dear navigator app...
Hello, save-me-from-trying-to-read-small-signs-in-traffic device, I really appreciate you. You have made a difference in helping me get around in unfamiliar locations. But there are a few things I'd like you to know.
1 - When you tell me to "stay left to stay left", I don't know what you're trying to communicate. "Take that not-very-obvious left-side ramp" would have been wonderful.
1a - It might have been more visible if it hadn't been raining heavily. I wonder how far we are from navigation apps responding to poor conditions by being more verbose?
2 - The desktop interface has a way to reroute, by dragging part of the path to another place on the map, but I could not figure out how to do that on my phone.
3 - But ok, the desktop interface has a "send to my phone" link. So I reasonably expected you to be pre-loaded with the route I'd carefully constructed.
4 - Instead, I got a list of directions that I guess I'm supposed to read while driving (nope!), but no "start" button to get the audio instructions that are the whole point of using the app.
5 - Playing "outsmart the app" by choosing destinations to force a particular route is not fun.
My group moved to a new office location last week. Today was my first time driving there from home. I helped with the move on Thursday, so I'd already driven home from there once and decided that the "best" path, while best in travel time, is not best for me, because of poor visibility in places. So I am very interested in finding an alternate route home. I found one via the desktop app but, well, getting my phone to implement it wasn't so straightforward. But tomorrow is another day.

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It's unfortunate that it can't send *the actual, current* route, but *super*-unfortunate that this fact isn't more visible.
Today I tried "send to phone" again and this time I had a "start" button for the navigation. So I guess I didn't have it yesterday because of some unknown-to-me effect of my attempts to drag route pieces around on the map, or something.
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There are some design issues that I think you'd be interested in, with doing GPS navigation on a dragged route as opposed to presenting a static set of steps on it. The thing is that in GPS navigation, when I drive off route, you recalculate to get me back to where I'm going. For a "from A to B" route, you recalculate "from current location to B", simple. For a "from A via V to B" route, do you calculate "from current location via V to B"? Well, then if I set V on Bridge 1 but go over Bridge 2, my GPS is going to keep insisting I go back and hit Bridge 1, even if it's pointless now. We can suggest some heuristics to try, like don't go back to V is that's more than K% slower than skipping it, but there is a lot of potential for giving the user the impression we're being flaky and unpredictable.
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Here's something I've been wondering about: my phone already (in general, I mean) notices if I say "OK Google" -- so it obviously always has an ear open, so to speak. Now I don't want the navigator app listening to noises in the car unbidden; that would be creepy, even if it might learn things from the occasional "dammit", snarl, etc. However, could it respond to "OK Google, no left turn" or the like? Or even, more simply, "OK Google, mark" combined with a way for me to later review and annotate the places where I said "mark"? As a drive I want to provide "on the ground" feedback that improves navigation, and given that the software knew where I was when something interesting happened, it seems like we could connect those dots.
Granted, this also means needing to be able to process arbitrary input like this, some of which will be garbage or wrong. You're trying to do this at scale, so you're looking for machine learning, not human verification. Maybe you can ask other local people to confirm things, much like my phone asks me assorted questions about restaurants I've been geo-located in (questions like "is this a good place for vegetarians" and "is there a good view"). I'm not the only person who's driven around that closed road the app doesn't know about; maybe you can put that to use somehow?
Just some rambling thoughts. I know it's a hard problem.
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Driving a car, on an unfamiliar route, and on top of that managing where the directions deviate from reality, all takes so much of the user's brain that I'd be pretty reluctant to ask them to talk to their car too. The idea of marking it for later commentary is interesting, I wonder if you could do that without the realtime mark? When you're home, if there's a "My Trips Today" view that shows: on this trip you left the route we thought -- open the trip and it brings up the specific step of deviation -- and you could indicate "yeah, those directions didn't work" / "directions would work, I just had my own reasons", plus add more detail if you like.