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tion. This indicates that MOCS might need a rela-
tively high number of populations and executions in
order to achieve its best performance. On the other
hand, the high number of iterations in the simulation
test showed clearly the tendency of MOPSO to ge-
nerate solutions which are more concentrated in the
neighborhood of the leader particle (best global solu-
tion). This tendency was not emphasized as clearly in
the second experiment where only a limited number
of iterations is used.
7 CONCLUSION
In this work, an auto-tuning method of PID control-
lers for robot manipulators is introduced. Two multi-
objective optimization methods are considered, na-
mely MOCS and MOPSO. The main contribution of
this work is to compare the performance of the two
algorithms in the sense of achieving a good tracking
accuracy of a predefined trajectory without causing
a control action with high variations. The necessary
metrics for the comparison are considered and des-
cribed. Statistics taken from a simulation of the ro-
bot Puma 560 show clearly that MOCS is performing
much better than MOPSO with respect to all the con-
sidered metrics. The main advantage of MOCS co-
mes from the fact that its Pareto solutions have higher
spread and cover bigger region of the objective space
than the solutions of MOPSO. However, an experi-
ment on a real robot, where only a limited number of
iterations is used, showed that both algorithms perfor-
med equally well. This indicates that sufficiently high
number of populations and iterations might be neces-
sary for MOCS to achieve its best performance.
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A Comparative Study on the Performance of MOPSO and MOCS as Auto-tuning Methods of PID Controllers for Robot Manipulators
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