Finding position when only 2 angles are known to 2 known points.

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MeDaZzA

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Hi everybody, lovely to be here. I'm working on a small robotics project and I'm trying to find the position of my robot's pointer. I have mapped the room the robot is in so I know the coordinates and lengths of the walls.

So, I want to be able to aim a light at a corner of the room, then aim it at a different corner (i will record the angle between these), then finally aim at another corner (again I will know this angle). So basically (I think!) I end up with an irregular Tetrahedron with the robot at one point and the corners at the remaining ones. I know the angles adjacent to the robot, and the positions of the other points (and their angles relative to each other) and I need to find the distances of each vertex from the robot to the relevant corner so that I can find its position (or even just its position).

I hope some of this makes sense!! I've spent months trying to find some information on solving this. The closest I came was resection in 3D but the work I found needed distances not angles.

Thank you!
 
Oh and just to add I've asked so many people about this (including mathematicians, geographers and even surveyors. They all said it was possible but weren't sure how!
 
I've drawn a diagram of the problem but this is in 2D while I'm looking for an answer in 3D. I know the coordinates (in 3D) (and angles) at W, X, Y, Z, the lengths A, B, C, D and the angles F G H. I'd like to find the ? distances and also the position of the robot in the centre.
 

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1) Why is it 3D? Are we just mapping the room, not sweeping the floor?
2) How do you know there are no obstructions?
 
Hi there tkhunny, the room will already have been mapped. The idea basically is that you can position the robot anywhere in the room and just by pointing at three corners, work out exactly where the robot is in the room. Obstruction aren't a problem but I also can't rely on LIDAR or other distance measurements.. I hope this makes sense!
 
I still don't know why it's 3D.
1) Can it float above the floor?
2) Maybe we're not assuming the floor is in one plane? Bent? Sagging? Crimped? Is this a real floor or an ideal floor?
3) Perhaps the floor is not orthogonal to the line from the center of the earth? (Ignoring curvature over what seems like a small distance.)
4) Can we make the problem 2D by using the floor as a reference plane?
 
Hi again

Yes it can be moved up and down. The room will have straight lines and as I said will already have been mapped before hand so its angles and lengths of each side is known.

Maybe solving this in 2D would be a start?
 
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