Underwater Robots - Gianluca Antonelli.pdf

6.6 Fuzzy Inverse Kinematics 129
It is underlined that some of the above items are critical; the alignment with
the current, however, can besignificant inorder to reduce power consumption
[20]. As an example, in the previous case study, the use of aweight factor
requires now alarger movement ofthe manipulator. This can lead to the occurrence
of kinematic singularities. In fact, if the trajectory is assigned in
real-time, it is possible that the manipulator isasked to move to the border
of its workspace, where the possibility toexperience akinematic singularity
is high. Also, when the manipulator isoutstretched, mechanical joint limits
can be encountered. Inthe simulations, the following joint limits have been
assumed:
q min =[− 100 − 210 − 210 − 150 − 80 − 170] T deg
q max = [100 30 10 150 80 170] T deg .
In Figure 6.17, the minimum distance to such limits for the previous case
study isshown. It can beobserved that the manipulator hits amechanical
limit at t ≈ 35 s.
d[deg]
50
40
30
20
10
0
0 10 20 30
O
40 50
time [s]
Fig. 6.17. Case study n. 3. Minimum distance of the 6joints from their mechanical
limits. It can be observed that large movements of the manipulator may cause
hitting of the joint limits
In order to match all the constraints of such problem, asolution as been
proposed based on the use of the singularity-robust task priority merged with
fuzzy techniques.
Let consider the following tasks:
• End-effector position/orientation. The primary task is given, asfor
the previous simulations by the end-effector position and orientation. The
corresponding Jacobian J p is J given in (2.68);