6 01 Spring Semester 2008 Work for Week 12 Issued Tuesday April 29 1 MASSACHVSETTS INSTITVTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6 01 Introduction to EECS I Spring Semester 2008 Work for Week 12 Issued Tuesday April 29 Overview of this week s work In software lab Work through the software lab Before the start of your design lab on May 1 or 2 Read the class notes and review the lecture handout Do the on line tutor problems in section 12 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 Do the nano quiz Work through the design lab Before the beginning of your next software lab on May 6 or 7 Do the on line tutor problems in section 12 2 Submit written solutions to questions 2 9 13 14 and 15 All written work must conform to the homework guidelines on the web page Note Exploration is due on Thursday May 8 That is the last legal due date Do athrun 6 01 update to get a directory lab12 that contains the relevant files In order to do this entire lab it will also be important to have the latest version of SoaR Athena machines and lab laptops will update automatically to update your laptop please download a new version of SoaR from the 6 01 software page 6 01 Spring Semester 2008 Work for Week 12 Issued Tuesday April 29 2 Software Lab State estimation part 1 In the next two software labs we ll use basic probabilistic modeling to build a system that estimates the robot s pose based on noisy sonar and odometry readings We ll start by building up your intuition for these ideas in a simple simulated world then we ll move on to using the real robots next week This week we ll start by working with a 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 import se 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 6 01 Spring Semester 2008 Work for Week 12 Issued Tuesday April 29 3 As a result you should see a window that looks like this 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 The state of the system is described with two integers which are the discrete x and y coordinates of the robot s actual location in the world The robot doesn t have access to this information though all it gets to do is make an observation of the color of the room it is in When the world is created and after every step it prints out the belief distribution over the array of possible robot locations Then it prints out what observation the robot actually makes of its world if the observation function is probabilistic then the robot might observe red even if it is standing in a square that is white Finally it prompts you for an action that the robot should try to take The simulator executes that action using the motion model in the world which may be stochastic updates the hidden state of the world the robot s location and generates a new observation 6 01 Spring Semester 2008 Work for Week 12 Issued Tuesday April 29 4 Question 1 To get the idea of how this works move the robot east few times Write down the numerical values associated with the robot s belief that it is in each of the squares Give a qualitative explanation for how the belief evolves You should be able to relate this at least roughly to the HMM example in the notes This model is a slight variation on a hidden Markov models HMM that we saw during lecture …
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