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the cost function to be minimized and finally to
numerous constraints to be simultaneously
respected. The OFMPP is originally an optimal
control one and has been transformed into a
parametric optimization problem. The optimization
parameters are time transfer T and the position of
nodes defining the shape of joint variables. The
research of T has been separated from that of the
others parameters in order to make the computing
process efficient and to handle constraints easily by
transforming them into explicit bounds on T possible
values. In fact, the various possible constraints have
been regrouped in four families according to their
possible effects on T values and then have been
handled sequentially during each optimization step.
Nodes, defining q(x) shape, are connected by cubic
spline functions and their positions are perturbed
inside a stochastic process until the objective
function value is sufficiently reduced while all
constraints are all satisfied. This ensured smoothness
of resulted profiles. The objective function has been
written under a weighting form permitting to make
balance between reducing T and magnitude of
implied torques.
Numerical examples, where a stochastic
optimization process, implementing the proposed
approach, has been used along with cubic spline
approximations, and dealing with complex
problems, such as those involving discontinuous
friction efforts and obstacle avoidance, have been
presented to show the efficiency of this technique.
Others successful tests have been made in parallel
for complex robotic architectures, like biped robots,
will be presented in a future paper.
ACKNOWLEDGEMENTS
We thank Prof. H. E. Lehtihet for his suggestions
and helpful discussions.
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A STOCHASTIC OFF LINE PLANNER OF OPTIMAL DYNAMIC MOTIONS FOR ROBOTIC MANIPULATORS
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