Abstract
In this paper, a new measuring system is :proposed which can measure the fine 6-DOF displacement of rigid bodies. Its measurement principle is based on detection of laser beam reflected from a specially fabricated mirror that looks like a triangular pyramid having an equilateral cross-sectional shape. The mirror has three lateral reflective surfaces inclined 45$^{\circ}$ to its bottom surface. We call this mirror 3-facet mirror. The 3-facet mirror is mounted on the object whose 6-DOF displacement is to be measured. The measurement is operated by a laser-based optical system composed of a 3-facet mirror, a laser source, three position-sensitive detectors(PSD). In the sensor system, three PSDs are located at three corner points of a triangular formation, which is an equilateral triangular formation tying parallel to the reference plane. The sensitive areas of three PSDs are oriented toward the center point of the triangular formation. The object whose 6-DOF displacement is to be measured is situated at the center with the 3-facet mirror on its top surface. A laser beam is emitted from the laser source located at the upright position and vertically incident on the top of the 3-fatcet mirror. Since each reflective facet faces toward each PSD, the laser beam is reflected at the 3-facet mirror and splits into three sub-beams, each of which is reflected from the three facets and finally arrives at three PSDs, respectively. Since each PSD is a 2-dimensional sensor, we can acquire the information on the 6-DOF displacement of the 3-facet mirror. From this principle, we can get 6-DOF displacement of any object simply by mounting the 3-facet mirror on the object. In this paper, we model the relationship between the 6-DOF displacement of the object and the outputs of three PSDs. And, a series of simulations are performed to demonstrate the effectiveness of the proposed method. The simulation results show that the proposed sensing system can be an effective means of obtaining 3-dimensional position and orientation of arbitrary objects.