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Unformatted text preview: CS221 Midterm Solutions 1 CS 221, Fall 2009 Midterm Solutions Question Points 1 Short Answers /60 2 Motion Planning /14 3 Search Space and A* /22 4 CSP /16 5 Decision Trees /14 6 Markov Decision Processes /14 Total /140 Name of Student: Exam policy: This exam is openbook and opennotes. Any printed material that you brought with you is allowed. However, the use of mobile devices is not permitted. This includes laptops, cellular phones and pagers. Time: 3 hours. The Stanford University Honor Code: I attest that I have not given or received aid in this examination, and that I have done my share and taken an active part in seeing to it that others as well as myself uphold the spirit and letter of the Honor Code. Signed: CS221 Midterm Solutions 2 1. Short Answers [60 points] The following questions require a yes/no or true/false accompanied by one sentence of explanation, or a very short answer (also accompanied by a brief explanation). To discourage random guessing, one point will be deducted for a wrong answer on multiple choice (such as yes/no or true/false) questions! Also, no credit will be given for answers without a correct explanation. (a) [4 points] Degrees of freedom Consider a perfectly circular, planar robot living in a room with a square box. The system we are interested in modeling includes both the robot and the box. The robot can push the box in any direction by running into it. i. [2 points] How many degrees of freedom does this system have? Answer: 5: ( x,y ) for the robot and ( x,y, ) for the box Grading criteria: 2 for correct answer with brief justification 0 otherwise ii. [2 points] Viewing the system of the robot and the box as a whole, is it a holonomic system? Answer: No, since the only controllable degrees of freedom are those of the robot, not of the box. This system cant always get from any position to any adjacent position in the configuration space directly; e.g., if robot is far away from box, the box cannot change positions. Grading criteria: 2 for correct answer with brief justification 1 for correct answer with vague/incomplete justification 0 for correct answer with no justification 1 for incorrect answer (b) [4 points] Heuristic Consider a grid maze like the ones considered in class (such as the one shown in the figure below): Suppose our robot can take diagonal steps as well as steps in the N/S/E/W directions. Design a reasonable, admissible heuristic h . Specifically, suppose your robot is at ( i,j ), and the goal is at ( i goal ,j goal ). Either give an explicit formula for h ( i,j ), or describe how you would compute it efficiently. CS221 Midterm Solutions 3 Answer: max(  i i goal  ,  j j goal  ) . This is the distance to the goal allowing diagonal moves and ignoring obstacles....
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This note was uploaded on 12/15/2009 for the course CS 221 taught by Professor Koller,ng during the Fall '09 term at Stanford.
 Fall '09
 KOLLER,NG

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