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Originally Posted by Gene F
Given that A and B are the lengths of the segments of the line between the beacons bisected by a perpendicular line to your robot of length C and the angles from that perpendicular to the beacons are given as T1 and T2.
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You're trig is fine.
I've also been playing around with using the IR beacons to keep track of absolute position, and I've come up against a few ... obstacles. So maybe you can help me.
It's just that it's not so easy to keep track of those two angles, T1 and T2.
At the beginning of a match, you know both your position and heading (because you know where you've put your bot). Hence you can quickly calculate T1 and T2, as well as A, B, and C.
(You may recall from your old trig class that this is the angle-side-angle triangle congruency theorem.)
If you go straight ahead, then you can still keep reading off T1 and T2 because the altitude constructed from your bot to the midline of the field is still in the same place.
In fact, as long as the bot is perpendicular to that midline, you can figure out exactly where you are.
If you turn somewhere along the line, you can still find T1 and T2 *as*long*as* you know the angle from that altitude to a line parallel to your robot. This angle is your heading. You have a number of ways to keep track of heading -- you can use a gyro to sense your angular velocity, you can mount encoders on your wheels to count revolutions, and so forth.
However, your absolute position (i.e., the values of A, B, and C) will only be as accurate as your heading; in fact it will be slightly less accurate because of the (presumably small) amount of error introduced by the IR sensors.
The upshot of all this is that if you want to know you're absolute position, it's probably a little easier and little simpler to just use gyros and/or rotary encoders, which in the above setup would be necessary anyway. My conclusion: that if your autonomous objective is to shoot towards the 10 point ball, use the IR trackers. You don't even need any trig to do that; it's easy to find your distance *relative* to one beacon or the other. But at this time (which is pretty late) I haven't come up with any way to use the IR trackers to gauge *absolute* position.
I'm not saying it can't be done; I just haven't found a way. For now, I'm stuck with plain, old, dead reckoning. If any other team has a solution, I would be eager to hear it.