Underwater Robots - Gianluca Antonelli.pdf

242 A. Mathematical models
using the strip theory, benefit from the simplified geometric assumption on
the link shapes [127, 256].
Foreach ofthe cylinder the mass is computed as:
⎡
m i + ρδi 0 0
⎢
M i = ⎢
⎣
0
0
∗
∗
m i + ρδi
0
∗
∗
0
m i +0. 1 m i
∗
∗
...
∗ ∗ ∗
∗ ∗ ∗
∗ ∗ ∗
∗ ∗ ∗
I x,i + πρL 3 i r 2 i / 12
0
0
I y,i + πρL
0
3 i r 2 0
i / 12
0
0
I z,i
where the link inertia are given in Table A.2. In this case, the cylinder length
is considered along the z i axis.
Table A.2. Link inertia [Nms 2 ]ofthe manipulator mounted on the underwater
vehicle
I x,i I y,i I z,i I xy,i I xz,i I yz,i
link 1 100 30 100 0 0 0
link 2 20 80 80 0 0 0
link 3 2 0 . 5 2 0 0 0
link 4 50 9 50 0 0 0
link 5 5 4 5 0 0 0
link 6 5 5 3 0 0 0
The linear skin and quadratic drag coefficients are given by D s =0. 4and
C d =0. 6, respectively. The lift coefficient C l is considered null.
A.4 ODIN
The mathematicalmodel of ODIN, an AUVdeveloped at the ASL, University
of Hawaii, has been used to test several, experimentally validated, control laws
([34, 35, 83, 216, 232, 233, 251, 320]):
⎤
⎥ ,
⎥
⎦