On fence design and the complexity of push plans for orienting parts
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Orienting polyhedral parts by pushing
Computational Geometry: Theory and Applications - Special issue on: Sixteenth European Workshop on Computational Geometry (EUROCG-2000)
Stable Sensorless Localization of 3-D Objects
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
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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.