Underwater Robots - Gianluca Antonelli.pdf

6.5 Singularity-Robust Task Priority 115
the model of the NPS AUV [145] is considered itcan be easily recognized
that, the drag in the x b direction isreally smaller with respect to the drag in
the y b .This suggests to attempt keeping the fore aft direction of the vehicle
aligned with the ocean current inorder to reduce energy consumption.
To implement the proposed approach, itisproposed to consider as primary
task both the end-effector position+orientation and the vehicle orientation,
i.e.,
x p =[x E y E ψ E ψ ] T ,
and assecondary task the vehicle position, i.e.,
x s =[x y] T .
In afirst simulation the end-effector has to maintain its position and
orientation while the vehicle will change its orientation to minimize the effect
of the ocean current; it is desired to keep the vehicle position constant, if
possible. Let the initial configuration ofthe vehicle be
x =0 m ,
y =0 m ,
ψ =0 rad ,
and the manipulator joint angles be
q =[1 . 47 − 1 0. 3] T
rad ,
corresponding tothe end-effector location
x E =5. 92 m ,
y E =4. 29 m ,
ψ E =0. 77 rad .
The desired values of the end-effector variablesand vehicle position are coincident
with their initial value. The desired final value of the vehicle orientation
is 0 . 78 rad asgiven, e.g., by acurrent sensor; the time history of the desired
value ψ d is computed according to aquintic polynomial interpolating law
with null initial and final velocities and accelerations and aduration of 10 s.
The algorithm’s gains are
K p =diag{ 10, 10, 10, 1 } ,
K s =diag{ 2 , 2 } .
The simulation results are reported in Figure 6.3 and 6.4. Itcan be recognized
that the task is successfully executed, inthat the end-effector location
and vehicle position are held while the vehicle body is re-oriented to align
with the ocean current. Remarkably, the obtained vehicle reference trajectory
is smooth.