Underwater Robots - Gianluca Antonelli.pdf

8.4 External Force Control 211
UVMS simulated has 9DOFs, 6DOFs of the vehicle plus a3-link manipulator
mounted on it [231]. The controller has been implemented with asampling
frequencyof200 Hz.The vehicle is abox of dimensions (2× 1 × 0 . 5) m, andthe
vehicle fixed frame is located inthe geometrical center of the body. The manipulator
has aplanar structure with 3rotational joints. Asketch ofthe system
seen from the vehicle xz plane is shown in Figure 8.4. In the shown configuration
it is η =[0 0 0 0 0 0] T m, deg, q =[45 − 90 − 45 ] T deg. The
stiffness ofthe environment is k =10 4 N/m. In the Appendix some details
on the dynamic model are given.
z
wall
x
z b
x b
force
direction
Fig. 8.4. Sketch ofthe simulated system for both controllers as seen from the xz
vehicle-fixed plane
The vehicle is supposed to start in anon dexterous configuration, soas
to test the redundancy resolution capabilities of the proposed scheme. The
initial configuration is:
η =[0 0 − 2 12 0 0] T m, deg ,
q =[− 90 15 0] T deg
that corresponds to the end-effector position
x =[x E y E z E ] T =[1 . 51 − 0 . 60 0 . 86 ] T m .
Since the vehicle is far from the plane ( z =1. 005 m), the manipulator is
outstretched, i.e., close to akinematic singularity.
The simulated task is to perform aforce/position task atthe end effector
as primary task; specifically, the UVMS is required tomove − 20 cm along x
and apply adesired force of 200N along z .The secondary tasks are to guarantee
manipulator manipulability and to keep roll and pitch vehicle’s angles
in asafe range of ± 10 ◦ .Indetail, the 3task variables are:
x p = x ,
x s =[φ θ] T ,
x t = q 2 ,
x 0
y 1
x 1
x 3
y 2
x 2
y 3