The problem you are describing is quite similar to line following from a controls perspective, there is a difference in how the line is detected.
Line following robots use a wide variety of ways to detect line. Simplest is probably photo-resistors or phototransistors, however magnetic stripes (lines) and hall effect sensors have been quite popular in the ...
I can't use any line-following method.
Actually, you are quite wrong, the way I understand the problem. It is a line-following. It is just that the line is not painted (like on the road). The line is the edge of the table.
The way I see it, your robot needs to look up, and detect the line "painted" by the edge of the table on the ceiling. Once the ...
This looks like a common angle wrapping mistake.
I am assuming you're defining your angles between -180° ($-\pi$) to +180° ($\pi$).
Let's say your current heading is -170°.
And you desired heading is 170°.
The error in angle is: 170 - (-170) = 340, so your robot has to do almost a full turn to get to the desired heading.
Since you're defining your angle in ...
For a similar problem (TT motors can't start the bot rolling on a carpet) I have been toying with the idea of setting up PID control for the angular velocity. If it stays stuck, the integral term will start upping the power. Once it suddenly breaks loose, the differential term will throttle it back. That's the idea, anyway -- someday I'll actually try it. ...
Once you have a map, you need to use a planning algorithm to get the robot from point A to point B. I'd reccomend reading up on RRT algorithm.
How to go from point A to point B is mostly independent of how you calculate the map and how you position yourself in the map.
The simplest method line following robots use is 3 sensor system:
Consider the 2 block sensors, let's assume they sense color. The middle one senses white, the remaining two senses grey. This robot follows the white line in the image.
It is difficult to provide a specific answer due to not knowing details of your design, but consider these factors for the deflection of a beam. They should give you ideas.
For a beam supported at the endpoints, with a load in the center, the deflection increases if:
The load increases.
The distance between endpoints increases.
The deflection decreases if ...