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

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CS221 Problem Set #1 1 CS 221 Problem Set #1: Search, Motion Planning, CSPs Due by 9:30am on Tuesday, January 27. 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 (100 points) NOTE: These questions require thought, but do not require long answers. Please try to be as concise as possible. 1. [12 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 configuration space coordinates . 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. [26 points] Optimization Search / Configuration Spaces For this problem, we consider the problem of moving a robot in various configuration 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, the search space is restricted to consist of only the following states in configuration space: 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. s is connected to s if s is “visible” from s ).
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ps1 - CS221 Problem Set#1 1 CS 221 Problem Set#1 Search...

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