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,


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 :
  1. 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 ``representations''.
  2. 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.
  3. 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.
In order to support these three theses the paper will be divided into four main sections.

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 incomplete knowledge.

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.

MaxEnt 94 Abstracts /