Measurement of 3-D position and orientation of rigid bodies using a 3-facet mirror

In this paper, a new measuring system is proposed which can measure the 3-dimensional position and orientation 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° to its bottom surface. We call this mirror 3-facet mirror. The 3-facet mirror is mounted on the object whose position and orientation are to be measured. The measurement is operated by a laser-based optical system composed of a 3facet mirror, a He-Ne 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 lying parallel to the reference plane. The sensitive areas of three PSDs are oriented toward the center point of the triangular formation. The object whose position and orientation are to be measured is situated at the center with the 3-facet mirror on its top surface. A laser beam is emitted from the He-Ne laser source located at the upright position and vertically incident on the top of the 3-facet mirror. Since each reflective facet faces toward each PSD, the laser beam is reflected at the 3-facet mirror and splits into three subbeams, 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-degree-of-freedom motion of the 3-facet mirror. From this principle, we can get the 3-dimensional position and orientation of any object simply by mounting the 3-facet mirror on the object. In this paper, we model the relationship between the 3-dimensional position and orientation of the object and the outputs of three PSDs. And, a series of experiments are performed to demonstrate the effectiveness and accuracy of the proposed method. The experimental results show that the proposed sensing system can be an effective means of obtaining 3dimensional position and orientation of arbitrary objects. The resolution of the experimental system is found to be approximately two micrometers in translation and five micro-radians in rotation. By virtue of the easiness in application, the measurement principle can be applied to a wide range of applications such as 3-D fine motion of robotic manipulators, machining tools, sliders flying on magnetic disks of HDDs, positioning stages, etc.