A minimal contractor for the polar equation: Application to robot localization

Contractor programming relies on a catalog on elementary contractors which need to be as efficient as possible. In this paper, we introduce a new theorem that can be used to build minimal contractors consistent with equations, and another new theorem to derive an optimal separator from a minimal contractor. As an application, we focus on the channeling polar constraint associated to the change between Cartesian coordinates and Polar coordinates. We illustrate our method on the localization problem of an actual underwater robot where both range and goniometric measurements of landmarks are collected.