Computation of Force Closure Grasps from Finite Contact Point Set

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Computation of Force Closure Grasps from Finite
Contact Point Set

• Nattee Niparnan
• Advisor Dr. Attawith Sudsang

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General Outline

• The story so far robotic grasping
• What lies behind us literature review
• Where shall we go the problem
• Who walk along the same road related work
• Problem Detail
• Grasping Basic
• How do we reach the goal attack point
• Boring stuffs
• work plan, objective, scopes, benefit

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Robotic Grasping

• To hold an object firmly
• Prevent motion of an object

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State of the Art
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Ultimate Goal of Grasping

• Sense the object
• Calculate grasping position
• Initiate a grasp

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Grasping Components
Task Model

• Purpose of grasp
• Power grasp
• Dexterous grasp
• Tool-specific grasp

Objective Function
Algorithm
Grasp PlanningAlgorithm

• Grasp Planning
• Where to grasp

• Physical of hands
• Power
• Degree of Freedom
• Hand property

Hand Model
Grasping constraints
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Example Grasping a Hammer

• Task Moving a Hammer
• Maximize stability
• Task Using a Hammer
• Maximize head speed
• Hand Parallel Jaw Gripper
• Hand 4-fingered Hand

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Grasp Planning Algorithm
Input
Output
Object to be grasped
Algorithm
GraspingConfiguration
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What comes before us
2000
1900
1800
Reuleaux
Sumov
80s
2006
90s

• Grasping Definition
• Hanafusa Asada 77, 79
• Ohwovoriore 80
• Salisbury 82
• Asada By 85
• Nguyen 88, 89

• Grasp Planning
• Ponce et al. 95
• Lui 99 05
• Li et al 03
• Zhu Wang 03

• Grasping Quality
• Li Sastry 88
• Kirkpatric et al. 90
• Ferarri Canny 92
• Trinkle 92

• Existence of Grasps
• Lakshminarayara 78
• Mishra et al. 87
• Markenscoff et al. 89

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Hand Model
Robonaut Hand
Utah/MIT Dextrous Hand
Barrette Hand
DLR Hand II
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Task Model
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Grasping Objective Function
ObjectiveFunction
Stability
Accuracy
Tolerance
Minimizeeffect
Tolerance
Minimizeeffect

• Kirkpatric et al
• Ferrari Canny

• Ponce et al
• Lui et al

• Ponce et al.
• Nguyen

• Ding et al

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Conventional Grasping
Hand Model
ObjectiveFunction
ObjectiveFunction
Hand Model
Task Model
Hand Model
Customized algorithm
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Issues

• No generally good grasp!!!
• No general task model
• No general hand model
• Different measurement and constraints
• Object modeling
• Modeling accuracy

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Object Modeling
Curve
ContactPoint

• Modeling accuracy
• Polygon
• Linear
• Low accuracy
• Curve
• High cost of curve fitting
• Nonlinear
• High Accuracy
• Contact points
• High number of contact points
• Almost the same accuracy of curve
• Practical

Polygon
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Where shall we go

• New grasp planning framework

Hand Model
Task Model
Generalized Algorithm
Use Contact Points (Model-less)
Take no a prioriknowledge
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Where shall we go

• Instead of finding one best grasp
• Just find firm grasps
• Find lots of grasps
• Use no a priori knowledge of Task/Hand
• Let task model and hand model choose appropriate
  grasp
• Using contact points
• Model-less input
• a large number of input

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Is It Hard?

• Consider one single firm grasp problem in
  Polygonal model
• Computational intensive
• Linear Programming / Ray Shooting / Point
  Inclusion
• Multiple grasping solution?
• Almost unobtainable until recently
• With contact point model?
• Polygon ? around 10-20 faces
• Contact Point ? around 1000 contact points
• Much more computational extensive

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Challenge

• SPEED!!!

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Usage of the Result

• Given Task/Hand
• enumerate solution to find the best one
• O(n)
• Result is associated to the object
• Normal use usually involve multiple step
• Regrasp

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Problem Statement First Draft

• Given a set of contact points
• Find
• As many good grasps as possible
• In a short time

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Naïve Approach

• one single firm grasp problem

• Still is an active topic
• Lui 99 05
• Li et al 03
• Zhu Wang 03
• Borst et al 03
• Zhu et al 04

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Naïve Approach

• Finding all solutions

• Combinatorial Problem
• 1000 points
• 4 fingers
• Must check
• O(N4) Search space

1000 4
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Who walk along the same road

• Contact point input
• Wallack Canny 94
• Brost Goldberg 96
• Wang 00

• Multiple solutions
• van der Stappen 04

• Multiple solutions Contact point Input
• None...

