5.3 Inverse Kinematics 345
then the end effector position is updated to F = E + clamp{T , t
min
, t
max
},where
clamp{T , t
min
, t
max
}=
⎧
⎨
⎩
t
max
, T>t
max
T , T ∈ [t
min
, t
max
]
t
min
, T<t
min
Slide to Line
Let the goal be G(s) = G
0
+ sG
1
for s ∈ R and where |G
1
|=1. If the goal line is
parallel to the direction of sliding, U × G
1
= 0, then no updating of E is necessary.
Otherwise, the lines are not parallel and the closest point on the ray containing E with
direction U is H = E + T U,whereT ≥ 0 (see Section 14.1.2). The update of E in the
previous subsection on sliding to a point can now be applied using H.
Slide to Plane
Let the goal be M
.
X = c,whereM is unit length. If the goal plane is parallel to the
direction of sliding, M
.
U = 0, then no updating of E is necessar ...