Underwater Robots - Gianluca Antonelli.pdf

5. Experiments of Dynamic Control of a
6-DOF AUV
5.1 Introduction
In this Chapter some experimental results on dynamic control of a6-DOF
AUV are given; practical aspects of the implementation are also discussed.
The experiments have been conducted in the pool of the University ofHawaii
using ODIN, an AUV developed at the Autonomous Systems Laboratory
(ASL) [81].
Implemented control law. The control law isbriefly rewritten:
u v = B † v [ K D s � v + Φ v ( Q , ν , ˙ν a ) ˆ θ v ] (5.1)
ˆθ
˙ − 1
v = K θ Φ T v ( Q , ν , ˙ν a ) s v (5.2)
where B † v is the pseudoinverse of matrix B v (see the Appendix), K θ > O
and Φ v is the vehicle regressor. The vectors s � v ∈ IR 6 and s v ∈ IR 6 are defined
as follows
s � v =
� �
˜ν 1
˜ν 2
+ � − 1
Λ + K D K �
P
� R B I ˜η 1
˜ε
= ˜ν + � − 1
Λ + K D K P
s v = ˜ν + Λ ˜y , (5.4)
�
� ˜y , (5.3)
with ˜η 1 =[x d − x yd − y zd − z ] T , ˜ν 1 = ν 1 ,d − ν 1 ,where the subscript d
denotes desired values for the relevant variables. The matrix Λ ∈ IR 6 × 6 is
defined as Λ =blockdiag { λ p I 3 ,λo I 3 } , Λ > O .The matrix K P ∈ IR 6 × 6 is
defined as K P =blockdiag { k p I 3 ,ko I 3 } , K P > O .Finally, itis
ν a = ν d + Λ ˜y
and K D > O .
5.2 Experimental Set-Up
ODIN is an autonomous underwater vehicle developed at the Autonomous
Systems Laboratory of the University ofHawaii. Apicture ofthe vehicle is
shown in Figure 5.1. It has anear-spherical shape with horizontal diameter
G. Antonelli: Underwater Robots, 2nd Edition, STAR 2, pp. 93–104, 2006.
© Springer-Verlag Berlin Heidelberg 2006