A Bayesian CAD modeler offers the possibility to describe the machines (positions, precision, kinematics and control parameters, etc.), the objects (locations and shapes), the sensors (range and accuracy) and the environment within a simple, unified and concise probabilistic description. Consequently, the main difference between a Bayesian CAD modeler and a classical one is that, when resolving calibration and inverse kinematics problems, it is possible to take into account all the uncertainties at hand.
Bayesian reasoning represents a powerful
and generic tool for computing uncertainties and constraints propagation.
Using Bayesian inference, we can deal with uncertainty and solve
many inverse problems found in CAD and robotics:
Calibration: most of the calibration and reconstruction
problems can be solved using our approach:
Inverse kinematics: new possibilities are offered when solving inverse kinematics problems, such as:
The kernel is made of a Bayesian inference engine dedicated to geometry. The a priori knowledge on the scene is represented as a joint distribution of all the variables necessary to describe the machines, the parts, the sensor readings and the environment. The inference engine is divided into three components:
To explain the principle of our method,
we give a simple inverse kinematics problem with a 2 dof planar
arm:
Click here to view this
example
We have developed the kernel and tested it on a simple Cad modeler for numerous problems:
This Figure represents a screen copy of this
CAD modeler. 
The
purpose of this movie is to give a feeling of what is a probabilistic
specification of a CAD scene. It presents several random draws
corresponding to the specified probability distribution. As there
are uncertainties on the joint's positions and link's lengths
of the robot and on car's location, their relative position is
only approximately known.
The
solution found when equal uncertainty levels were assumed on
the two arms.
The
solution found when more uncertainty on command values of the
right arm is assumed. We can see that the right arm bends at
maximum to minimize the influence of the uncertainty of its command
values on the uncertainty of the relative position between the
two parts.
This
movie describes the measurement procedure and the internal data
structure used to localize an object with a range finder (laser)
mounted the extremity of a robot arm.The capability to take in account all uncertainties at hand in CAD problems would be a major breakthrough for this field. We are now convinced that it is possible. Our goal is to develop with industrial partners a Bayesian Calibration Module product to solve these problems.
The fundamental research part of this project has been achieved:
The applied research part and industrial development may start, it supposes to:
Consequently, we are looking for industrial partners interested to work with us on these three objectives.
Emmanuel Mazer, Kamel Mekhnacha, Pierre Bessière
GRAVIR - SHARP
INRIA Rhône-Alpes - ZIRST
655 avenue de l'Europe
38334 St Ismier Cedex
FRANCE
E-mail: Mazer, Mekhnacha, Bessière Phone: +33(0)4.76.61.55.09 Fax: +33(0)4.76.61.54.54 WWW: http://www-laplace.imag.fr