Underwater Robots - Gianluca Antonelli.pdf

o
o b
y
x
y b
x b
3.5 Model-Based Controller Plus Current Compensation 53
Fig. 3.2. Planar view parallel to the xy earth-fixed frame of two different configurations
under the constant current ν I c
variables has also been considered as in [35] tocounteract the current effects,
i.e.,
τ v = Φ v,P � ( R I B ) ˆ θ v + K D s v
(3.16)
˙ˆθ
− 1
v = K θ Φ T v,P � s v . (3.17)
3.5 Model-Based Controller Plus Current Compensation
T. Fossen and J. Balchen, in1991 [125], propose acontrol law that explicitly
takes into account the ocean current without need for the current measurement.
Being:
s e = ˙˜η + σ ˜η with σ>0 , (3.18)
the controller is given by:
τ v = Φ v ( R I B , ν , ν a , ˙ν a ) ˆ θ v + ˆv + J T e ( R I B ) K D s e
ν I c
o b
x b
ψ
y b
(3.19)
where K D ∈ IR 6 × 6 ,isapositive definite matrix ofgains. Notice that the
PD action is similar to the transpose of the Jacobian approach developed for