![](bg6.png)
solar azimuth in less than a second on a PC. It can
easily be built into the processor of any robot.
Besides the accuracy of the method it has the
advantage that it gives the solar azimuth anywhere
within 360
o
, with no ambiguity of π as in some other
algorithms. It is partially independent of
environmental conditions since some ommatidia
may be looking at blue sky while others are looking
at lightly clouded sky. The position of the zeros is
unchanged as long as a polarization pattern is
detectable below the cloud, which is more likely for
ultraviolet light detectors (Pomozi et al., 2001).
So the greatest difficulty in building a skylight
compass for a robot based on this algorithm is the
detection of the four zeros. One design uses an array
of about 100 pairs of orthogonal photoreceptors in a
circle round the robot. The problem is that each pair
would have to observe a patch of sky with an
accurate azimuth; the elevation, due to Equation
(14), would be less critical. In another design the
robot has one accurate pair of photoreceptors which
is rotated continually through 360
o
(like radar)
measuring the azimuth as it moves at a constant high
elevation (e.g. 70
o
).
3 CONCLUSIONS
We have shown that an accurate celestial compass
for a robot can be built round the principle of finding
4 zeros in the differences between the two signals
obtained from pairs of orthogonally polarised
photoreceptors. The algorithm was derived from
published studies on the anatomy of insect eyes and
on published experiments with insect navigation. In
particular Equation (16) explains why errors occur
when the view of an insect is restricted. The
algorithm is also simple enough for the small brain
of an insect; so we believe that the algorithm, or
something like it, is part of the celestial compass
within the brain of an insect.
At the heart of the algorithm are searches in
arrays of exactly 16 elements as in Table 1. So we
might expect evidence for this within the brain of an
insect. It is interesting to note that a topographic
representation of E-vector orientation has been
found to underlie the columnar organisation of the
central complex of the brain of a locust, and this
consists of stacks of arrays, each composed of a
linear arrangement of 16 columns (Heinze and
Homberg, 2007).
REFERENCES
Bernard, G D, Wehner, R, 1977. Functional similarities
between polarization vision and color vision, Vision
Res., 17, 1019-28.
Fent, K, Wehner, R, 1985. Ocelli: A celestial compass in
the desert ant Cataglyphis, Science, 228, 192-4.
Goodman, L. J., 1970. The structure and function of the
insect dorsal ocellus. Adv. Insect Phys., 7, 97-195.
Heinze, S, Homberg, U, 2007. Maplike Representation of
Celestial E-Vector Orientations in the Brain of an
Insect, Science, 315, 995-7.
Kirschfeld, K, Lindauer, M, Martin,H, 1975. Problems in
menotactic orientation according to the polarized light
of the sky, Z. Naturforsch, 30C, 88-90.
Labhart, T, 1980. Specialized Photoreceptors at the dorsal
rim of the honeybee’s compound eye: Polarizational
and Angular Sensitivity, J Comp. Phys., 141, 19-30.
Labhart, T, 1988. Polarised-opponent interneurons in the
insect visual system, Nature, 331, 435-7.
Lambrinos, D, Maris, M, Kobayashi, H, Labhart, T,
Pfeifer, P, Wehner, R, 1998. Navigation with a
polarized light compass, Self-Learning Robots II: Bio-
Robotics (Digest 1998/248) IEE, London, 7/1-4.
NASA, 2005. www.nasatech.com/Briefs/Oct05/
NPO_41269.html
Pomozi, I, Horvath, G, Wehner, R., 2001. How the clear-
sky angle of polarization pattern continues underneath
clouds, J. Expt. Biol, 204, 2933-42.
Rayleigh, Lord, 1871. On the light from the sky, its
polarisation and colour, Phil Mag,, 41, 107-20, 274-9.
Rossel, S, 1993. Mini Review: Navigation by bees using
polarised skylight, Comp. Biochem. Physiol, 104A,
695-705.
Rossel, S, and Wehner, R, 1982. The bee’s map of the e-
vector pattern in the sky, Proc. Natl. Acad. Sci. USA,
79, 4451-5.
Sommer, E W, 1979. Untersuchungen zur topo-
graphischen Anatomie der Retina und zur
Sehfeldoptologie im Auge der Honigbiene, Apis
mellifera (Hymenoptera). PhD Thesis,Un.Zurich.
Tyndall, J, 1869. On the blue colour of the sky, the
polarisation of skylight, and on the polarisation of
cloudy matter, Proc. Roy. Soc., 17, 223.
Von Frisch, K, 1949. Die Polarisation des Himmelslichts
als Orientierender Faktor bei den Tanzen der Bienen,
Experientia, 5, 142-8.
Wehner, R, 1989. The hymenopteran skylight compass:
matched filtering and parallel coding, J Exp. Biol.,
146, 63-85.
Wehner, R, 1997. The Ant’s celestial compass system:
spectral and polarization channels, In Orientation and
Communication in Arthropods, Ed. M. Lehler,
Birkhauser, Berlag, Basel, Switzerland, 145-85.
Wehner, R, and Raber, F, 1979. Visual spatial memory in
desert ants, Cataglyphis bicolor (Hymenoptera:
Formicidae), Experientia, 35, 1569-71.
BIOSIGNALS 2008 - International Conference on Bio-inspired Systems and Signal Processing
190