CS564: Homework Assignment 2

Landmark Learning (Due Novemebr 5)

For this exercise you need to have a good understanding of  Section 3.4, pages (151-155) from the text book (Metaphorical Brain 2 by M. Arbib)


1.[2pts] Assume that the robot always starts to learn from the SE corner of the space and is  never allowed to enter the NW quadrant  during learning. After the robot learns to navigate towards the tree from the SE corner, if we place the robot to the NW corner what do you expect the robot to do ? Do you think it can navigate towards the tree in (almost) a straight trajectory as it has been doing from the SE corner? Justify your answer using the weight update rule in the text book  (TMB2 page 153, equation 3).

2.[4pts] Implement the landmark learning model described in the book. Specifically you need to replicate the result given in Figure3.4.8 in TMB2 (page 152). Use the guidelines below.

- The attractant tree is located at the origin (20, 20).
- The coordinates of the landmarks are: (0, 20), (40, 20), (20, 0), and (20, 40).
- The strength of landmark smell (cue or signal) reduces linearly with the distance (d).
        Use the function  smell(d) = 0.5*(1-d/r), if d<=r , 0 otherwise (take r=28 for   both the landmarks and the central tree).
        Note that the smell function serves as the Xi's for the landmarks and Z for the central tree (Xi and Z is defined in TMB2).
- To visualize the process in NSL define a 41x41 matrix where you can encode the current position of the system (e.g. a  matrix filled with all -1s, except the current position of the robot, which is marked with a +1.  You can use zeros to encode the position of the landmarks)
- If you wish you may use a plain model structure such as the one given at the bottom of the page.

For this part of the homework submit the following:

3.[4pts] What if the number of landmarks is not 4, but less (3, 2)? Will the system still be able to learn the configuration of landmarks? Justify your answer and modify your program to make this experiment and supply the following: