This isn't exactly a constructive criticism, but that is essentially the most useless comment you could possibly make here. "This very general class of algorithms that I've heard about a lot would probably work here.". That is true! It's sort of like saying "Some kind of processor (Intel) would probably work well". It's completely incidental to the problem at hand, and most likely not worth saying.
It's also just a bad suggestion, because you almost certainly don't need to resort to the "high-interest credit card of technical debt" for what is a control and kinematics problem. Even if there's not a nice closed-form solution, there are 100 other approaches that are more appropriate for this sort of thing than just jumping straight to a neural network. I'm not going to go into an explanation of control theory, but "use a neural network" is not the universal answer to every problem in engineering and computer science. /rant