How to prevent character controller from tipping when moving along terrain?

When I use simple move to move a character along terrain, any spot where the terrain bumps up, the character model will tip backwards when going over it. Is there some way to keep the character staying fully upright as it moves?

On your Rigidbody component there should be a constraints toggle.
you can freeze the rotation on x,y, z.
freeze the rotation on x and z.

that should stop you from falling over when you hit a small bump in the terrain.