Underwater Robots - Gianluca Antonelli.pdf

194 7. Dynamic Control of UVMSs
matics algorithm. The errors are quite large since the aim of the simulation
was toshow the benefit of the adaptive action in a virtual decomposition approach.
The end-effector errors are the composition of all the tracking errors
along the structure; the manipulator, characterized by smaller inertia and
higher precision with respect to the vehicle, will be in charge of compensating
for the effects of the vehicle tracking errors on the end-effector. Forthis
specific simulation, thus, the end-effector tracking error is comparable with
the vehicle position/orientation tracking error.
joint errors [deg]
5
0
−5
0 10 20 30
time [s]
Fig. 7.29. Virtual decomposition control. Time history of the joint errors
In Figure7.30 the time history of the jointtorques is reported. Notice,that
only the torque ofthe second joint ismainly affected by the manipulator restoring
forces. At the very beginning the restoring compensation ( ≈ 200 Nm)
presents alarge difference with respect to the final value ( ≈ 500 Nm) corresponding
to the same configuration due to the error inthe parameter estimation.
7.9.3 Virtual Decomposition with the Proper Adapting Action
In the previous section, an adaptive control law inwhich the serial-chain
structure of the UVMS is exploited is discussed. The overall motion control
problem isdecomposed in aset of elementary control problems regarding the
motion ofeach rigid body in the system, namely the manipulator’s links and
the vehicle. For each body, acontrol action is designed to assign the desired
motion, to adaptively compensate for the body dynamics, and to counteract
force/moment exchanged with its neighborhoods along the chain.
On the other hand, inChapter 3it is shown, that, for asingle rigid body, a
suitable regressor-based adaptive control law (the mixed earth/vehicle-fixed-