Underwater Robots - Gianluca Antonelli.pdf

3.9 Numerical Comparison Among the Reduced Controllers 61
An aspect to be considered for proper reading ofthis study is that the
control problem athand ishighly nonlinear, coupled and the controller to be
compared are intrinsically different one from the other. Any effort to chose
the gains soastoensure similar performance to the controllers has been
made; nevertheless, this is impossible in astrict sense. Forthis reason, the
presented results have to be interpreted mainly looking at the error behavior
rather then focusing on direct numeric comparison. On the other hand, itwas
chosen tonot emphasize vehicle-related effects that would not bepresent in
general applications. In particular, ODIN has asmall metacentric height,
yielding low restoring moments; simulations of the controllers to vehicles of
larger metacentric height would make even more evident the drawbacks in
the compensation of the restoring forces.
Test trajectory In order to demonstrate the effects discussed in this paper,
the simplest task to be considered is one involving successive changes of the
vehicle orientation in presence ofocean current. The simulation length can
be divided indifferent period of60s duration. The vehicle is firstly put in
the water at the position
η d ( t =0)=[0 0 1 0 0 0] T
[m/deg]
without knowledge of the current but with an estimation of the restoring
parameters. The first 60 sare used toadapt the effect ofthe current. Inthe
successiveperiodthe vehicle is requiredtomove in roll and pitchfrom0deg to
10 deg and − 15 deg, respectively and come back tothe original configuration.
In the successive two periods the vehicle is required tomove of 90 deg in yaw
and come back to the initial position. Finally, 60s of steady state are given.
Figure 3.3 plots the desired trajectory.
Initial conditions Table 3.3 reports the initial condition for the adaptive/integral
parameters of the controllers, it can be observed that the same
values have been used in the estimation ofthe restoring forces. This isalso
true for the controller A ,where the gravity estimation ˆg �
RB, even ifnot adaptive,
isobtained resorting to
ˆθ v,R =[− 9 0 0 50] T .
From the model in the Appendix it can be noticed that the true value of the
restoring parameters is
θ v,R =[− 8 . 0438 0 0 61 . 3125 ] T .
The vehicle initial position is also
η =[0 0 1 0 0 0] T
[m,deg] ,
meaning that the vehicle is supposed tostart its motion under the water, at
1m depth, moreover, there is no initial estimation of the ocean current.