A Telerobotic System for Transnasal Surgery

. Author manuscript; available in PMC: 2014 Aug 1.

Published in final edited form as: IEEE ASME Trans Mechatron. 2013 Jun 19;19(3):996–1006. doi: 10.1109/TMECH.2013.2265804

Algorithm 1 Objective Function f(d) for optimal component tube design

Input:

d: component tube design

a, b, c: radii of ellipsoid E

[x₀, y₀, z₀]^T: position of E

V_E = (4/3)πabc: Volume of E

Output:

c: uncovered percentage of E for d

list = {}
for all discrete actuator positions q do
p ← ForwardKinematics(q,d)
if
$({(\frac{p (x) - x_{0}}{a})}^{2} + {(\frac{p (y) - y_{0}}{b})}^{2} + {(\frac{p (z) - z_{0}}{c})}^{2}) \leq 1$
then
list.append(p)
end if
end for
V_C ← V( ConvexHull (list))
return
$1 - \frac{V_{C}}{V_{E}}$