Sensors and Methods for Mobile Robot Positioning

Chapter 2: Heading Sensors 37
be precisely equal in length to an integral number of wavelengths at the resonant frequency. This
means the wavelengths (and therefore the frequencies) of the two counter- propagating beams must
change, as only oscillations with wavelengths satisfying the resonance condition can be sustained
in the cavity. The frequency difference between the two beams is given by [Chow et al., 1985]:
f 2fr6
c
2r6
(2.3)
where
f = frequency difference
r = radius of circular beam path
6 = angular velocity of rotation
= wavelength.
In practice, a doughnut-shaped ring cavity would be hard to realize. For an arbitrary cavity
geometry, the expression becomes [Chow et al., 1985]:
f 4A6
P
(2.4)
where
f = frequency difference
A = area enclosed by the closed-loop beam path
6 = angular velocity of rotation
P = perimeter of the beam path
= wavelength.
For single-axis gyros, the ring is generally formed by aligning three highly reflective mirrors to
create a closed-loop triangular path as shown in Figure 2.6. (Some systems, such as Macek’s early
prototype, employ four mirrors to create a square path.) The mirrors are usually mounted to a
monolithic glass-ceramic block with machined ports for the cavity bores and electrodes. Most
modern three-axis units employ a square block cube with a total of six mirrors, each mounted to the
center of a block face as shown in Figure 2.6. The most stable systems employ linearly polarized light
and minimize circularly polarized components to avoid magnetic sensitivities [Martin, 1986].
The approximate quantum noise limit for the ring-laser gyro is due to spontaneous emission in the
gain medium [Ezekiel and Arditty, 1982]. Yet, the ring-laser gyro represents the “best-case” scenario
of the five general gyro configurations outlined above. For this reason the active ring-laser gyro
offers the highest sensitivity and is perhaps the most accurate implementation to date.
The fundamental disadvantage associated with the active ring laser is a problem called frequency
lock-in, which occurs at low rotation rates when the counter-propagating beams “lock” together in
frequency [Chao et al., 1984]. This lock-in is attributed to the influence of a very small amount of
backscatter from the mirror surfaces, and results in a deadband region (below a certain threshold of
rotational velocity) for which there is no output signal. Above the lock-in threshold, output
approaches the ideal linear response curve in a parabolic fashion.
The most obvious approach to solving the lock-in problem is to improve the quality of the mirrors
to reduce the resulting backscatter. Again, however, perfect mirrors do not exist, and some finite