The ``Beam In The Bin'' Experiment
Using ``Probability as Logic'' as a theory of cognition
in a simple robotic experiment
Pierre Bessiere, Eric Dedieu, and Emmanuel Mazer,
CNRS --- IMAG/LIFIA
Maximum Entropy, Bayesian techniques, Probability as Logic,
Cognitive Sciences, Robotics
The goal of this paper is to support, illustrate and discuss the three
following theses :
In order to support these three theses the paper will be divided into four
For both a living organism and a robot nothing exists but
the signals coming from its sensors and sent to its
motors. The space corresponding to these variables is called
the phase space of the system. This space is highly structured.
When the values of some of the sensory-motor variables have been fixed, the
possible values of the other variables are very constrained.
The central problem of autonomy is to discover, explore, learn, memorize
and exploit these dependencies between sensory-motor variables.
As the relevant space is the sensory-motor space, the interaction between
the system and its environment is the only means to build correct internal
It is possible and necessary for an autonomous sensory-motor
system to build useful ``representations'' of its interactions with its
environment. These representations should be neither
symbolic, nor analytic or geometric. These
approximated models of the interaction with the environment are the only way
to take into account the complexity of real physical worlds. This kind
of internal representations is the only one able to deal with uncertain
and incomplete knowledge.
Probability theory is an adequate theoretical foundation
for this approach. Probability distributions
on subspaces of the sensory-motor space
are powerful representations of the interactions between the systems and
their environment. A lot of mathematical tools already exist to deal with
uncertain and incomplete knowledge and may be used to learn, stock
and exploit the dependencies between sensory-motor variables.
The first section will discuss the difficulties of the classical approach to
robotics. We will demonstrate that these difficulties are a particular
case of the general ``symbol grounding'' problem. It will be stressed that
the ability to take into account uncertain and incomplete knowledge
is a main requirement for autonomous robots.
The second section will recall the basics of probabilistic reasoning
and explain how it deals with uncertain knowledge. It will also state the
``principle of maximum entropy'' and show how this principle, as a way to
take into account ignorance, is a central mechanism to reason despite
The third section will present the ``beam in the bin'' experiment. This
experiment is the most simple one we could imagine with a real robot
in a real physical environment. The robot has only one motor variable
and one sensor variable. The environment is made of a green plastic
dustbin lit by a single lamp. Despite its simplicity this experimental
set-up illustrates all the difficulties the classical approach to
robotics has to face. Due to its simplicity this experiment
demonstrates clearly how probabilistic reasoning may be used in
autonomous robotics and why this approach is powerful and interesting.
Finally, the last section will present a generic methodology to program
autonomous robots based on the previous ideas. Usually the programmer
imposes his conception of the environment to the robot. This conception is
stated in abstract terms either symbolic, geometric or analytic. We propose
to invert this approach. The robot builds probabilistic representations
of its interactions with its environment and proposes these ``models'' to
the programmer. We will discuss in some detail the advantages and
drawbacks of this new programming methodology.
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