Probablity robotics, Bayes filter reasoning problem

[cncnewbee]

Hi,
On section 2.4.2. of the "Probabilistic robotics" book, there is an example to demonstrate the way a Bayes filter works. I only can't understand one point in the example, I hope you help to get it.

This is the whole example:

The point I can't get to, is the formula (2.42). I think there is assumptions that are not mentioned there. I guess that for 2.42, the Writer assumption is that the door is functioning well and the robot actuator is also working correctly, and finally, the Xt is a sensing output, because the 0.2 is exactly the same error I see in the formula, one line above the formula 2.40, when the door is closed but is sensing open (sensory noise). From the other side, from reading the text it seems to me that P(X=x | Ut, Xt-1) is at all not about the sensing, but about the control, action and this together with assuming Xt an output of the sensor brings me to contradiction.

I would be very happy to know what is the reason behind 2.42.
From that point onward or backward, all is clear.

Thank you,

 

[mfb]

2.42 just follows from the text above the equation. If the door is closed, and the robot tries to open it, it is open with p=.8 afterwards (first line), and closed with p=.2 (second line).

because the 0.2 is exactly the same error I see in the formula, one line above the formula 2.40

That is not related to 2.42.

 

[cncnewbee]

2.42 just follows from the text above the equation. If the door is closed, and the robot tries to open it, it is open with p=.8 afterwards (first line), and closed with p=.2 (second line).
That is not related to 2.42.

Thanks, now more clear if they are not related.

Still I can't get this: where form does the Author obtained that information / assumption? If thinking of the assumption on the noise of the sensor, I imagine that they repeated a sequence of experiments, placing hypothesis and concluded that the reliability of sensing is 0.8 in case the door is closed. Could it be that they tried many times to open a closed door by robot's actuator, and then counting success and failure, to state the probability?

If so, then for such an algorithm to be implemented on a concrete robot, it must be first tested to get to these, but then, the internal state of robot is constantly changing (sensors getting worst, actuator slightly malfunctioning) and so this algorithm is more theoretical than practical?

I'm first time reading a book on the subject, not sure of my own reasoning.

 

[mfb]

It is just part of the example. Those are free parameters, and the author can choose them. It has nothing to do with the sensors.
To get those numbers in a real setup, you could watch the robot trying to open the door 100 times and observe the result manually.

 

[cncnewbee]

It is just part of the example. Those are free parameters, and the author can choose them. It has nothing to do with the sensors.
To get those numbers in a real setup, you could watch the robot trying to open the door 100 times and observe the result manually.

Thank you very much for helping me!