This paper presents a visual servoing strategy for a clevis and tenon joint assembly as typically performed in aircraft manufacturing. The desired velocity in the image acquired by the cameras observing the parts is extracted from a vector field that guides the motion of the moving part so that it follows an accurate 3D straight line trajectory. The vector field is designed so that it is continuous and globally exponentially stable whatever the initial configuration. The strategy has been successfully implemented and validated on a full-scale demonstrator, with coarse camera localization, while ensuring an assembly without any collision thanks to a maximal error less than 1 mm along a 10 cm trajectory.

Given a set of axis-parallel n-dimensional boxes, the q-intersection is defined as the smallest box encompassing all the points that belong to at least q boxes. Computing the q-intersection is a combinatorial problem that allows us to handle robust parameter estimation with a numerical constraint programming approach. The q-intersection can be viewed as a filtering operator for soft constraints that model measurements subject to outliers. This paper highlights the equivalence of this operator with the search of q-cliques in a graph whose boxicity is bounded by the number of variables in the constraint network. We present a computational study of the q-intersection. We also propose a fast heuristic and a sophisticated exact q-intersection algorithm. First experiments show that our exact algorithm outperforms the existing one while our heuristic performs an efficient filtering on hard problems.

Researchers from interval analysis and constraint (logic) programming communities have studied intervals for their ability to manage infinite solution sets of numerical constraint systems. In particular, inner regions represent subsets of the search space in which all points are solutions. Our main contribution is the use of recent and new inner region extraction algorithms in the upper bounding phase of constrained global optimization. Convexification is a major key for efficiently lower bounding the objective function. We have adapted the convex interval taylorization proposed by Lin and Stadherr for producing a reliable outer and inner polyhedral approximation of the solution set and alinearization of the objective function. Other original ingredients are part of our optimizer, including an efficient interval constraint propagation algorithm exploiting monotonicity of functions. We end up with a new framework for reliable continuous constrained global optimization. Our interval B&B is implemented in the interval-based explorer Ibex and extends this free C++ library. Our strategy outperforms the best reliable global optimizers.