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(a)
(b)
Fig. 15.4
(a) Robot velocities; and (b) camera kinematic screw
T
Fig. 15.5
Description of the control components during the very beginning of the task
Ta s k 1
. During the first task, the robot must follow the wall with a prescribed
linear velocity
v
r
, while its on-board camera must be controlled in order to keep
the target in its line of sight. Three kinds of sensory data are simulated. Odometry
is used to regulate the robot linear velocity
v
1
; ultrasounds are used to detect the
distance to the wall and the relative robot direction in order to control its angular ve-
locity
v
2
; vision is used to control the camera angular velocity
v
3
. The task function
e
1
(
q
,
t
) is defined by
⎡
⎤
⎦
,
s
c
−
v
r
t
⎣
e
1
(
q
,
t
)=
y
e
+
γθ
(15.47)
e
Y
2
where
s
c
is the arclength abscissa of the robot trajectory,
v
r
is the robot reference
linear velocity,
y
e
is the distance between the point
M
and the wall,
θ
e
is the direction
of the robot with respect to the wall,
Y
2
is the ordinate of the projection of the target
center in the camera image-plane and
z
2
is its depth with respect to
R
C
;
γ
>
0isa
constant. The time-derivative of this task function reads
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