Underwater Robots - Gianluca Antonelli.pdf

122 6. Kinematic Control of UVMSs
difficult tohandle all these terms without akinematic control approach. Nevertheless,
the existing techniques do not allow tofind aflexible and reliable
solution.
To overcome this drawback afuzzy theory approach has therefore been
considered at two different levels. First, it is required to manage the distribution
of motion between the vehicle and the manipulator; second, it is required
to consider multiple secondary tasks that are activated only when the corresponding
variable is outside (inside) adesired range. This can be done using
different weight factors adjusted on-line according tothe Mamdani fuzzy inference
system ([103]) shown inFigure 6.10.
Crisp
input
fuzzifier
fuzzy rule
fuzzy
inference
engine
Fig. 6.10. Mamdani fuzzy inference system
defuzzifier
Crisp
output
In detail, the crisp outputs are the scalar β of (6.15) that distributes the
desired end-effector motion between the vehicle and the manipulator and a
vector of coefficients α i that are used in the task priority equation as follows
ζ = J †
W ( ˙x �
E,d + K E e E )+ I − J †
W J W
� � �
i
α i J †
s,i w s,i
�
, (6.16)
where w s,i are suitably defined secondary task variables and J s,i are the
corresponding Jacobians. Both β and α i ’s are tuned according to the state of
the system and to given behavioral rules. The inputs ofthe fuzzy inference
system depend on thevariablesofinterest in the specific mission. As an example,
the end-effector error, the ocean current measure, the system’s dexterity,
the force sensor readings, can be easily taken into account bysetting up a
suitable set of fuzzy rules.
To avoid the exponential growth of the fuzzy rules to be implemented as
the number of tasks is increased, the secondary tasks are suitably organized
in ahierarchy. Also, the rules have to guarantee that only one α i is high at a
time to avoid conflict between the secondary tasks. An example of application
of the approach is described in the Simulation Section.