Underwater Robots - Gianluca Antonelli.pdf

132 6. Kinematic Control of UVMSs
• Asecond task ( α 2 ), with lower priority with respect to the first, has to be
added. Rule n.3,thus, is aimed at avoiding activation ofthis task when
the primary ( α 1 )ishigh.
• Rule n. 4and n. 5are aimed at activating α 2 .Notice that the activation of
α 2 is in and with the condition that does not activate the higher priority
task ( α 1 ).
• Repeat for the third task, inorder of priority, the same rules as done for
the second task by taking into account that two tasks are now ofhigher
priority.
Table 6.3 is aimed at clarifying the rules development with respect to
two tasks, 1and 2inwhich the first is of higher priority with respect to the
second. The fuzzy sets are very simple, i.e., aninput u i high requires the
activation ofthis task by imposing α i high. It can berecognized, thus, that
α 2 respects its lower priority.
Table 6.3. Examples of the fuzzy set rules for two tasks: u 1 is the input of ageneric
task of higher priority with respect to u 2 corresponding to asecondary task. α 1 and
α 2 are the corresponding output
u 2 =low
u 2 =high
u 1 =low u 1 =high
α 1 =low
α 2 =low
α 1 =low
α 2 =high
α 1 =high
α 2 =low
α 1 =high
α 2 =low
It is worth noticing that the rules presented could be grouped, e.g., rules
n. 1and n. 3. The list presented, however, keeps the logical structure used
to develop the rules and should be clearer to the reader. Obviously, inthe
simulation the rules have been compacted. With this logical approach the
rules are complete, consistent and continuous [103].
The and – or operations have been calculated by resorting to the min– max
operations respectively,the implication–aggregation operationstoo have been
calculated by resorting to the min– max operations respectively, the values
of α i ∈ [0, 1] are obtained bydefuzzification using the centroid technique and
anormalization. Finally, the value of β ∈ ]0, 1] is given by β =1− maxi ( α i ).
Notice that the extremities of the range in which β is defined do not involve
asingular configuration since, if β =1the manipulator alone is moving and
it is not close to akinematic singularity. On the other hand, itispreferable
to have acertain degree of mobility ofthe manipulator avoiding β =0;this
to guarantee that the manipulator reconfigures itself in adexterous posture.
Asimulation has been run with the proposed kinematic control leading to
satisfactory results. Figures 6.19–6.24 show some plots of interest. In detail,