Unfortunately, discontinuities are common in any real system, e.g. much of robotics is in figuring out how to deal with contact forces (e.g. when picking up objects) because of the discontinuities that arise. (A term to look for is “hybrid systems”.)
I’m not sure I understand what you mean—I know almost nothing about robotics—but I think that, in most cases, there is a function whose discontinuity gives a strong indication that something went wrong. A robotic arm has to deal with impulsive forces, but its movement in space is expected to be continuous wrt time. The same happens in the bouncing ball example, or in the example I gave in the post: velocity may be discontinuous in time, but motion shouldn’t.
Unfortunately, discontinuities are common in any real system, e.g. much of robotics is in figuring out how to deal with contact forces (e.g. when picking up objects) because of the discontinuities that arise. (A term to look for is “hybrid systems”.)
I’m not sure I understand what you mean—I know almost nothing about robotics—but I think that, in most cases, there is a function whose discontinuity gives a strong indication that something went wrong. A robotic arm has to deal with impulsive forces, but its movement in space is expected to be continuous wrt time. The same happens in the bouncing ball example, or in the example I gave in the post: velocity may be discontinuous in time, but motion shouldn’t.
Thanks for the suggestion on hybrid systems!
Fair enough. What about e.g. watching TV? Scene changes on TV seem like a pretty discontinuous change in visual input.
That’s an interesting example I had not considered. As I wrote in the observations: I don’t think the discontinuity check works in all cases.