Eki Halkka
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In short, the challenge of stabilizers is this: There is no way to distinct gravitation from other forces acting on an object.
I'm trying to solve a problem rather similar to this... what i am trying to come up with is not a stabilizer, but rather just a 3D camera tracker using sensors. Kinda the first half of what you wish to do. There are a few affordable "9 degrees of freedom" daughter cards for Arduino microcontrollers that might be up to the task.
The challenges we have are very close to those with UAV's, unmanned aerial vechiles. There are some affordable solutions for those that look very promising too: https://store.diydrones.com/category_s/1.htm