Appropriate mobile game controls

I’ve played a number of mobile games with on screen d-pads and buttons for controlling characters in action/reflex/arcade type games. Basically none of them provide the intended experience. They are a frustrating experience because your thumb usually gets lost at a critical moment, causing you to hit the wrong button and die.

The sad thing is that many of these types of games are very well suited to casual mobile gaming but are very hard for casual gamers to learn to control properly. We need completely different ideas about how a player could effectively interact with these games, rather than trying to emulate games which run on a machine where the user has enough fingers to push 10 different buttons at the same time, rapidly and accuracy hitting a variety of different buttons.

What sort of ideas do people have for appropriate controls for mobile games requiring high fidelity interaction on devices which have naturally low fidelity input?

Split the screen vertically, then split the right side horizontally (or again vertically) for two “buttons” (jump and shoot)? The left side is used as a analog sitck -> user puts his finge on the area and slides in the direction he wants to go. Im probably describing some game’s controls that i saw a long time ago, but im not sure.