Bayesian Programming

Probability as an extension of logic


The Bayesian map

A hierarchical probabilistic model for mobile robot navigation.

PhD thesis of Julien Diard (2003)

What is a map ? What is its utility ? What is a location, a behaviour ? What are navigation, localization and prediction for a mobile robot facing a given task ?

These questions have neither unique nor straightforward answer to this day, and are still the core of numerous research domains. Robotics, for instance, aim at answering them for creating successful sensori-motor artefacts. Cognitive sciences use these questions as intermediate goals on the road to understanding living beings, their skills, and furthermore, their intelligence.

Our study lies between these two domains. We first study classical probabilistic approaches (Markov localization, POMDPs, HMMs, etc.), then some biomimetic approaches (Berthoz, Franz, Kuipers). We analyze their respective advantages and drawbacks in light of a general formalism for robot programming based on bayesian inference (BRP).

We propose a new probabilistic formalism for modelling the interaction between a robot and its environment : the Bayesian map. In this framework, defining a map is done by specifying a particular probability distribution. Some of the questions above then amount to solving inference problems. We define operators for putting maps together, so that « hierarchies of maps » and incremental development play a central role in our formalism, as in biomimetic approaches. By using the bayesian formalism, we also benefit both from a unified means of dealing with uncertainties, and from clear and rigorous mathematical foundations.


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