[Robotgroup] Triangulation using a Rich Skyline Telescope

[Bruce Waters]

I agree with others who have mentioned the difficulty
of achieving the accuracy (centimeters) at the costs
allowed using classical RF triangulation.   If you are
willing to consider a rather dramatic modification of 
the beacons, you might find meeting those specs more 
realistic.   My approach would be to use a large number 
of led's (eg. Christmas light strings) nonuniformly 
arranged around the boundary(or elsewhere) to provide 
a high angular resolution "skyline".   To reduce
ambiguity it is important to insure that the interlight
spacing not be excessively uniform.

I would use a cheap telescope (with a right/left pair of 
light edge sensors at the focus) at the same height as the 
led's.  I would sweep or rotate the telescope.  I would 
train the robot on the spacing of the led's from some 
known near-central point.   I would move the robot 
directly at some specific led beacon(a non-rotating 
second telescope might facilitate this) and develop a 
mathematical (initially tabular, then add sophistication) 
model of the variations in angles to the rest of the 
skyline.     I would return to the central point and pick 
some number of additional headings to train the bot.  
Consider mounting the telescope low and using 
software techniques to ignore the wheels.

Learning the skyline allows very low precision(just 
string chunks of it around the boundary) initial
placement the skyline.  It allows software 
improvements to accuracy and data volume 
requirements.  It provides an angular resolution 
related to the telescope power and the number of 
led's in the skyline.   It allows local incremental 
improvement of the resolution by adding skyline in 
appropriate places.   It is an interesting continuing 
project to improve the performance without spending 
more on hardware.   It can be wonderfully cheap for 
the performance delivered.

A valuable improvement you should consider is an 
elevation tracking gimbal mount for the telescope 
to reduce the exaggerated sensitivity to tilt of the 
robot and vertical variations in the skyline as the 
telescope rotates.   The light sensor for this 
improvement should be upgraded to at least 
four quadrant and could go (fast, low res)
video.  Note that the skyline does not have to be 
continuous but that precision does require that 
adjacent beacons be visible at angles that are not 
too acute in several major compass headings.

Just like radio beacons, chance light sources in the
skyline may be used as beacons in some cases so
your robot may function adequately in some
environments without additional beacons.  The
elevation control and perhaps a zoom control
on the telescope can greatly enhance such 
serendipitous operation.   The flexibility and
adaptability of this approach is outstanding.
It is a wonderful platform to explore fuzzy
logic, data volume reduction techniques, and 
high reliability software concepts.

Bruce Waters