6.01, Spring Semester, 2008—Work for Week 12, Issued Tuesday, April 29 1MASSACHVSETTS INSTITVTE OF TECHNOLOGYDepartment of Electrical Engineering and Computer Science6.01—Introduction to EECS ISpring Semester, 2008Work for Week 12, Issued Tuesday, April 29Overview of this week’s workIn 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 youget 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 tothe 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 orderto do this entire lab, it will also be important to have the latest version of SoaR. Athenamachines and lab laptops will update automatically; to update your laptop, please downloada new version of SoaR from the 6.01 software page.6.01, Spring Semester, 2008—Work for Week 12, Issued Tuesday, April 29 2Software Lab: State estimation part 1In the next two software labs, we’ll use basic probabilistic modeling to build a system that estimatesthe robot’s pose, based on noisy sonar and odometry readings. We’ll start by building up yourintuition 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 workwith a partner on this.Don’t use the Idle Python Shell for this lab. You can use the Idle editor, but you cannotrun 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 thePython commands in the Idle Python Shell.Then, open a Terminal window (if you’re on Athena, remember to do add -f 6.01), and connectto the lab12 directorycd ~/ Desktop /6 .01/ lab12and type python.> pythonPython 2.5 ( r25 :51918 , Sep 19 2006 , 0 8:49:13 )[ GCC 4.0.1 ( Apple Computer , Inc . build 5341)] on darwinType " help " , " co pyright " , " credits " or " l icense " for more i nform ation .>>>If you are using your own laptop, download the lab12 files from the calendar page on the web. Ifdon’t know how to do the operations above on your own computer, then you can start Python, andtype>>> im port os>>> os . chdir ( ’ wherever \ you \ store \ your \ lab12 \ files ’)And continue as follows.In this Python, type>>> im port se>>> from se i mport *As the lab goes along, if you edit se.py, then you’ll need to go back to this window and type>>> re load ( se )And if you define a new name in se.py, you’ll have to do>>> from se i mport *again as well.You’ll see a set of procedures at the end of the se.py file, which will make example worlds ofdifferent kinds. We’ll start by working with the world defined by make51p (which stands for 5 by1, perfect). In your Python (not Idle) shell, type>>> w = make51p ()6.01, Spring Semester, 2008—Work for Week 12, Issued Tuesday, April 29 3As 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 theleft). The possible colors of the states are white, black, red, green, and blue. In this example, foursquares are white and one is green. There is a small orange rectangle representing the square thatour 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. Thisis called the belief state. The colors illustrating the belief state are: black, when the value is whatthe uniform distribution would assign (0.2 for 5 states), shades of green when the probability ishigher 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 thelocations of black squares, the second red, the third green, the last blue. Squares unspecified inany 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 workSo, this grid world is 5-by-1, with one green square, the robot initially at location (0,0), and perfectsensor 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 willremain. 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 coordinatesof the robot’s actual location in the world. The robot doesn’t have access to this informationthough; all it gets to do is make an observation of the color of the room it is in. When the worldis created, and after every step, it prints out the “belief” distribution over the array of possiblerobot locations. Then, it prints out what observation the robot actually makes of its world (if theobservation function is probabilistic then the robot might observe “red” even if it is standing in asquare that is white). Finally, it prompts you for an action that the robot should try to take. Thesimulator 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 4Question 1: To get the idea of how this works, move the robot east few times. Write down thenumerical values associated with the robot’s belief that it is in each of the squares. Give aqualitative explanation for how the belief evolves. You should be able to relate this, at leastroughly, to the HMM example in the notes.This model is a slight variation on a hidden Markov models
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