Magnetic Trackers: Robot Control and Vasculature Imaging - Microsurgery: Advances, Simulations, and Applications - page 247

taken during one LSM cycle and the system inds a reference point
between them, the LSM will react with a maximum delay of one cycle
and a maximum error of C 0( n- 1) will be introduced to the total error
of the ACIS to detect a reference point.
The error introduced by the MMCS, e m , can be modeled by Eq. 7.9,
em = ke mt (7.9)
where e m is the listed error of the MMCS. The parameter k will
change according to misalignment of reference frames, distortion
of magnetic tracker frame of reference and external interference
produced by ferrous metals and oscillating magnetic ields. In this case
k will be almost equal to 1 because the control technique proposed
at the beginning of the chapter was used to build the controllers.
Then the error introduced by the magnetic tracker to the system is
minimized to the sensor speciications for position accuracy. As LSM
cycle last for one second and changes in its motion are executed once
during that cycle, if during that second the Eq. 7.3 is valid then the
coniguration deined at reference point will be executed at the end
of the cycle. Therefore, the system will only be affected inside the
detection range, by oscillating magnetic ields with frequency below
0.5 Hz as if the oscillation is faster its magnitude will become zero
at least one time during LSM cycle. Therefore, the error of this ACIS
at the path reconstruction experiments mainly depends on three
factors, the cross section diameter of the model d n , the step length of
LSM C 0( n- 1) , and the error introduced by the sensor e m . Equation 7.10
is proposed to make a mathematical model of ACIS error to change
its coniguration in a point P n of the sparse LUT M ,

p p

edC e (7.10)

An 0( n 1 ) m

where e A is the total error of this ACIS.

Table 7.4 Detection range and reaction range for the two-dimensional

path reconstruction

Reference point Detection range (mm) Reaction range (mm)
P a 0 6 4.22
P a 1 6 5.40
P a 2 6 3.96
P a 3 6 —
P a 4 6 2.01
Note: P a 3 is not detected because the catheter insertion trajectory is reproduced
properly.