Underwater Robots - Gianluca Antonelli.pdf

3.6 Mixed Earth/Vehicle-Fixed-Frame-Based, Model-Based Controller 55
action (3.20) which works in vehicle-fixed coordinates; this implies that, as
for counteraction of the ocean current, this control law suffers from the same
drawback as that discussed for the law C .
Reduced Controller. The model-based compensation has been reduced to
the restoring generalized force alone:
τ v = Φ v,R ( R I B ) ˆ θ v,R + ˆv + J T e ( R I B ) K D s e
(3.24)
˙ˆv = W − 1 − 1
J e ( R I B ) s e (3.25)
˙ˆθ
− 1
v,R = K θ Φ T v,R ( R I − 1
B ) J e ( R I B ) s e , (3.26)
3.6 Mixed Earth/Vehicle-Fixed-Frame-Based,
Model-Based Controller
In 2001, G.Antonelli, F.Caccavale, S.Chiaverini and G.Fusco [13, 14] propose
and adaptive tracking control law that takes into account the different
nature of thehydrodynamic effects acting on the AUV(ROV); this is achieved
by suitably building each dynamic compensation action inaproper (either
inertial or vehicle-fixed) reference frame. Infact, since adaptive orintegral
control laws asymptotically achievecompensation of the constant disturbance
terms, itisconvenient to build the compensation action in areference frame
with respect to which the disturbance term itself is seen as much as possible
as constant. The analysis has been extended in [9, 16].
Let consider the vehicle-fixed variables:
� � B
R
˜y I ˜η 1 =
˜ε
˜ν = ν d − ν ,
where ˜η 1 = η 1 ,d − η 1 ,being η 1 ,d the desired position, and ˜ε is the quaternion
based attitude error. Let define as ˆ θ v the vector of parameters to be adapted,
s v = ˜ν + Λ ˜y , (3.27)
with Λ =blockdiag { λ p I 3 ,λo I 3 } , Λ > O .The control law is given by:
τ v = K D s v + K ˜y + Φ v,T ˆ θ v
(3.28)
where K D ∈ IR 6 × 6 and K = blockdiag { k p I 3 ,ko I 3 } are positive definite
matrices ofthe gains tobedesigned, and
ˆθ
˙ − 1
v = K θ Φ T v,T s v , (3.29)
where K θ is also apositive definite matrix ofproper dimensions.