6 01 Spring Semester 2008 Software Lab 13 Issued Tuesday May 6 1 MASSACHVSETTS INSTITVTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6 01 Introduction to EECS I Spring Semester 2008 Software Lab 13 Issued Tuesday May 6 Overview of this week s work In software lab Work through the software lab Written solutions to problems 1 21 will be due in design lab Your answers can be terse but you must show all computations Before the start of your design lab on May 8 or 9 Hand in written solutions to all software lab problems Do the survey in tutor problems 13 1 Read the entire description of the design lab so that you will be ready to work on it when you get to lab In design lab Work through the design lab No written hand in required for this lab but you must be completely checked off 6 01 Spring Semester 2008 Software Lab 13 Issued Tuesday May 6 2 Software Lab State estimation part 2 Recap of how to use this software This week we ll continue working with the non deterministic grid world simulator You should work with a partner on this Don t use the Idle Python Shell for this lab You can use the Idle editor but you cannot run the code from inside Idle In the lab12 folder you will find se py Open this file in Idle but do not try to evaluate the Python commands in the Idle Python Shell Then open a Terminal window if you re on Athena remember to do add f 6 01 and connect to the lab12 directory cd Desktop 6 01 lab12 and type python python Python 2 5 r25 51918 Sep 19 2006 08 49 13 GCC 4 0 1 Apple Computer Inc build 5341 on darwin Type help copyright credits or license for more information If you are using your own laptop download the lab12 files from the calendar page on the web If don t know how to do the operations above on your own computer then you can start Python and type import os os chdir wherever you store your lab12 files And continue as follows In this Python type from se import As the lab goes along if you edit se py then you ll need to go back to this window and type reload se And if you define a new name in se py you ll have to do from se import again as well You ll see a set of procedures at the end of the se py file which will make example worlds of different kinds We ll start by working with the world defined by make51p which stands for 5 by 1 perfect In your Python not Idle shell type w make51p As a result you should see a window that looks like this 6 01 Spring Semester 2008 Software Lab 13 Issued Tuesday May 6 3 This is a world with 5 possible states each of which is represented as a colored square on the left The possible colors of the states are white black red green and blue In this example four squares are white and one is green There is a small orange rectangle representing the square that our simulated robot is actually occupying On the right are five squares that start out being black the color in those squares represents how likely the robot thinks it is that it s in that square This is called the belief state The colors illustrating the belief state are black when the value is what the uniform distribution would assign 0 2 for 5 states shades of green when the probability is higher than the uniform and shades of red when it is below the uniform value The arguments to the makeGridSim function are The dimension of the world in x The dimension of the world in y Four lists of coordinates each specifying the location of colored squares The first list gives the locations of black squares the second red the third green the last blue Squares unspecified in any of those lists are white A pair of indices specifying the robot s initial location A model of how the sensors work A model of how the actions work So this grid world is 5 by 1 with one green square the robot initially at location 0 0 and perfect sensor and motion models You can issue commands to the robot by typing w run and responding to the text prompts Typing done returns control to Python but the window will remain Do not kill the window until you are completely done with it You can type w reset w run to start interacting with the window again after you ve typed done Belief state update The robot s belief state is a probability distribution over possible states of the world In this world there is one underlying world state for each square each of these states has a probability value assigned to it and these values sum to 1 In the simulator the current belief state is shown by the squares on the right with redder values closer to zero and greener values closer to one It is also printed out whenever you move in fact it is printed twice once after the transition update and again after the sensing update as explained below If you get tired of seeing the printout you can always type w verbose False to shut it up Just as in the HMM the belief state is updated in two steps based on the state transition model and the observation model Study the state update rules in the notes and convince yourself that at the end of this all of the entries in the belief state will sum to 1 6 01 Spring Semester 2008 Software Lab 13 Issued Tuesday May 6 4 Practice This stuff is hard to build up an intuition for We ll ask you to work through the state estimation equations for some simple examples so you can come to understand in detail how things work Let s start by practicing in a world without noise In our set up w is just such a perfect world Either make a new instance of it or do w reset which will set the belief state to 0 2 0 2 0 2 0 2 0 2 This is often called a uniform distribution The robot has no idea where it is and considers all states equally likely Calculate an answer to these questions by hand before trying it in the simulator If you get a different result than you expected convince yourself either that there is a bug in the simulator or why it s right Show your computation in detail when you hand in answers Question 1 First what is the robot s prior belief b si for each of the states Question 2 When you do w run it automatically does a stay action What is the belief state after taking the state transition but not the observation into account Start by computing P si sj stay for all …
View Full Document
Unlocking...