The definition of symbolic descriptions that consistently represent relevant geometrical aspects in manipulation tasks is a challenging problem that has received little attention in the robotic community. This definition is usually done from an observer perspective of a finite set of object relations and orientations that only satisfy geometrical constraints to execute experiments in laboratory conditions. This restricts the possible changes with manipulation actions in the object configuration space to those compatible with that particular external reference definitions, which greatly limits the spectrum of possible manipulations. To tackle these limitations we propose an object-centered representation that permits characterizing a much wider set of possible changes in configuration spaces than the traditional observer perspective counterpart. Based on this representation, we define universal planning operators for picking and placing actions that permits generating plans with geometric and force consistency in manipulation tasks. This object-centered description is directly obtained from the poses and bounding boxes of objects using a novel learning mechanisms that permits generating signal-symbols relations without the need of handcrafting these relations for each particular scenario.