6 081 Spring Semester 2007 Work for Lucky Week 13 1 MASSACHVSETTS INSTITVTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6 081 Introduction to EECS I Spring Semester 2007 Work for Lucky Week 13 Software lab for Tuesday May 8 No pre lab or tutor problems this week Robot lab for Thursday May 10 No Post lab problems Robot localization In Simulation Download the file ps13 code zip It should have the following files AvoidWanderTB py GridMap py GridStateEstimator py KBest py Map py search py Sequence py utilities py WanderEstBrain py WriteIdealReadings py XYDriver py XYEstBrain py XYGridPlanner py Edit WanderEstBrain py so that the variable dataDirectory is defined to be whatever path you unpacked the code file into Now start up SoaR in simulation using the She world and use WanderEstBrain py as the brain When it starts up you ll see two new windows The first window labeled Belief shows the outline of the obstacles in the world and a grid of colored squares Squares that are colored black represent locations that cannot be occupied by the robot For the purposes of this window for each x y location we find the value that is most likely and then draw a color that s related to the probability that the robot is at pose x y The colors go in order from more to less likely yellow red blue gray At the absolutely most likely pose the robot is drawn with a nose in green The second window labeled P O S shows each time a sonar observation o is received max Pr o x y for each square x y That is it draws a color as above that shows how likely the current observation was in each square using the most likely possible orientation Note though that the values drawn 6 081 Spring Semester 2007 Work for Lucky Week 13 2 in this window aren t normalized they don t sum to 1 we ve scaled the colors to make them sort of similar to the colors in the belief window but they aren t directly comparable The brain WanderEstBrain py just uses our standard avoid and wander program from week 2 but keeps the robot s belief state about its pose updated as it does so Run the simulation Watch the colored boxes and be sure they make sense to you Try kidnapping the robot dragging the simulated robot in the window and see how well the belief state tracks the change We recommend clicking the SoaR stop button then dragging the robot then clicking the run button It makes it less likely that the robot will get stuck in some random place along the way Question 1 Explain the relationship between the two windows and why they often start out similar and diverge over time Question 2 Why is it that when you put the robot in a corner all of the corners have high values in the P o s window Question 3 What happens when the robot is kidnapped Checkpoint Tuesday 4 00 PM Find a staff member and explain your answers to the previous set of questions The Code Here is much of the code from WanderEstBrain py with an explanation of what s going on It is similar in high level structure to the planner brains we used before We start by telling this program where to look for its data files You can do that by editing the dataDirectory line The file maxRange2 465 she20 dat contains the ideal sensor readings at every x y pose on a 20 20 20 grid assuming that the walls of the She World in the simulator are fixed It takes a long time to compute them so it s better to do it off line and then just look them up when we re running the state update routine dataDirectory yourPathNameHere ps13code maxRange2 465 Next we make an instance of the GridStateEstimator class first specifying the size of the world and then calling the initializer def setup xmin xmax ymin ymax 0 0 4 0 0 0 4 0 m Gr id St at eE st im at or Map sheBoxes xmin xmax ymin ymax 20 dataDirectory she20 dat numBestPoses 5 Now we make two windows one for displaying the belief state and one for displaying the perception probabilities To display a belief state we start by finding for each grid value of x and y the value of so that P x y is maximized What does this mean It s the orientation that would be most likely for the robot if it were in that location Now we take all those values and draw the squares with the highest values in yellow next highest in red next highest in blue and least high in gray We also show the most likely pose both the location and orientation in green 6 081 Spring Semester 2007 Work for Lucky Week 13 3 xrange yrange xmax xmin ymax ymin wxmin wxmax wymin wymax xmin 0 05 xrange xmax 0 05 xrange ymin 0 05 yrange ymax 0 05 yrange beliefWindow DrawingWindow 300 300 wxmin wxmax wymin wymax Belief percWindow DrawingWindow 300 300 wxmin wxmax wymin wymax P O S m drawBelief beliefWindow m initPose pose In all the previous labs when we issued a motor command to the robot it would continue moving with those velocities until it got the next command In this lab we re going to do it differently because doing belief state update can sometimes take a long time to compute and if we go for a long time without giving the robot a new command it could run into the wall before we have a chance to give it a stop command So this time we are going to run the robot in discrete motor mode where it moves for a tenth of a second at the commanded velocities and then stops until it gets another command def discreteMotor trans rot d i sc r e te M o to r O ut p u t trans rot 0 1 Because the belief update is so expensive we don t want to do it on every primitive step But we re going to need to make a function that can be executed on every primitive step So here we define a function makeBeliefUpdateEveryN that takes n as an argument allocates a counter that will keep track of how long it has been since the last update Then we return a function that refers to that counter it checks to see whether it has been n steps since the last update If so it resets the counter and updates the belief state based on the current sonar readings and the current pose and redraws the windows Why are we handing the current pose into the belief state update when the robot doesn t really know where it is in the world The answer is that the belief state update needs to know the action we just took since we need to use the combination of a previous belief state action and observation to update the probability …
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