I have a small four-wheeled platform weighing 1.3kg with a height of 30cm. Its center-of-mass is located at 75% of the height, making it a little top-heavy.
I empirically measured the angle at which the platform topples over when not moving to be 20 degrees. However, when it encounters a small ledge or depression of 1cm while moving at 4cm/sec, the platform topples over, even though the depression only represents a tilt of about 10 degrees.
Is this is happening because the platform's momentum is applying an extra amount of force during the fall into the depression, causing it to topple forward even though its center-of-mass hasn't moved beyond the footprint of the wheels?
I'm trying to compensate for this by using a servo, attached to the top of the platform, to swing a counterweight backwards when a sudden acceleration forwards is detected. How would I calculate the mass of the counterweight and acceleration of the swing needed to keep the platform upright?