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?