Motion and Manipulation 2008/09 Frank van der Stappen Game and Media Technology

Context RoboticsGames (VEs) Geometry

Motion Planning Robotics

Motion Planning Autonomous Virtual Humans (Creatures)

Motions User in VE: Collision detection Autonomous entity: motion planning

Linkages Kinematic constraints

Linkages

VR Hardware

Holding and Grasping

Conventional Manipulation Anthropomorphic robot arms/hands + advanced sensory systems = expensive not always reliable complex control

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

Manipulation Tasks Fixturing, grasping Feeding push, squeeze, topple, pull, tap, roll, vibrate, wobble, drop, … Parts Feeder

Parallel-Jaw Grippers Every 2D part can be oriented by a sequence of push or squeeze actions. Shortest sequence is efficiently computable [Goldberg 93].

Feeding with ‘Fences’ Every 2D part can be oriented by fences over conveyor belt. Shortest fence design efficiently computable [Berretty, Goldberg, Overmars, vdS 98].

Feeding by Toppling Shortest sequence of pins and their heights efficiently computable [Zhang, Goldberg, Smith, Berretty, Overmars 01].

Vibratory Bowl Feeders Shapes of filtering traps efficiently computable [Berretty, Goldberg, Overmars, vdS 01].

Course Material Steven M. LaValle, Planning Algorithms, 2006, Chapters 3-6. Hardcopy approximately € Free! Robert J. Schilling, Fundamentals of Robotics: Analysis and Control, 1990, Chapters 1 and 2 (partly). Copies available. Matthew T. Mason, Mechanics of Robotic Manipulation, Price approximately € 50.

Teacher Frank van der Stappen Office: Centrumgebouw Noord C226; phone: ; Program leader for Game and Media Technology; MSc projects on manufacturing and motion planning

Classes Monday 9:00-10:45 in BBL-513, starting September 8. Wednesday 9:00-10:45 in BBL-503, starting September 3.

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

Geometric Models Moving robot, stationary obstacles Boundary representation vs. solid representation Polygons/polyhedra –Convex / nonconvex Semi-algebraic parts Other models

Representations Obstacles/robot polygons/polyhedra (convex/non-convex) semi-algebraic sets Represented as solids by their boundaries p q convex X

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 ), …

Polygonal Models Solid representation for convex polygons: intersection of half-planes

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

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 }

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.

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.

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

Semi-Algebraic Sets

Holes