I'm pondering some things I just read saying we need to emphasise the distinction between science and engineering more. I feel like the boundaries between things are usually hazy, especially between theoretical and applied things.
Roboticists are keenly interested in problems of optimal control, which, when solvable, seem crucially to involve a notion they call "differential flatness." Probably this is some sort of integrability condition (in the Frobenius-Cartan sense), but it seems nobody knows, exactly.
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I strongly suspect that translating between the engineering literature on exactly-solvable problems of optimal robotic control and the literature of Cartanian differential geometry would lead to fascinating insights attractive to readers of both. Mathematics is everywhere.
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