19 – Move Function Solution – Artificial Intelligence for Robotics

Here is the solution. We start with the empty list. We go through all the elements in p. This is the tricky line. We will construct Q element-by-element by accessing the corresponding p, and p is shifted by U and if this shift exceeds the range of p on the left, we apply the modulo operator with the number of states as an argument. In this case, it’ll be 5. Now, the reason why there is a minus sign is tricky. To shift the distribution to the right, U = 1, we need to find in p the element 1 place to the left. Rather than shifting p to the right directly, what I’ve done is I’ve constructed q by searching for where the robot might have come from. That’s of course, in hindsight, from the left. Therefore, there is a minus sign over here. So think about this, as it’s a little bit nontrivial, but it’s going to be important as we go forward and define probabilistic convolution and generalize this to the noisy case.

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