I've designed a quadcopter and have it printed out on a 3D printer. Now I need to control it.

I have formulated an MDP (Markov decision process) and want the helicopter to learn when it is in a stable hovering position.

I have an on-board INS (inertial navigation sensor) that outputs $(x,y,z), (\dot{x}, \dot{y}, \dot{z}), (\phi,\theta,\psi), (\dot{\phi}, \dot{\theta},\dot{\psi})$ - [position], [velocity], [attitude] and [attitude rotation speed] respectively).

Therefore, the MDP is formulated as follows:

States:

• $x$
• $y$
• $z$
• $\dot x$
• $\dot y$
• $\dot z$
• $\phi$
• $\theta$
• $\psi$
• $\dot\phi$
• $\dot\theta$
• $\dot\psi$

Actions:

• rotor1
• rotor2
• rotor3
• rotor4

Rewards:

• 1 if hovering; 0 otherwise

The trouble is, I don't know how to get a transition probability matrix. Do I get this from flight data? How best to go about this?

Is it necessary to build a quadcopter in a physics simulator (I've never done this before...)

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There is not enough information to answer this question; however, if possible you should consider your rewards as $+\infty$ for hover and $-\infty$ for not. Depending on the type of learning model you use, the basis functions need not be bounded (ie a polynomial neural network). Letting the outputs be unbounded (when possible) generally leads to better behavior. – Emily Sep 18 '12 at 17:37
I'll make it +\infinity -\infinity... – Eamorr Sep 18 '12 at 19:39