I am from Denmark and speak Danish, but set my computer to us local in order to get better search results when I search for a text.

Just tried my action cam - a Sony AS-100V - which create nice images mounted on my bike. You will get the fish eye view as those cameras gives. But! The camera takes nice stills in 13 mega pixels, but when you set it on interval it will only do HD resolution (about 2 mega pixels). There is no way of doing full resolution. The cameras GPS works fine, get both direction and altitude - but the resolution. Come on, Sony. That is just lousy (so don’t get this camera for mappilary).

Any good suggestions for ways to mount a camera without too much shaking?

I have not tried with an action camera yet, but my phone on a phone mount gave a lot of rolling shutter blur for mappilary. I also tried a full size video camera once, using heavy duty Manfrotto mounts, but even that gave a lot of shaking.

I would prefer to be able to use a phone and still get an image quality like I held it in my hand.

A helmet mount would probably do, but it does not give a consistent image, like mounted directly on the bike.