Underwater Robots - Gianluca Antonelli.pdf

196 7. Dynamic Control of UVMSs
and thus only the inverse of the (6 × 6) manipulator Jacobian J m is required
in the inverse kinematics algorithm.
Aconstantocean currentaffect the motionwith the following components:
ν I c =[0 . 1 0. 3 0 0 0 0] T m/s .
As reported in [14, 13], some ofthe parameters of the controllers are related
tothe knowledge ofthe mass and the first moment of gravity/buoyancy.
Their initial estimate are set so as to give anestimation error larger then
20% of the true values. The other parameters are related to the presence of
the current. Those, will be initialized to the null value.
The control law parameters have been set to:
Λ 0 =blockdiag { 0 . 4 I 3 , 0 . 6 I 3 } ,
Λ i =1, 6 =blockdiag { 0 . 9 I 3 , 0 . 9 I 3 } ,
K v,0 =blockdiag { 9100I 3 , 9800I 3 } ,
K v,i =1, 6 =blockdiag { 600I 3 , 800I 3 } ,
K θ,0 =100I 9 ,
K θ,i =1, 6 =40 I 9 ,
where I 9 is the (9 × 9) identity matrix.
The results are reported in Figures 7.31–7.32 interms of end-effector
position/orientation tracking errors; it can be recognized that, in spite ofthe
demanding task commanded to the system, the errors are kept small in the
transients and reach zero values at steady state.
e.e. position error [m]
0.1
0.05
0
−0.05
y
−0.1
0 10 20 30
time [s]
Fig. 7.31. Virtual decomposition control +proper adaptive action. End-effector
position error
Moreover, the results inFigures 7.33–7.35 show that the control force
and moments acting on the vehicle, aswell as the control torques applied
z
x