I am currently MS student in artificial intelligence (AI) and working on my thesis on reinforcement learning, which robot should learn by itself how to control a quadcopter.
Long story short, I have come up with a method for such purposes, but before I jump into quadcopter and deal with its non-linear controlling problems, which could take a month to program, I need to test the method to see if it's really a solution for this kind of problem. I've defined a simplified version of my problem, such as following:
Simplified scenario:
I have a ball dropped at an altitude and the program must learn the force it needs to apply on the ball to hold it still in the air at a pre-defined altitude.
(i.e if target altitude is higher than the altitude that ball's dropped, it should up-force the ball until it reaches the altitude, otherwise, it should moderately stabilize the ball in the target altitude).
In this scenario it doesn't matter how the force will apply to the ball, i.e. there is no rope attached or etc. it just gets applied.
The last time I read something related to physics was 6-7 years ago, so the motion equation of this problem is beyond my specialty, but it seems to me that the defined scenario is a classic physic problem.
Questions:
- What are the equations to formulate the scenario (falling ball with an external force besides gravity) to be able to write its simulator?
- What about adding some noise to the problem, like air resistance factor or wind, how would the equations look then?
I would really appreciate if someone help a C.S. fellow here.
Thanks in advance.
PS: Please let the equations be simple as they could be, I am not quite good at reading complicated physic equations.
UPDATE:
From this site and details @Jodes kindly explained, I have come up with following equations:
$$ x = {1 \over 2}at^2 + v_0t + x_0 $$ where $a = g + \sum {F_i \over m_{\text{ball}}}$ and $F_i$ are the external forces applied to the ball.
If I'm right, the noises could also be combined to the equation as external forces
- Does this formulation valid for the defined scenario?
- If so, how to make it work in 2D and 3D environment(does simply vectorizing the $\vec{x}, \vec{a}, \vec{v}$ will do the job?)?