Optimal contractor for triangle constraint

Abstract

This paper presents an optimal method for contracting a triangle Constraints Satisfaction Problem, composed of three distance constraints. Unlike traditional interval analysis methods, this approach takes into account all three constraints globally and focuses on the edges of the CSP boxes, rather than on their entirety, to compute the smallest boxes containing the CSP solution. It is based on constraint propagation, interval analysis tools and some topological properties of the boundary solution of the triangle CSP. This contractor can be applied in various contexts, and in particular to improve localization in robotics.