6 01 Spring Semester 2008 Assignment 11 Issued Thursday April 24 1 MASSACHVSETTS INSTITVTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6 01 Introduction to EECS I Spring Semester 2008 Assignment 11 Issued Thursday April 24 Overview of this week s work No lecture or software lab Before the start of your design lab on Apr 24 or 25 Read the week 10 11 class notes Do the on line tutor problems in section 11 1 In design lab Do the nano quiz Work through the design lab By the beginning of your next software lab on Apr 29 or 30 Do the on line tutor problems in section 11 2 Submit written solutions to questions 6 7 8 9 11 and 12 All written work must conform to the homework guidelines on the web page Do athrun 6 01 update to get a directory lab11 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 SoaRfrom the 6 01 software page 6 01 Spring Semester 2008 Assignment 11 Issued Thursday April 24 2 Planning in the real world This week we ll assume that the robot can know exactly where it is in the world and plan how to get from there to a goal Generally speaking this is not a very good assumption and we ll spend the next two weeks trying to see how to get the robot to estimate its position using a map But this is a fine place to start our study of robot planning We will do one thing this week that doesn t seem strictly necessary but will be an important part of our software structure as we move forward we are going to design our software so that the robot might in fact change its idea of where it is in the world as it is executing its plan to get to the goal This is very likely to happen if it is using a map to localize itself you ve probably all had the experience of deciding you weren t where you thought you were as you were navigating through a strange city This week the only way it can happen is if in the simulator a malicious person drags the robot to another part of the world as it is driving around If we re going to use search algorithms to plan paths for the robot the biggest question as always is how to represent the real world problem in our formal model We need to define a search problem by specifying the state space successor function goal test and initial state The choices of the state space and successor function typically have to be made jointly we need to pick a discrete set of states of the world and an accompanying set of actions that can move between those states Here is one candidate abstract state space formulation states Let the states be a set of grid squares described by the robot s indices i and j into a twodimensional grid of square cells overlaid on the original x y coordinate space of the robot In this abstraction the planner won t care about the orientation of the robot it will think of the robot as moving from grid square to grid square without worrying about its heading or about its detailed position within that square actions The robot s actions will be to move North South East or West from the current grid square by one square unless such a move would take it to a square that isn t free that is that could possibly cause the robot to collide with an obstacle The successor function returns a list of states that result from all actions that would not cause a collision We will sometimes call these abstract actions macro actions goal test The goal test can be any Boolean function on the location grids This means that we can specify that the robot end up in a particular grid square or any of a set of squares somewhere in the top row for instance We cannot ask the robot to move to a particular x y coordinate at a finer granularity than our grid to stop with a particular orientation or to finish with a full battery charge initial state The initial state can be any single grid square The planning part of this is relatively straightforward The harder part of making this work is building up the framework for executing the plans once we have them We still have to be able to control the robot s wheel velocities in a way that will allow it to move reliably from square to square to support the abstraction we ve designed The HGBrain works roughly as follows It finds its current actual pose 6 01 Spring Semester 2008 Assignment 11 Issued Thursday April 24 3 It converts the current world location to grid coordinates and plans a path from there to a goal grid location It executes the first macro action in the plan by driving approximately one grid square to the north south east or west Once it finishes the macro action it plans again just in case someone has kidnapped it1 and executes the first macro action in the new plan Once it is near the goal location it quits driving though it keeps rechecking its location again just in case of kidnapping Try it out Question 1 Read the handout up to this point And be sure to read the text in the handout as you go Question 2 Try out the planner and see how it works Start Soar Pick Simulator then she py which specifies the She World named after three LAs who defined it for the simulator Pick Brain then HGBrain py from the 6 01 lab11 directory You ll see a new window with a picture of the environment drawn as a grid of squares with the occupied ones drawn in black and the free ones in white Furthermore it shows the robot s current plan The green square is centered on the robot s actual current pose The gold square is the goal and the blue squares show the rest of the steps in the plan Click start The robot will drive through the world with the plan redrawing each time a subgoal is achieved until it gets to the goal While the robot is moving drag the robot somewhere else See what happens GridWorld py In the next couple of sections we will walk through some of the code that makes this work starting with GridWorld py This file defines two classes The Map class is used to specify the locations of obstacles in the world and the GridWorld class specifies a state machine model of a robot moving on a grid corresponding to a map A Map object just stores a set of boxes that describe where the obstacles in the world are All of our obstacles are rectangles represented by …
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