This seems way to complicated why not just have a device under your car that injects the power socket. Like for example park the front wheels on a platter that by the weight of the car injects the socket.
I believe the idea here is that this robotic snake idea should have zero impact on the user, and zero impact on installation, it should be a swap out replacement for the current charger. The only difference being that the user no longer has to plug it in manually. It may be a complex engineering problem but it's a simple, elegant design solution.
And it's not that hard to make it easy for people to line up - modern docks use a sort of fuzzy connector that doesn't need to lock in perfectly, just as long as you are within a certain range.
The roomba is the best example that I can think of for this - I can pretty much set my roomba down anywhere roughly on the dock, and it will start charging. I could definitely park my car with the same accuracy.
The EV industry is just emerging and in huge flux. Charging the cars from the floor would make much more sense, especially if we're going to charge them even without cables, wirelessly, in the future (and yes, once again breaking the several year old "standard" in the name of progress).
...plus you'd have to dig up your garage floor or at least put some sort of bolts into it to hold the thing in place. No, a roving tentacle works much better, and I can't believe I wrote that either.