Underwater Robots - Gianluca Antonelli.pdf

162 7. Dynamic Control of UVMSs
[deg]
4
2
0
−2
φ
−4
0 50 100 150 200
time [s]
Nm
600
400
200
0
K
0 50 100 150 200
tim
Fig. 7.9. Adaptive control. Left: vehicle attitude in terms of Euler angles. Right:
vehicle control moments
[deg]
1.5
1
0.5
0
−0.5
−1
q 2
q 1
−1.5
0 20 40 60 80 100
time [s]
400
300
200
100
τ q,1
τ q,2
0
0 20 40 60 80 100
Fig. 7.10. Adaptive control. Left: joint position errors. Right: joint control torques
Figure 7.10 shows the time histories of manipulator joint errors and torques.
It is worth noting that the initial value of the joint torques is non null
because of gravity and buoyancy compensation, while they are null at steady
state in view of the particular final system configuration. The large initial
joint error isdue to mismatching in the restoring torques compensation; the
integral action provided by the parameters update gives anull steady state
error.
Figure 7.11 finallyshows aperformance comparisonbetween (7.22)–(7.23)
with and without adaptation. Remarkably at the very beginning of the trajectory
both control laws perform the same error; afterward the adaptive
controller provides asignificant error reduction.
7.8 Output Feedback Control
Underwater vehicles are typically equipped with acoustic sensors or video
systems for position measurements, while the vehicle attitude canbeobtained