@article {Nakajima:1989:0169-1864:151,
title = "An ultrasonic orientation sensor with distributed receivers",
journal = "Advanced Robotics",
parent_itemid = "infobike://tandf/arb",
publishercode ="tandf",
year = "1989",
volume = "4",
number = "2",
publication date ="1989-01-01T00:00:00",
pages = "151-168",
itemtype = "ARTICLE",
issn = "0169-1864",
eissn = "1568-5535",
url = "https://www.ingentaconnect.com/content/tandf/arb/1989/00000004/00000002/art00004",
doi = "doi:10.1163/156855390X00125",
author = "Nakajima, Shin-Ichi and Takahashi, Yoshikazu",
abstract = "This paper is concerned with an ultrasonic orientation sensing system, which measures the orientation of an objective surface, using the phase information of the reflected echoes. At least two phase differences obtained from three receivers are necessary to determine the three-dimensional
orientation. However, the phase difference cannot be distinguished over one period of the reflected echo. Hence, the measuring range is restricted to a relatively small orientation angle. In this paper, a method is proposed to overcome the difficulty by increasing the number of receivers.
Closely arranged receivers encircling a transmitter can provide a smaller difference between adjacent reflecting paths. They keep the individual phase difference to a sufficiently small value and allow measurement of the orientation over a wide range. This paper shows the principle of measuring
two directional angles of a surface normal based on the least-squares method. The redundant phase information obtained by the many receivers also contributes to the improvement of the accuracy. Two prototype sensing systems with six or eight receivers are constructed and the experimental results
demonstrate the basic performance of the system.",
}