The main interests of the project are computational geometry and geometric issues in robotics. The research is motivated by the many applications domains, and most notably robotics, that requires to solve geometric problems efficiently.
The goal of our work in computational geometry is to design algorithms and to analyze their behaviour from both a theoretical and a practical point of view. This year, our research has been three fold. First, we worked on new general algorithmic techniques (output sensitive algorithms, randomized algorithms), Voronoi diagrams and geometric optimization problems. We also work on the problems raised by geometric computing, especially numerical instability, and develop a library of geometric algorithms named CGAL in joint collaboration with six other group in Europe. Lastly, we apply our techniques to some applied problems in geology and CAD/CAM.
The research in robotics is conducted along two main directions : mechanism theory and modelling, and motion planning. The work on parallel manipulators has been continued, aiming at simplifying the computation of the direct kinematics and providing tools for designing such manipulators. Our work on motion planning focused on the computation of optimal paths for mobile robots and on systems with many degrees of freedom.