Moving and turning an object using device tilt

I’m looking for some ideas for how to move and rotate an object based on the tilt of the device. I want it to be controlled, somewhat like a top down view of a person walking around (or a car driving). So there is a max speed, even if the device is tilted significantly. Leveling the device should bring the object to a stop. Tilting one way should start it moving and turn the object in the direction of the tilt.

My inclination is to use the accelerometer to determine the velocity (with a limiter for max speed). Anyone have any handy code snippets or examples that might suggest a reasonable solution? I’ve seen the shape tumbler example but using physics seems too uncontrolled. Maybe I’m wrong about that though.

Many thanks for your ideas!