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I was recently at EPFL drone days and enjoyed a demo of a robot that could follow a black line like in the sketch (I can improve the sketch on demand):

Then I remembered my good all times at the qualitative theory of differential equations where we learnt about the conditions for a particle not to go out of a certain region under the influence of a scalar field.

So I came up with the following idea, why not do design a robot that would behave according to a scalar field in the plane and that could be used for teaching differential equations, specially the qualitative theory.

This would supersede the old idea of just "visualizing" the vector field generated by the differential equation.

Perhaps this has been done before?

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    $\begingroup$ This site is built around pairing questions with answers, and I am not sure that I understand what your question is. Can you please edit your post to more clearly state what question it is that you are wanting to have answered? $\endgroup$ Sep 3 '18 at 14:39
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    $\begingroup$ Can you explain what the robot would do exactly and how/why? $\endgroup$
    – Jasper
    Sep 4 '18 at 15:42
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I think projects like this are useful for the first undergrad class in control systems (required majors course for engineers).

I don't think it would be that useful for a standard undergrad diffyQ course, which is rather rushed and has a hard time spending lots of time on applications, estimation methods etc. (course is just the proverbial ten pounds in five pound bag...it is). If you spend time doing this lab experiment, you are likely slighting time that should be spent on the standard methods. Note, I LOVE applications. But I also believe in prioritization and efficiency.

I do think it is a very cool lab experiment though.

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