Underwater Robots - Gianluca Antonelli.pdf

Simulations
6.6 Fuzzy Inverse Kinematics 123
The proposed fuzzy technique has been verified infull-DOFs case studies.
An UVMS has been considered constituted by avehicle with the size of
the NPS Phoenix [145] and amanipulator mounted on the bottom of the
vehicle. The kinematics of the manipulator considered isthat ofthe SMART-
3S manufactured by COMAU. Its Denavit-Hartenberg parameters are given
in Table 6.2. The overall system, thus, has 12 DOFs. Figure 6.11 shows the
configuration inwhich all the joint positions are zero according to the used
convention.
Table 6.2. D-H parameters [m,rad] of the manipulator mounted on the underwater
vehicle
a d θ α
link 1 0. 150 0 q 1 − π/2
link 2 0. 610 0 q 2 0
link 3 0. 110 0 q 3 − π/2
link 4 0 0 . 610 q 4 π/2
link 5 0 − 0 . 113 q 5 − π/2
link 6 0 0 . 103 q 6 0
The simulations are aimed at proving the effectiveness of the fuzzy kinematic
control approach; for seek of clarity, thus, only the kinematic loop
performance is shown (see Figure 6.1). The real vehicle/joint position will be
affected by alarger error since the tracking error too has to be taken into
account. It is worth noticing that, as long asthe law level dynamic controller
is suitably designed, this tracking error is bounded. Moreover, it does not
affects the kinematic loop performance.
The primary task is to track aposition/orientation trajectory of the end
effector. The system starts from the initial configuration:
η =[0 0 0 0 0 0] T
m,deg
q =[0 − 30 − 110 0 − 40 90 ] T deg
that corresponds to the end-effector position/orientation
η ee1 =[0 . 99 − 0 . 11 2 . 99 ] T m
η ee2 =[0 0 − 90 ] T
deg .
The end effector has to track asegment of − 30 cm along z ,stop there, and
track asegment of1malong x .Both segments have to be executed with a
quintic polynomial time law in12s.During the translation, the end effector
orientation has tobekept constant. The initial configuration and the desired