Underwater Robots - Gianluca Antonelli.pdf

6.5 Singularity-Robust Task Priority 119
Starting from the same initial system configuration as before, in the simulation
the same end-effector trajectory has been assigned while manipulator
joint 2isdriven far from zero; it is desired to keep the vehicle position constant,
if possible.
The desired final value of q 2 is − 0 . 78 rad; the time history of the desired
value q 2 ,d is computed according toaquintic polynomial interpolating law
with null initial and final velocities and acceleration and aduration of 10 s.
The algorithm’s gains are
K p =diag{ 10, 10, 10, 1 } , (6.13)
K s =diag{ 2 , 2 } . (6.14)
The simulation results are reported in Figure 6.7 and 6.8.
[m]
10
8
6
4
2
0
−2
−4
−6
−8
−10
−10 −5 0 5 10
[m]
Fig. 6.7. Tracking of agiven end-effector trajectory with manipulator dexterity
It can be recognized that the primary task is successfully executed, in
that the end-effector location and manipulator joint 2achieve their target.
On the other hand, the vehicle moves despite the secondary task demands
for station keeping. Remarkably, the obtained vehicle reference trajectory is
smooth.
To underline the energetic difference in the station keepingtask considered
in the first case study when executed with and without vehicle re-orientation,