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Motion and Manipulation 2009/2010 Frank van der Stappen Game and Media Technology
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Context RoboticsGames (VEs) Geometry
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Path Planning Robotics
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Path Planning Autonomous Virtual Humans (Creatures)
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Motions User in a virtual environment: Collision detection Autonomous entity: Path planning
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Linkages Kinematic constraints
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Linkages
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VR Hardware
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Holding and Grasping
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Conventional Manipulation Anthropomorphic robot arms/hands + advanced sensory systems = expensive not always reliable complex control
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RISC ‘Simplicity in the factory’ [Whitney 86] instead of ‘ungodly complex robot hands’ [Tanzer & Simon 90] Reduced Intricacy in Sensing and Control [Canny & Goldberg 94] = simple ‘planable’ physical actions, by simple, reliable hardware components simple or even no sensors
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Manipulation Tasks Fixturing, grasping Feeding push, squeeze, topple, pull, tap, roll, vibrate, wobble, drop, … Parts Feeder
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Parallel-Jaw Grippers Every 2D part can be oriented by a sequence of push or squeeze actions. Shortest sequence is efficiently computable [Goldberg 93].
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Feeding with ‘Fences’ Every 2D part can be oriented by fences over conveyor belt. Shortest fence design efficiently computable [Berretty, Goldberg, Overmars, vdS 98].
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Feeding by Toppling Shortest sequence of pins and their heights efficiently computable [Zhang, Goldberg, Smith, Berretty, Overmars 01].
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Vibratory Bowl Feeders Shapes of filtering traps efficiently computable [Berretty, Goldberg, Overmars, vdS 01].
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Course Material Steven M. LaValle, Planning Algorithms, 2006, Chapters 3-6. Hardcopy approximately € 50-60. http://msl.cs.uiuc.edu/planning/index.html. Free! http://msl.cs.uiuc.edu/planning/index.html Robert J. Schilling, Fundamentals of Robotics: Analysis and Control, 1990, Chapters 1 and 2 (partly). Copies available. Matthew T. Mason, Mechanics of Robotic Manipulation, 2001. Price approximately € 50.
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Teacher Frank van der Stappen http://people.cs.uu.nl/frankst/ Office: Centrumgebouw Noord C226; phone: 030 2535093; email: frankst@cs.uu.nlfrankst@cs.uu.nl Program leader for Game and Media Technology; MSc projects on manufacturing and motion planning
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Classes Wednesday 15:15-17:00 in BBL-503. Friday 9:00-10:45 in BBL-503. No class on Wednesday September 16! Written test: –first chance: Friday November 6, 10:00-12:00 –second chance: Wednesday December 23, 14:00-16:00 Dates are tentative, check website regularly!
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Exam Form Written exam about the theory of motion and manipulation; weight 60%. Summary report (> 10 pages of text) on two assigned papers followed by a 15-minute discussion; weight 40%. Additional requirments: –Need to score at least 5.0 for written exam to pass course. –Need to score at least 4.0 to be admitted to second chance
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Geometric Models Moving entity (robot), stationary obstacles Boundary representation vs. solid representation Polygons/polyhedra –Convex / nonconvex Semi-algebraic parts Other models
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Representations Obstacles/entity polygons/polyhedra (convex/non-convex) semi-algebraic sets Represented as solids by their boundaries p q convex X
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Polygonal Models Boundary representation (x 1,y 1 ) (x 2,y 2 ) (x 3,y 3 ) (x 4,y 4 ) List vertices in counterclockwise order: (x 1,y 1 ), (x 2,y 2 ), (x 3,y 3 ), (x 4,y 4 ), …
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Polygonal Models Solid representation for convex polygons: intersection of half-planes
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Polygonal Models Solid representation for convex polygons: intersection of half-planes Bounded by a line y=ax+b or ax+by+c=0 Zero level set of f(x,y)=ax+by+c
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Half-planes f 1 (x,y)=2x+y+1f 2 (x,y)=-2x-y-1 H 1 ={ (x,y) | f 1 (x,y)≤0 }H 2 ={ (x,y) | f 2 (x,y)≤0 }
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Convex Object: Exercise Describe the convex object O with vertices (0,2), (-4,2), (-4,-2), and (4,-2) as the intersection of four half-planes. Answer: O = { (x,y) | -x - 4 ≤ 0 } ∩ { (x,y) | -y - 2 ≤ 0 } ∩ { (x,y) | y - 2 ≤ 0 } ∩ { (x,y) | x + y - 2 ≤ 0 }
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Polygonal Models Convex m-gon: intersection of m half-planes H i, X = H 1 ∩ H 2 ∩... ∩ H m. Polygon with n vertices: union of k convex polygons, X = X 1 U X 2 U … U X k. Complex polygonal sets: unions of intersections too.
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Polyhedral Models Boundary representation: vertices, edges, polygonal faces, e.g. doubly-connected edge list (DCEL). Solid: union of intersection of half-spaces H = { (x,y,z) | f(x,y,z) ≤ 0 } with f(x,y,z) = ax+by+cz+d.
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Semi-Algebraic Sets Union of intersection of sets H = { (x,y) | f(x,y) ≤ 0 }, where f(x,y) is now a polynomial in x and y with real coefficients (in 2D). f(x,y)=x 2 +y 2 -4 H H f(x,y)=-x 2 +y bounded non-convex
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Semi-Algebraic Sets
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Holes
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