A new practical strategy to localize a 3D object without sensors

Sensorless localization of 3D objects has been a significant research topic for many years. Researchers have focused on this problem from both theoretical and practical perspective where the goal is to reduce uncertainties in the orientation of a 3D object. However, to the best of our knowledge, no effective practical methods have been proposed so far to localize a polyhedron from any initial orientation to a unique orientation without sensors. In our previous work [1], two broad classes of 3D objects have been introduced, which can be localized from an arbitrary state to a unique state on a flat plane (the surface resting on the flat plane is established) without sensors. In this paper, a much broader class of polyhedra is introduced, which can be localized to a unique state without sensors. The main contributions of this paper are given as follows: • It is found that a polyhedron with an arbitrary initial state on the flat plane can be rotated to a fixed orientation (the orientation of the surface resting on the flat plane is fixed), provided that the polygon corresponding to each surface of the polyhedron can be oriented to a unique orientation in a 2D space. The method of rotating the polyhedron to a fixed orientation is given. • Base on the above result, both conditions and the strategy are given for a polyhedron to be localized to a unique state. • An example is given to show the validity of the strategy.