Underwater Robots - Gianluca Antonelli.pdf

146 7. Dynamic Control of UVMSs
In figure 7.3 the end-effector step response is given and its settling time
can be observed. It can beremarked that, without the proposed decoupling
strategy, the end effector does not even reaches the given set point.
The overall improvement was of afactor 6with respect to the vehicle
without control and afactor 2 . 5with respect to aseparate control action.
The applied thrust only showed anincrease of about 5%.
7.3 Feedback Linearization
Reference [285] presents amodel based control law. In detail, the symbolic
dynamic model is derived using the Kane’s equations [286]; this is further
used in order to apply afull dynamic compensation. Simulations of a6-DOF
vehicle carrying two 3-link manipulators are provided. Asimilar approach
has been presented in [255, 256].
From the mathematical point ofview, the dynamics of an UVMS can be
completely cancelled by resorting to the following control action:
τ = M ( q ) ˙ ζ a + C ( q , ζ ) ζ + D ( q , ζ ) ζ + g ( q , R I B ) (7.3)
where the 6+n dimensional vector
� �
˙ζ
˙ν a
a =
¨q a
is composed by a6× 1vector defined as
˙ν a = J e ¨η e + ˙ J e ˙η
¨η e = ¨η d + K pv ˜η + K vv ˙˜η + K iv
and an × 1vector defined as
¨q a = ¨q d + K pq˜q + K vq ˙˜q + K iq
� t
0
� t
The stability analysis isstraightforward; assuming perfect dynamic compensation,
infact, gives two different linear models for the earth-fixed vehicle
variables and the joint positions. With aproper choice ofthe matrix gains,
moreover, the designer can shape the response of asecond-order dynamic
system.
7.4 Nonlinear Control for UVMSs with Composite
Dynamics
In [67, 68, 69, 220] the singular perturbation theory has been considered due
to the composite natureofUVMSs. The differentbandwidth characteristics of
0
˜η
˜q .