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Jean-Paul Laumond ( email@example.com) is a CNRS director of
research at LAAS, Toulouse, France.
Nicolas Mansard ( firstname.lastname@example.org) is a CNRS
researcher at LAAS, Toulouse, France.
Jean Bernard Lasserre ( email@example.com) is CNRS
director of research at LAAS, Toulouse, France.
© 2015 ACM 0001-0782/15/05 $15.00
higher performances, but only offline.
Reaching the same performance online
requires either more powerful computers (running the same algorithms) or
more clever algorithms.
The notion of robot motion optimality
is diverse in both its definitions and its
application domains. One goal of this
article was to summarize several points
of view and references spread out over
various domains: robotics, control,
differential geometry, numerical optimization, machine learning, and even
The objective was to stress the expressive power of optimal motion in
robot action modeling and to present current challenges in numerical
optimization for real-time control of
complex robots, like the humanoids.
A second objective was to report recent issues in inverse optimal control. While its stochastic formulation
is popular in machine learning, other
paradigms are currently emerging in
differential geometric control theory
and polynomial optimization.
As testified in a companion article,
robotics offers rich benchmarks for optimal control theory. Due to real-time
computation constraints imposed by
effective applications, robotics also induces challenges to numerical optimization. The difficulty for roboticists is
to find the right compromise between
generality and specificity. General algorithms suffer from the classical curse
of dimensionality that constitutes a
bottleneck for robot control. Therefore,
they may be used for offline motion
generation, but they are inefficient for
real-time applications. Real-time robot
control requires very fast computations.
It requires dedicated numerical optimization methods. We have seen how
bipedal walking illustrates this tension
between generality and specificity. Roboticists are today asking optimization
theorists for more efficient algorithms,
while they are developing at the same
time a specific know-how to this end.
Last but not least, let us conclude by
referring to a controversy introduced
by neurophysiologist K. Friston. In a
11 he asks the provocative
question: “Is optimal control theory
useful for understanding motor behav-
ior or is it a misdirection?” He opposes
to optimal control the competitive no-
tion of active inference. While the paper
is mainly dedicated to motor control in
life sciences, the issue is of crucial and
utmost interest for roboticists and calls
for a reinforcement of the cooperation
between life and engineering sciences.
This article benefits from comments
by Quang Cuong Pham, from a careful reading by Joel Chavas, and above
all, from the quality of the reviews. The
work has been partly supported by ERC
Grant 340050 Actanthrope, by a grant
of the Gaspar Monge Program for Optimization and Operations Research of
the Fondation Mathématique Jacques
Hadamard (FMJH) and by the grant
ANR 13-CORD-002-01 Entracte.
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