[1] https://arxiv.org/abs/2012.02113 [2] http://www.tac.mta.ca/tac/volumes/35/45/35-45.pdf
I can’t stress enough that Koditschek group are serious people who are using this stuff because it addresses problems they’ve been grappling with.
"We aim to construct a physically-grounded compositional framework for hybrid system synthesis, particularly targeted at applications in robotics. Compositionality lies at the heart of language in general [WHM12] and its formalization underlies much of computer science in particular [Lee90]. However the behavioral modularization of physical synthesis for digital computing that arguably ushered in the information technology revolution [MC80] has proven much harder to achieve in analog computing technology [Mea89]. There are fundamental reasons for this challenge to become more severe in machines intended to perform mechanical work on their environments [Whi96]."
Since you know enough about this field to cite it, does it appear to you that this stuff could be written in a more comprehensible way, without losing expressive power? Or is this level of ornament necessary to say whatever it's saying?
Unless I can prove it is used, then it doesn't meet my bar. Maybe it's too new, but that means it still has to prove itself. Good luck to them!
You can also look at Aaron Ames’s PhD thesis and how that work in hybrid dynamical systems, driven by category theory, has shaped his current output (which is 20-50 papers/year as a full professor at CalTech).
I once watched John talk down to some sort of research electrical engineer at a conference because his diagrammatic calculus didn’t line up with John’s approach, when anyone with a lick of sense would want to understand why their approach didn’t suffice and how these changes addressed its shortcomings - this person was a subject matter expert and Baez condescended to him about his own field! I think his attitude has, unfortunately, rubbed off on a lot of the people in his orbit.