Underwater Robots - Gianluca Antonelli.pdf

212 8. Interaction Control of UVMSs
where x t expresses the third task to be projected inthe null space of the higher
priority tasks; in fact since the manipulator has a3-link planar structure
ameasure of its manipulability issimply given by q 2 ,where q 2 =0corresponds
to akinematic singularity. In the initial position the3tasksare activated
simultaneously and are performed by exploiting kinematic redundancy.
Moreover anunexpected impact along x is considered (for x E =1. 32 m).
Aweighted pseudoinverse has been used to compute J # p characterized
by the weight matrix W =blockdiag { 10I 6 , I 3 } .Tosimulate an imperfect
hovering of the vehicle acontrol law with lower gain for the vehicle was
implemented; the performance of the simulated vehicle, thus, has an error
that is of the same magnitude as that of areal vehicle in hovering.The motion
controller implemented is the virtual decomposition adaptive based control
presented inSection 7.9. Equation (8.16) has then been used to compute the
desired velocities. The secondary task regarding the vehicle orientation has
to be fulfilled only when the relevant variable is outside ofadesired bound.
The control gains, in S.I. units, are:
k fp =3· 10 − 3 ,
k fi =8· 10 − 3 ,
k fv =10 − 4 ,
Λ p =0. 6 I 3 ,
Λ s = I 3 .
The simulations have been run byadopting separate motion control schemes
for the vehicle and the manipulator, since this is the case of many
UVMSs. Better results would be obtained by resorting to acentralized motion
control scheme in which dynamic coupling between vehicle and manipulator
is compensated for. The initial value of the parameters has been chosen such
that the gravity compensation at the beginning isdifferent from the real one,
adding an error bounded to about 10% for each parameter.
In Figure 8.5 the time history of the end-effector variables for the proposed
force control scheme without exploiting the redundancy and without
unexpected impact is shown. During the first 3s the end effector is not in
contact with the plane and the algorithm to handle loss of contact has been
used. Itcan be noted that the primary task is successfully achieved.
In Figure 8.6 the same task has been achieved by exploiting the redundancy.
The different behavior of the force can be explained by considering
that the system impacts the plane in adifferent configuration with respect to
the previous case because of the internal motion imposed by the redundancy
resolution. This also causes adifferent end-effect velocity atthe impact.
Figure 8.7 shows the time history of the secondary tasks in the two previous
simulations, without exploiting redundancy (solid) and with the proposed
control scheme (dashed). It can be recognized that without exploiting
the redundancy the system performs the task in anon dexterous configuration,
i.e., with abig roll angle and with the manipulator close to akinematic