Underwater Robots - Gianluca Antonelli.pdf

74 3. Dynamic Control of 6-DOF AUVs
Afurtherplot can be used(Figure 3.15) to understand the problem arising
when compensating incorrectly the current, the controller C is compared with
controller E in anormalized polar representation ofthe sole compensation
of the ocean current during the yaw rotation. Itcan be noticed that, with
the controller E (and similar) the compensation of the current rotates with
the vehicle so that it still compensate with respect to aconstant, earth-fixed
disturbance.
law E
ν I c
law C
Fig. 3.15. Earth-fixed-frame polar representation ofsamples of the current compensation:
controller E (left) and controller C (right). Notice that the compensation
term built bythe law C rotates together with the vehicle-fixed frame
The given simulation does not exhibit asignificant error inthe orientation
that should be caused by the wrong restoring compensation of the controllers
A and F .The numerical study has been conducted with amodel largely
used in the literature and tested in experimental cases; moreover, reasonable
parameters’ estimation has been considered; in particular only the third
component ofthe vector W r G − B r B is different from zero; finally small rotations
in pitch and yaw have been commanded. Under these considerations
both the controllers behave very well; the control effort, moreover, was similar
to that of other controllers. It has been considered fair, thus, to report the
good numerical result of these controllers despite their theoretical drawback
and toavoid specific case studies where those might fail such as, e.g., with
large enough φ and θ for the controller F and adifferent vector W r G − B r B .
It might benoticed that this singularity isarepresentation singularity and
that might arise even with the vehicle in the hovering position due toan
unsatisfactory choice ofthe body-fixed frame or the roll-pitch-yaw convention;
however, due to the common marine convention, this possibility isso
uncommon that is not areal drawback.
ν I c