Method and apparatus for determining the position of a retroreflective element

A method for determining the position of at least one position retroreflective element located in a predetermined coordinate frame of reference having an X axis, said method comprising the steps of:

• (a) providing a light transmitting and detecting means for transmitting a rotating beam of light, detecting reflections of said beam of light, providing an index position along said rotation of said beam of light;
• (b) providing a reference retroreflective element capable of reflecting said beam of light back toward said light transmitting and detecting means;
• (c) providing an intermediate benchmark position located at third coordinates;
• (d) positioning said light transmitting and detecting means at a primary benchmark position at known first coordinates in said coordinate frame of reference;
• (e) positioning said reference retroreflective element at a secondary benchmark position at known second coordinates in said coordinate frame of reference;
• (f) transmitting said beam of light to illuminate said at least one position retroreflective element and said reference retroreflective element during a first rotation of said beam of light;
• (g) monitoring said first rotation of said beam of light as it travels between said index position, said at least one position retroreflective element and said reference retroreflective element;
• (h) repositioning said reference retroreflective element at said intermediate benchmark position;
• (i) transmitting said beam of light to illuminate said at least one position retroreflective element and said reference retroreflective element during a second rotation of said beam of light;
• (i) monitoring said second rotation of said beam of light as it travels between said index position, said at least one position retroreflective element and said reference retroreflective element;
• (j) repositioning said light transmitting and detecting means at said secondary benchmark position;
• (k) transmitting said beam of light to illuminate said at least one position retroreflective element and said reference retroreflective element during a third rotation of said beam of light;
• (l) monitoring said third rotation of said beam of light as it travels between said index position, said at least one position retroreflective element and said reference retroreflective element;
• (m) repositioning said reference retroreflective element at said primary benchmark position;
• (n) transmitting said beam of light to illuminate said at least one position retroreflective element and said reference retroreflective element during a fourth rotation of said beam of light;
• (o) monitoring said fourth rotation of said beam of light as it travels between said index position, said at least one position retroreflective element and said reference retroreflective element;
• (p) repositioning said light transmitting and detecting means at said intermediate benchmark position;
• (q) transmitting said beam of light to illuminate said at least one position retroreflective element and said reference retroreflective element during a fifth rotation of said beam of light;
• (r) monitoring said fifth rotation of said beam of light as it travels between said index position, said at least one position retroreflective element and said reference retroreflective element;
• and
• (s) determining the position of said at least one position retroreflective element in said coordinate system based on said first, second and third coordinates and at least two of said first, second, third, fourth, and fifth rotations of said beam of light.

A method for initializing a position sensing system capable of determining the position of a point in a predetermined coordinate frame of reference having an X axis, said position sensing system having a light transmitting and detecting means for transmitting a rotating beam of light, for detecting reflections of said beam of light, for providing an index position along said rotation of said beam of light, and for providing a reference position which is parallel to said X axis irrespective of said orientation of said light transmitting and detecting means, said method comprising the steps of:

• (a) providing a reference retroreflective element capable of reflecting said beam of light back toward said light transmitting and detecting means;
• (b) positioning said light transmitting and detecting means at a primary benchmark position at known first coordinates in said coordinate frame of reference;
• (c) positioning said reference retroreflective element at a secondary benchmark position at known second coordinates in said coordinate frame of reference;
• (d) transmitting said beam of light to illuminate said at least one position retroreflective element and said reference retroreflective element during a first rotation of said beam of light;
• (e) measuring, during said first rotation of said beam of light, a first angle of rotation of said beam as it travels from said index position to said at least one retroreflective element, and a second angle of rotation of said beam as it travels from said index position to said reference retroreflective element;
• (f) repositioning said light transmitting and detecting means at said secondary benchmark position and said reference retroreflective element at said primary benchmark position;
• (g) transmitting said beam of light to illuminate said at least one position retroreflective element and said reference retroreflective element during a second rotation of said beam of light;
• (h) measuring, during said second rotation of said beam of light, a third angle of rotation of said beam of light as it travels from said index position to said at least one position retroreflective element, and a fourth angle of rotation of said beam of light as it travels from said index position to said reference retroreflective element;
• and
• (i) determining the position of said at least one position retroreflective element based on said first coordinates, said second coordinates and said first, second, third and fourth angles of rotation of said beam of light;
• and
• (j) using the position of said at least one position retroreflective element to determine the position of a point in said coordinate frame of reference.

A system for determining the position of at least one position retroreflective element in a predetermined coordinate frame of reference having an X axis, said system comprising:

• light transmitting and detecting means, positionable at one of a primary benchmark position and a secondary benchmark position, for generating a rotating beam of light, for providing an index position along said rotation of said beam of light, for providing a reference position parallel to said X axis irrespective of the orientation of said light transmitting and detecting means and for detecting reflections of said beam of light from a reference retroreflective element positioned at the other of said primary and secondary benchmark positions and said at least one position retroreflective element, for generating a plurality of first signals in response to said reflections of said beam of light when said light transmitting and detecting means is located at said primary benchmark position and for generating a plurality of second signals in response to said reflections of said beam of light when said light transmitting and detecting means is located at said secondary benchmark position;
• and
• computer means for computing said position of said at least one position retroreflective element in said frame of reference from said reference position, said plurality of first signals, said plurality of second signals and said known first and second coordinates of said primary and secondary benchmark positions.