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Suppose we have a moving object (a horizontal projectile motion as one of the most basic examples). Is there any way to predict where it will hit finally? Please note that I'm looking for a machine learning method not a closed form solution.

Although we can track the motion, using Kalman filter, That is only applicable when we want to predict the new future(As far as I'm considered). But I need to predict the ultimate goal of a moving object.

To better express the problem let see the following example:

Suppose a goalkeeper robot that of course uses filtering methods to smooth the ball motion. It needs to predict if the ball is going to enter the goal or not, before it decide to catch the ball or neglect it to go out.

Input data is a time series of location and velocity [x,y,z,v].

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  • $\begingroup$ Could you describe a bit more the data that is to be worked with? How much data and what kind (temporal resolution, accuracy/precision, etc). $\endgroup$ – Damjan Dakic Jul 9 '14 at 19:02
  • $\begingroup$ Hi, Thanks for your comment. The Input data is a time series of location and velocity [x,y,z,v]. $\endgroup$ – a.toraby Jul 10 '14 at 8:34
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Unless you are talking about something higher-order (like learning the behavior of an autonomous agent and predicting how it will move in the future), what you are looking for is to create a simple physics simulator.

It will be closed-form, unless you are asking how to build a system that can "learn" the laws of physics.

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  • $\begingroup$ Hi thank you for your answer. It seems reasonable, But what about a real goalkeeper? Do you think he knows about the laws of physics? I don't think so! I think it would be possible to approach this problem with a machine learning method. $\endgroup$ – a.toraby Jul 12 '14 at 14:36
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    $\begingroup$ @a.toraby, while it certain is possible to approach the problem with a machine learning method, you need to first think if that's at all a good idea. Do you have chained full-adders in your brain to sum two numbers? I don't think so! But that doesn't mean you should use machine learning to train an ALU to do summation! The goal keeper doesn't have the ability to do precise physical calculations. If he could, then he would most likely be a much better goal keeper. $\endgroup$ – Shahbaz Jul 15 '14 at 8:04
  • $\begingroup$ Here's a good explanation of when to use physics-based models and when to use learning: spectrum.ieee.org/automaton/robotics/robotics-hardware/… $\endgroup$ – Ian Jul 16 '14 at 15:43
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Ball catching - which I believe should cover your intention - has been investigated a fair bit in robotics. There is some nice work on this from Udo Frese, which has been demonstrated on DLR's two arm humanoid Justin. They use a multi hypothesis filter to track the ball, and predict the landing [1].

Using the laws of physics will make it easier for you, and you should get a good enough accuracy. I would start out with something that is already working. Using a learning approach you could definitely enhance on the result. You could for example use the difference of your initial prediction with the final result as a signal for a reinforcement learning approach.

[1] Birbach, Oliver, Udo Frese, and B. Bauml. "Realtime perception for catching a flying ball with a mobile humanoid." Robotics and Automation (ICRA), 2011 IEEE International Conference on. IEEE, 2011.

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  • $\begingroup$ Thank you. I read the paper and it was full of useful information, though The ball catching is not the main question, and I mentioned it just as an example of application. You know, the question is somehow more general and the moving object can have different dynamics than a simple falling ball. $\endgroup$ – a.toraby Jul 15 '14 at 13:57

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