[stcredzero]

Put it this way: The head on the end of the mast is a significant mass at the end of a long lever. To dynamically stabilize that, you're going to need big, hefty, expensive motors. Well, you already have big, hefty expensive motors to move the thing around in the first place, so it actually costs less money to dynamically stabilize the whole robot.

[jasonwatkinspdx]

Check out the inverted pendulum on a cart problem, or go balance a couple bats on your hand. When near vertical the inertia of the pendulum mass helps you out, it's the inertia of the cart the motors need to overcome. The better the control loop the fewer and smaller the corrections will be, tending towards zero.

[mhb]

I have a video camera with optical image stabilization. It uses teeny, tiny cheap motors to move some optics around to stabilize the image. It is not obvious that stabilizing video justifies giving up the passive stability of a tripod.