Motivation
Motivation
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 manetic 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 compasses useless.
As seen from the Antarctic during Summer in the southern hemisphere, the sun circles overhead never disappearing beneath the horizon, with the possible exceptiond 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, accuracy.
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 sphere.
Experiment
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.
Data Collection
The data collection occurred in three phases, and the resulting sun trace appears below. The first section of suntrace 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 images.
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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.
The orientation of the camera was measured and recorded for ground truth.
Sun Localization
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 supressed 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.
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Results
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 the error.
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 above.
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.
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