Underwater Robots - Gianluca Antonelli.pdf

vehicle attitude [deg]
20
10
0
−10
6.6 Fuzzy Inverse Kinematics 127
−20
0 10 20 30 40 50
time [s]
Fig. 6.14. Case study n. 2. Vehicle attitude in terms of Euler angles. Despite the
weight factor, the vehicle can reach non-dexterous configurations
resolution [78]. The same task is now simulated with the introduction of the
secondary task:
� �
φ
x s =
θ
with x s,d =[0 0] T ,meaning that the vehicle has tomaintain anhorizontal
configuration all along the task execution. Its Jacobian is simply given by:
�
0
J s =
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
�
0
.
0
Notice that, for this simple matrix, it is J † s = J T s .Obviously, the vehicle
position and yaw are not limited.
Figure 6.15 reports thesketchofthe finalconfiguration;itcan be observed
that the pitch is now close to zero, as can be seen also from Figure 6.16.
Case Study n.4
In this simulation, the implementation ofthe proposed kinematic control
approach is presented. In an UVMS several variables are of interest inorder
to achieve asuccessful mission:
• avoidance of kinematic singularities;
• keeping the joints far from the mechanical limits;
• keeping the vehicle with small roll and pitch;
• avoidance of obstacles;
• alignment of the vehicle fore-aft direction with the ocean current.
θ
φ
ψ