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Problem Detail
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Grasping Basic

• Force Closure
• Formal definition of firm grasp
• Hand can influence the object such that any
  external disturbance can be nullified

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Influence of a hand

• via contact points between a hand and an object
• Described by
• Contact positions ( r )
• Contact directions ( n )

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Influence of a Contact Point

• Force (contact direction)
• Force vector ( f )
• Torque (contact position direction)
• Torque vector ( r x f )

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Wrench

• To combine force and torque into one component
• Easier to describe
• Wrench force vector concatenates with torque
  vector
• w ( f, r x f )
• Model a contact point by a wrench

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Wrench Example
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Force Closure in terms of Wrenches

• External disturbance can also be written as a
  wrench
• Contact points can exert
• Their respective wrenches
• Also positive combinations of the wrenches
• Force Closure any wrench can be expressed by a
  positive combination of contact point wrenches

GraspingHand
Contact Points
Forces Torques
Wrenches
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Problem Transformation

• Equivalence
• Wrenches achieve force closure
• Wrenches positively span R6 (or R3)
• A Convex hull of wrenches contains the origin

Force Closure?
GraspingHand
Contact Points
Forces Torques
Wrenches
Positively Spanning?
The origin inside CH?
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Positively Spanning

• any vector can be expressed by a positive
  combination of given vectors

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Point in Convex Hull

• The origin is strictly inside the convex hull of
  contact point vectors
• In the interior of the convex hull

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Contact Model (Friction)

• With friction
• One contact point is associated with many wrenches

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Check Point

• Grasping problem is
• A mathematical problem
• A computational geometry problem
• Emphasize on deriving of an efficient algorithm
  for reporting several solutions from contact
  point input

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Problem Configuration
Role
Contact Model
Object Model
Finger
Frictional
Optimizer
n fingers
Frictionless
Contact point
Classifier
7 fingers (3D)
Curved object
4 fingers (2D,3D)
3 fingers (2D)
Polygon
2 fingers
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The Problem Revisited

• Input A set of contact points
• Output A set of grasping solutions
• Combinatorial problem

Sol
Sol
ContactPoints as wrenches
2D Frictional (3 fingers)
Sol
Sol
Sol
2D Frictionless (4 fingers)
Algorithm
Sol
Sol
Sol
3D Frictional (4 fingers)
Sol
Sol
3D Frictionless (7 fingers)
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How do we reach the goal

• Exploit multiple solution nature of the problem
• Try to use pre-computation
• Sorting, searching, suitable data structure, etc.
• Problem reformulation
• Reduce dimension of wrench space

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Work Plan

• Study the works in the related fields
• Preliminary works on a heuristic algorithm
• Study a reformulation of the problem
• In-depth study of grasp planning algorithms
• Perform extensive comparison of various grasping
  condition
• Develop algorithms
• Comparison
• Publish a journal article
• Prepare and engage in a thesis defense

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Recent Works

• Fast Computation of 4-Fingered Force-Closure
  Grasps from Surface Points. Proc. of the IEEE/RSJ
  International Conf. on Intelligent Robots and
  Systems, pp 3692-3697, 2004.
• Regrasp Planning of Four-Fingered Hand for
  Parallel Grasp of a Polygonal Object. Proc. of
  the IEEE International Conf. on Robotics and
  Automation, pp 791-796, 2005.
• A Heuristic Approach for Computing Frictionless
  Force-Closure Grasps of 2D Objects from Contact
  Point Set. Proc. of the IEEE International
  Conference on Robotics, Automation and
  Mechatronics, 2006
• Planning Optimal Force-Closure Grasps for Curved
  Objects by Genetic Algorithm. Proc. of the IEEE
  International Conference on Robotics, Automation
  and Mechatronics, 2006
• 4-Fingered Force-Closure Grasps from Surface
  Points using Genetic Algorithm . Proc. of the
  IEEE International Conference on Robotics,
  Automation and Mechatronics, 2006

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Objective

• To develop efficient algorithms that report
  several force closure grasps from a set of finite
  contact points

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Scope of the Research

• Considers force closure grasping in both 2D and
  3D in friction and frictionless case
• Derived algorithms must work faster than an
  enumerative approach that uses the fastest
  computation
• Performance measurement can be either an actual
  running time (in case of a heuristic algorithm)
  or a complexity analysis (in case of a complete
  algorithm)

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Scope of the Research
2D Frictional (3 fingers)
2D Frictionless (4 fingers)
3D Frictional (4 fingers)
3D Frictionless (7 fingers)
Compare with the best known single solution
algorithm

• Evidence of superiority
• Proof of complexity analysis
• Running Time Comparison

• Evidence of superiority
• Proof of complexity analysis
• Running Time Comparison

• Evidence of superiority
• Proof of complexity analysis
• Running Time Comparison

• Evidence of superiority
• Proof of complexity analysis
• Running Time Comparison

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Expected Contribution

• Having algorithms that report several force
  closure grasps from a set of discrete contact
  points.

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Thank You

• Comments are heartily welcomed

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Coulomb Friction
a tan-1(u)
fn
ft ufN
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DLR Hand

• Sensor per each finger
• 3 joint position sensors
• 3 joint torque sensors
• 3 motor position/speed sensors
• 1 six-dimensional finger tip force torque sensor
• 3 motor temperature sensors
• 3 sensors for temperature compensation
  integrated sensors