Sun Tracking Experiment
An essential requirement for autonomous navigation is the ability to determine
orientation. Dead reckoning offers little hope, since errors induced by
wheel slip and uneven terrain quickly accumulate into gross position and
orientation errors. Gyroscopes offer a sense of changes in orientation,
but they lack an external reference and are prone to drift. On Earth, and
other bodies with appreciable magnetic fields, the use of magnetic compass
for heading is a nice solution. However, near the magnetic poles, this field
is largely normal to the surface and has a high divergence, and magnet
compasses have significantly reduced performance. In addition, many bodies
in our solar system do not have an appreciable global magnetic field, rendering
As seen from the Antarctic during Summer in the southern hemisphere,
the sun circles overhead never disappearing beneath the horizon, with the
possible exception due to occlusions from nearby terrain such as mountain
ranges. When combined with known solar ephemeris and vehicle pitch and
roll, measuring the azimuth to the sun offers a "fix" on the orientation
of the vehicle with respect to the global reference frame. Panoramic imaging
is ideal for this application since the camera essentially always sees
the sun and can measure the azimuth to the sun with sub-pixel, hence sub-degree,
This method has two advantages over gyroscopes: it does not drift, and
the orientation measurement is referenced to the globe. It also has advantages
over magnetic compasses for navigation on bodies with no appreciable magnetic
In order to test the feasibility of sun tracking for orientation measurement,
the panoramic camera was left running for one 24 hour period near the Patriot
Hills base camp. The camera snapped an image every 15 minutes using a circular
polarizing filter and two strong (ND 2.0 and ND 3.0) neutral density filters;
the first to cut glare and the latter two to reduce incident light to capture
only the disk of the sun.
The data collection occurred in three phases, and the resulting sun trace
appears below. The first section of sun trace came between around 01:30
and 08:15 on January 18th, 1998. At around this time, the generator went
down and data collection ceased until being restarted at 13:00 that same
day. The second phase collected data from 13:00 until 17:30, at which point
I fixed a bug in the time stamping and restarted collection from 18:00
until 02:00 on January 19th, 1998. The sun trace appears below, on the
left is an animated version, and on the right is a composite of thresholded
In each image, the sun appears as the larger white dot sweeping around
the center in a counter-clockwise direction. The smaller white dots are
spectral reflections of the sun from the metal camera housing.
Animation of sun trace
Click for larger image
Composite of sun trace
Click for larger image
The orientation of the camera was measured and recorded for ground truth.
To localize the sun in the images, the algorithm thresholds the image so
that only the sun's disk remains, and then the center of mass of the remaining
pixels is calculated.
In many of the frames, a second bright spot can be seen near the sun
but at a distance further from the center of the image. These spots are
caused by a specular reflection of the sun in the camera mounting hardware.
Much of the reflection is suppressed during thresholding, but some is just
as bright as the sun and with simple thresholding it cannot be removed.
If this is not accounted for, then the center of mass calculation is erroneous.
Surprisingly, the geometry of the camera is such that the azimuth computation
is not affected by this error, since the reflections are always appear
directly radially outward from the sun location. The position of the sun
in the image plane is incorrectly reported, but the azimuth computation
still comes out correct.
This is only OK for computing azimuth to the sun. If we want to compute
the elevation also, then we will need to add a region growing step to find
the actual connected disk of the sun first, and then compute the center
of mass of that blob.
Below is a set of images showing the sun a typical image. The red portion
shows the pixels in the image that were of higher intensity than the threshold.
Preliminary results for sun position calculation appear in the plots below.
The first shows the image plane location computed for the sun in each image.
Notice the strange "outliers" in the upper left of the ellipse, which are
erroneous measurements. They correspond to the images in the above animation
where the sun is in the lower left and there is a significant reflection
component farther out from the center. Because this error only affects
the radial direction, the azimuth computation is relatively unharmed by
Location of sun in images
In the second plot, the azimuth angle is shown. The azimuth is calculated
from the location of the sun above and the location of the camera center,
which for now is not calibrated as well as it could be. The azimuth should
be essentially linear, but there are two spots where the line appears broken
which correspond to the same image frames where some time passed between
images for different reasons. Notice once again that the azimuth is linear
even for those points which were adversely affected by the reflections
Solar azimuth for each image
Conclusions / Future Work
Sun localization appears to be quite feasible at this point. It appears
that sub-degree precision in orientation is possible from the images taken
in the Antarctic. Currently, we are working on computing solar ephemeris
for the times at which these images were taken and comparing that to the
measurements made here. Only then will we have a good idea of the precision
and accuracy of this method as an orientation sensor.
Back to Panoramic
Robotic Search for Antarctic Meteorites 1998
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This document prepared by Michael