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COPRIN Research team

Constraints solving, optimization and robust interval analysis

  • Leader : Jean-pierre Merlet
  • Research center(s) : CRI Sophia Antipolis - Méditerranée
  • Field : Perception, Cognition, Interaction
  • Theme : Robotics

Team presentation

The research topic of the COPRIN project-team is the solving of system of constraints using both consistency methods (originating from the constraint programming community) and interval analysis. These two types of method have individually shown their efficiency for some problems but have never been really been used in combination. Furthermore symbolic computation will systematically be used to specialize the solving algorithms accordind to the structure of the problem in view of a better efficiency. Finally distributed implementation of the algorithm will always be provided.

The second major research axis of the project is robotics, especially the design of new structures that must satisfy stringent performance requirements, while taking into account uncertainties that are unavoidable for robotized systems. The mathematical tools that are developed as first research axis of the project are especially useful for that kind of problems.

Research themes

Our first research axis is hence the development of methods for solving constraints system using an hybrid approach, either for general or specific systems. These methods will be based on tools for filtering, choosing the bisected variable and decomposing the system.

Our second research axis is dealing with special cases of optimization problem using methods directly derived from the solving methods, which will provide an approximation of the global extremum.

The third research topic is the theoretical and experimental evaluation of the efficiency of the methods together with the study of the possible contribution of symbolic computation to the solving methods.

All the results of these researches will be implemented in a generic software platform which will be, at least partially, interfaced with a symbolic computation tool.

The application domains are first the improvement of existing commercial softwares for solving constraints systems and, second, CAD and control theory.

A major application area is mechanism theory (especially robotics) for which the project performs both theoretical and practical research that may go up the building of mechanism and robot prototypes. We are especially interested in parallel robots synthesis, i.e. finding the dimensions of the robot so that it will satisfy stringent performance requirements in spite of manufacturing tolerances and control errors. The goal of our methods is to provide a good approximation of all possible dimensions and then to propose solutions that are robust with respect to manufacturing tolerances and are representative of the possible performance compromises.

International and industrial relations

Our main industrial partners are Alcatel, Amadeus, Constructions mécaniques des Vosges.

In Europe we have an active collaboration with Innsbruck University, EPFL, ETHZ, University of Duisburg-Essen, the TU of Braunschweig, Chemnitz, Cassino University, Scuola Superiore Santa-Anna of Pise, UPC of Barcelona, Bilbao University and the University of Athens.

In US and in Canada we have a strong partnership with Brown, Rutgers, John Hopkins, Stanford University, the MIT, Laval, McGill and Simon Fraser.

We have also ongoing collaboration with MEL (Japan), Osaka University, Tsing Hua University (Taiwan) and with the Technion of Haifa.

Keywords: Constraints solving Optimization Interval analysis Uncertainties Consistency Numerical analysis Numerical-symbolic computation Geometry Mechanism theory Robotics