Stable Sensorless Localization of 3-D Objects

In general, localization is a very important step in the manufacturing process, which can be considered as a prior process of assembly, machining, transportation, etc. Localization can be achieved with or without sensors. Compared with localization with sensors, localization without sensors can be more reliable, cheaper, and can have lower requirements on the environment. For example, localization without sensors can be achieved in a dark environment. However, it is more restrictive to the condition of the system. Localization of 2-D objects without sensors has been deeply investigated. Some theoretical results on 3-D-object localization without sensors have been given. On the other hand, some work has been carried out that tries to find methods to reduce uncertainties in the 3-D orientation of a polyhedron (i.e., the orientation of the polyhedron in a 3-D space). However, to the best of our knowledge, no practical and effective methods have been proposed, so far, to localize a polyhedron from any initial 3-D orientation to a unique 3-D orientation without sensors. This paper aims to find conditions and strategies for 3-D objects to be rotated from an unknown initial stable state to a unique stable state without sensors. The main contributions of this paper are given as follows: 1) It is discovered and proved that there are two classes of 3-D objects that can be rotated into a unique state from an arbitrary initial state without sensory feedback. 2) For these two classes of objects, the practical strategies are presented, and one example for each class is given to show the validity of the strategy. 3) Based on the above results, the robotic system and localization operations are illustrated, and some experimental results are given.