Motion and Manipulation

2009/2010Frank van der Stappen

Game and Media Technology

Context

Robotics Games (VEs)

Geometry

Path Planning

• Robotics

Path Planning

• Autonomous Virtual Humans (Creatures)

Motions

• User in a virtual environment: Collision detection• Autonomous entity: Path planning

Linkages

• Kinematic constraints

Linkages

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 Feede

r

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 € 50-60. http://msl.cs.uiuc.edu/planning/index.html. 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, 2001. Price approximately € 50.

Teacher

Frank van der Stappenhttp://people.cs.uu.nl/frankst/

• Office: Centrumgebouw Noord C226; phone: 030 2535093; email: frankst@cs.uu.nl

• Program leader for Game and Media Technology; MSc projects on manufacturing and motion planning

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-

16:00Dates are tentative, check website regularly!

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 entity (robot), stationary obstacles• Boundary representation vs. solid

representation• Polygons/polyhedra

– Convex / nonconvex• Semi-algebraic parts• Other models

Representations

Obstacles/entity• polygons/polyhedra (convex/non-convex)• semi-algebraic sets

Represented• as solids• by their boundaries p

q

convex

X

Xqp, allfor Xpq

Polygonal Models

• Boundary representation

(x1,y1)

(x2,y2)

(x3,y3)

(x4,y4)

List vertices in counterclockwise order: (x1,y1), (x2,y2), (x3,y3), (x4,y4), …

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

• f1(x,y)=2x+y+1 • f2(x,y)=-2x-y-1

H1={ (x,y) | f1(x,y)≤0 } H2={ (x,y) | f2(x,y)≤0 }

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 }

Polygonal Models

• Convex m-gon: intersection of m half-planes Hi, X = H1 ∩ H2 ∩ ... ∩ Hm.

• Polygon with n vertices: union of k convex polygons, X = X1 U X2 U … U Xk.

• 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-spacesH = { (x,y,z) | f(x,y,z) ≤ 0 } withf(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)=x2+y2-4

H H

f(x,y)=-x2+y

bounded non-convex

Semi-Algebraic Sets

Holes