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cs221-ps1 - CS221 Problem Set#1 1 CS 221 Problem Set#1...

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CS221 Problem Set #1 1 CS 221 Problem Set #1: Search, Motion Planning, CSPs Due by 9:30am on Tuesday, October 13. Please see the course information page on the class website for late homework submission instructions. SCPD students can also fax their solutions to (650) 725-1449. We will not accept solutions by email or courier. Written part (70 points) NOTE: These questions require thought, but do not require long answers. Please try to be as concise as possible. 1. [10 points] Configuration Spaces d robot arm floor ceiling base gripper ρ α Consider the robot arm pictured above with two degrees of freedom, operating in a two dimensional workspace. The robot arm has a revolute joint and a prismatic joint. The revolute joint has a range of 0 α π , where α is the angle of the arm relative to the floor. The prismatic joint has a range of ρ min ρ ρ max , where ρ is the length of the arm from the base to the gripper. The ceiling is a distance d from the floor, with ρ min < d < ρ max . The width of the arm and gripper may be considered negligible.
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CS221 Problem Set #1 2 θ a o h =o/h θ sin cos θ =a/h Draw the configuration space of the robot arm, using α and ρ as the coordinates of the configuration space (i.e., the horizontal and verical axes in your figure should be labeled α and ρ ). Please specify the coordinates of the important points of the obstacles in configuration space (e.g. leftmost point, rightmost point, etc.). Also, while a freehand drawing is ac- ceptable, please make sure that the shape of the obstacle is clear from your drawing. 2. [14 points] Optimization Search / Configuration Spaces We consider the problem of moving a robot in various two dimensional (2D) configura- tion spaces with obstacles. We start with a simple configuration space, with only convex obstacles, and then make it more complicated by allowing non-convex obstacles as well. convex obstacle nonconvex obstacle A discrete search space for this planning problem can be defined using the visibility graph method . In this method, we place landmarks in configuration space at the initial position of the robot, the goal position of the robot, and the vertices of the polygonal obstacles. Further, the search operators only allow the robot to walk in a straight line between two of these points: a state s in the search space is connected to any other state s which can be reached from s by walking along a straight line either completely in free space or along the boundary of an obstacle (i.e.,
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