Underwater Robots - Gianluca Antonelli.pdf

8.5 Explicit Force Control 219
where x t expresses the third task; infact, since the manipulator has a3link
planar structure, ameasure of its manipulability issimply given by q 2 ,
where q 2 =0corresponds to akinematic singularity.
Let us suppose that the system starts the mission in the non-dexterous
configuration
η =[0 0 − 0 . 001 15 0 − 4] T m, deg ,
q =[46 − 89 − 44 ] T deg
corresponding to the end-effector position x =[2 . 45 − 0 . 42 0 . 91 ] T m.
Aweighted pseudoinverse was used to compute J # characterized by the
weight matrix W =blockdiag { 10I 6 , I 3 } .Tosimulate an imperfect hovering
of the vehicle the control law was implemented with lower gains for the
vehicle; the performance of the simulated vehicle, thus, has an error that is
of the same magnitude of areal vehicle in hovering.
To accomplish the above task, firstly the force control scheme 1isused
together with the sliding mode motion control law described in Section 7.6;
notice that non-perfect gravity and buoyancy compensation was assumed.
Figure 8.11 reports the contact force and the end-effector error components
obtained. Since the desired final position is given as aset-point, the initial
end-effector position errors are large. In Figure 8.12, the position and orientation
components of the vehicle are shown; it can be recognized that, despite
the large starting value, the roll angle is kept in the desired range.
To take advantage of dynamic compensation actions, the force control
scheme 2isused to accomplish the same task as above together with the
singularity-free adaptive control presented inSection 7.9; notice that only
the restoring force terms have been considered to be compensated and a
constant unknown error, bounded to ± 10%, of these parameters has been
assumed. There are 4parameters for each rigid body of the UVMS, giving
16 parameters in total. Moreover, during the task execution an unexpected
impact occurs along x .
In Figure 8.13, the contact force and the end-effector error components
are shown. It can be recognized that the unexpected impact, occurring atabout
3s, is safely handled: atransient force component along x is experienced;
nevertheless, at the steady state the desired force is achieved with null error.
It can be noted that the expected coupling between the force and the
motion directions affects the x direction also before the unplanned impact.
This coupling, due tothe structure and configuration of the manipulator, is
not observed along y .
In Figure 8.14, the vehicle’s position and orientation components are
shown. It can be recognized that the vehicle moves byabout 10 cm; nevertheless,
the manipulator still performs the primary task accurately. Moreover,
the large initial roll angle is recovered by exploiting the system redundancy
since this task does not conflict with the higher priority task.
In the force control scheme labeled 1the force error directly modifies the
force/moments/torques acting on the UVMS, leading to an evident physical