1. Motion and Manipulation 2009/2010 Frank van der Stappen Game and Media Technology

2. Context RoboticsGames (VEs) Geometry

3. Path Planning Robotics

4. Path Planning Autonomous Virtual Humans (Creatures)

5. Motions User in a virtual environment: Collision detection Autonomous entity: Path planning

6. Linkages Kinematic constraints

7. Linkages

8. VR Hardware

9. Holding and Grasping

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

11. 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

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

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

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

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

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

17. 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.

18. 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

19. 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!

20. 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

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

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

23. 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 ), …

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

25. 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

26. 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 }

27. 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 }

28. 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.

29. 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.

30. 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

31. Semi-Algebraic Sets

32. Holes