Cameraspace kinematics of the onboard, holonomic part of the robot.

1
Lecture 10

• Camera-space kinematics of the on-board,
  holonomic part of the robot.

2
What would gx gy gz be for the holonomic part
of our robot?
Ackn B. Marek.
3
What would gx gy gz be for the holonomic part
of our robot?
Ackn B. Marek.
4
(No Transcript)
5
(No Transcript)
6
(No Transcript)
7
(No Transcript)
8
(No Transcript)
9
(No Transcript)
10
(No Transcript)
11
(No Transcript)
12
(No Transcript)
13
(No Transcript)
14
(No Transcript)
15
Direction cosine matrix between 1 and 2 frames
16
Relative displacement of origin of 2 frame w.r.t.
origin of 1 frame referred to the 1 frame.
17
Cascading
18
After multiplication/simplification
19
Consider point P fixed to the blue member.
20
Since P is fixed to the blue member, the
components below are permanent and independent of
the pose of the robot.
21
The forward kinematics of our robot for point P
become functions of q1 and q2 via the homogeneous
transformation matrix below which is used to
produce
22
The forward kinematics of our robot for point P
become functions of q1 and q2 via the homogeneous
transformation matrix below which is used to
produce
23
The forward kinematics of our robot for point P
become functions of q1 and q2 via the homogeneous
transformation matrix below which is used to
produce
24
The forward kinematics of our robot for point P
become functions of q1 and q2 via the homogeneous
transformation matrix below which is used to
produce
25
The forward kinematics of our robot for point P
become functions of q1 and q2 via the homogeneous
transformation matrix below which is used to
produce
26
The forward kinematics of our robot for point P
become functions of q1 and q2 via the homogeneous
transformation matrix below which is used to
produce
27
Application of the forward kinematics to our
camera-space kinematics model.
28
Application of the forward kinematics to our
camera-space kinematics model.
29
(No Transcript)
30
(No Transcript)
31
(No Transcript)
32
(No Transcript)
33
(No Transcript)
34
(No Transcript)
35
(No Transcript)
36
(No Transcript)
37
Consider a batch of data entailing q1 q2 xc and
yc.
38
Consider a batch of data entailing q1 q2 xc and
yc.
39
Minimize
40
Minimize
41
Minimize
42
Minimize
43
Same
44
Same
45
(No Transcript)
46
(No Transcript)
47
(No Transcript)
48
(No Transcript)
49
(No Transcript)
50
(No Transcript)
51
(No Transcript)
52
(No Transcript)
53
(No Transcript)
54
(No Transcript)
55
(No Transcript)
56
(No Transcript)
57
(No Transcript)
58
(No Transcript)
59
(No Transcript)
60
(No Transcript)
61
(No Transcript)
62
(No Transcript)
63
(No Transcript)
64
(No Transcript)
65
(No Transcript)
66
(No Transcript)
67
(No Transcript)
68
(No Transcript)
69

70

New bo is set equal to the old bo plus Db
iteration continues until convergence.
71
Our objective is usually to position some other,
less visible point.
72
Our objective is usually to position some other,
less visible point.
73
Introduction of a second, third or fourth cue
makes observability of the camera-space
kinematics of the point of interest much improved.
74
Introduction of a second, third or fourth cue
makes observability of the camera-space
kinematics of the point of interest much improved.
75
Introduction of a second, third or fourth cue
makes observability of the camera-space
kinematics of the point of interest much improved.
76
(No Transcript)
77
(No Transcript)
78
(No Transcript)