end effector, the
sensor calibration stays constant and has to be calculated only once. The tool
calibration, on the contrary, is required whenever the tool or tool mount changes.
Even though the tool's weight typically remains constant, the tool's centroid
changes with respect to mounting position and orientation. Note that the centroid is
expressed in relation to the FT sensor's origin.
Once we have calibrated the tool to the sensor (and the sensor to the end
effector), we can estimate the expected coil's forces F 0 and torques M 0

for any

R T E using:
F 0 ¼ E T FT

robot orientation

1 R T E 1 F 0 ;

and ð 5 : 2 Þ

M 0 ¼ F 0 s ; ð 5 : 3 Þ
with F 0 denoting the tool's zero force which corresponds to its weight. Subse-
quently, the user's applied force F user and torque M user are calculated by sub-
tracting the expected force F 0

and torque M 0 for the current robot orientation from

the measured values F and M, respectively:

F user ¼ F F 0 ;

and ð 5 : 4 Þ

M user ¼ M M 0 : ð 5 : 5 Þ
F user and M user are now applied for the implementation of the FT-control for the
robotized TMS system. Prior to this, however, we need to introduce the mentioned
calibration methods.

5.1.1 Sensor Calibration

In this step, we calculate the transform E T FT from the robot end effector's coor-
dinate frame E to the FT sensor coordinate frame FT as illustrated in Fig. 5.1 .As
only the spatial orientation changes the forces and torques, a translational shift is
without effect on the FT recordings. Thus, the translational part is not important for
the transform E T FT and we solely estimate the 3 3 rotational part of E T FT . For
calibration, we mount a rigid, arbitrary tool to the sensor and use a set of n
measurements that are randomly distributed in spatial orientation. For every