Underwater Robots - Gianluca Antonelli.pdf

218 8. Interaction Control of UVMSs
The use of the integral action inthe force controller gives ahigher priority
to the force error with respect to the position error. In the motion control
directions the desiredforce is null. An unexpected impact in adirection where
the desired force is zero, thus, is handled by the controller yielding asafe
behavior, which results in anon-null position error at steady state and anull
force error, i.e., zero contact force.
If f e,d /∈R( K ), i.e. the direction of f e,d is not parallel to n ,the controller
is commanded to interact with the environment in directions along
which noreaction force exists. Inthis case, adrift motion in that direction
is experienced.
These two force control schemes too, possess the safe behavior as the
external force control scheme.
The possibility that the end effector loses contact with the environment
is also taken into account. The same algorithm as presented in Section 8.4.4
were implemented.
8.5.2 Simulations
To test the effectiveness of the proposed force control schemes several numerical
simulations were run under the Matlab c� / Simulink c� environment.
The controllers were implemented in discrete time with asampling frequency
of 200 Hz. The environmental stiffness is k =10 4 N/m.
The simulated UVMS has 9DOFs, 6DOFs of the vehicle plus a3-link
manipulator mounted on it [231]. The vehicle is abox of dimensions (2 ×
1 × 0 . 5) m; the vehicle-fixed frame is located in the geometrical center of the
body. The manipulator is a3-link planar manipulator with rotational joints.
Figure 8.4 shows asketch ofthe system, seen from the vehicle’s xz plane, in
the configuration
η =[0 0 0 0 0 0] T m, deg ,
q =[45 − 90 − 45 ] T deg
corresponding to the end-effector position x =[2 . 41 0 1] T m.
A case study is considered aimed at the following objectives: as primary
task, to perform force/motion control of the end effector (exert aforce
of 200 Nalong z ,moving the end effector from 2 . 41 mto2. 21 malong x ,
while keeping y at 0m); as secondary task, to guarantee vehicle’s roll and
pitch angles being kept in the range ± 10 ◦ ;astertiary task, to guarantee the
manipulator’s manipulability being kept in asafe range. In detail, the 3task
variables are:
x p = x ,
x s =[φ θ] T ,
x t = q 2 ,