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Transcript of Computation of Force Closure Grasps from Finite Contact Point Set Nattee Niparnan Advisor: Dr....
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Computation of Force Closure Computation of Force Closure Grasps from Finite Contact Grasps from Finite Contact
Point SetPoint SetNattee NiparnanNattee Niparnan
Advisor: Dr. Attawith SudsangAdvisor: Dr. Attawith Sudsang
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General OutlineGeneral Outline
The story so far: The story so far: robotic graspingrobotic grasping What lies behind us: What lies behind us: literature reviewliterature review Where shall we go: Where shall we go: the problemthe problem Who walk along the same road: Who walk along the same road: related workrelated work Problem DetailProblem Detail
Grasping BasicGrasping Basic
How do we reach the goal: How do we reach the goal: attack pointattack point Boring stuffs
work plan, objective, scopes, benefit
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Robotic GraspingRobotic Grasping
To hold an object firmlyTo hold an object firmlyPrevent motion of an objectPrevent motion of an object
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State of the ArtState of the Art
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Ultimate Goal of GraspingUltimate Goal of Grasping
Sense the objectSense the objectCalculate grasping positionCalculate grasping position Initiate a graspInitiate a grasp
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Grasping ComponentsGrasping Components
Task Model
Algorithm
Hand Model
Purpose of grasp
• Power grasp
• Dexterous grasp
• Tool-specific grasp
Physical of hands
• Power
• Degree of Freedom
• Hand property
Grasp Planning
• Where to grasp
Objective Function
Graspingconstraints
Grasp PlanningAlgorithm
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Example: Grasping a HammerExample: Grasping a Hammer
Task: Moving a HammerTask: Moving a HammerMaximize stabilityMaximize stability
Task: Using a HammerTask: Using a HammerMaximize head speedMaximize head speed
Hand: Parallel Jaw GripperHand: Parallel Jaw GripperHand: 4-fingered HandHand: 4-fingered Hand
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Grasp Planning AlgorithmGrasp Planning Algorithm
AlgorithmObject to be grasped
GraspingConfiguration
InputOutput
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What comes before usWhat comes before us
80’s 200690’s
Grasping Definition
•Hanafusa Asada ’77, ’79
•Ohwovoriore ‘80
•Salisbury ’82
•Asada By ’85
•Nguyen ’88, ’89
Existence of Grasps
•Lakshminarayara ’78
•Mishra et al. ’87
•Markenscoff et al. ’89
200019001800Reuleaux
Grasping Quality
•Li Sastry ’88
•Kirkpatric et al. ’90
•Ferarri Canny ’92
•Trinkle ’92
Grasp Planning
•Ponce et al. ’95
•Lui ’99 – ’05
•Li et al ’03
•Zhu Wang ’03
Sumov
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Hand ModelHand Model
Utah/MIT Dextrous Hand
Barrette Hand DLR Hand II
Robonaut Hand
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Task ModelTask Model
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Grasping Objective FunctionGrasping Objective Function
ToleranceMinimize
effect ToleranceMinimize
effect
Stability Accuracy
ObjectiveFunction
•Kirkpatric et al
•Ferrari Canny
•Ponce et al
•Lui et al
•Ponce et al.
•Nguyen
•Ding et al
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Conventional GraspingConventional Grasping
ObjectiveFunction Hand ModelHand Model
Hand Model
ObjectiveFunctionTask Model
Customizedalgorithm
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IssuesIssues
No generally good grasp!!!No generally good grasp!!!No general task modelNo general task modelNo general hand modelNo general hand modelDifferent measurement and constraintsDifferent measurement and constraints
Object modelingObject modelingModeling accuracyModeling accuracy
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Object ModelingObject Modeling
Modeling accuracyModeling accuracy PolygonPolygon
LinearLinear Low accuracyLow accuracy
CurveCurve High cost of curve fittingHigh cost of curve fitting NonlinearNonlinear High AccuracyHigh Accuracy
Contact pointsContact points High number of contact pointsHigh number of contact points Almost the same accuracy of curveAlmost the same accuracy of curve PracticalPractical
Polygon
CurveContact
Point
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Where shall we goWhere shall we go
New grasp planning frameworkNew grasp planning framework
Hand ModelTask Model
GeneralizedAlgorithm Take no a priori
knowledge
Use Contact Points(Model-less)
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Where shall we goWhere shall we go
Instead of finding one best graspInstead of finding one best graspJust find “firm” graspsJust find “firm” grasps
Find lots of graspsFind lots of graspsUse no a priori knowledge of Task/HandUse no a priori knowledge of Task/HandLet task model and hand model choose Let task model and hand model choose
appropriate graspappropriate graspUsing contact pointsUsing contact points
Model-less inputModel-less inputa large number of inputa large number of input
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Is It Hard?Is It Hard?
Consider one single “Consider one single “firm graspfirm grasp” problem in ” problem in Polygonal modelPolygonal model Computational intensiveComputational intensive Linear Programming / Ray Shooting / Point InclusionLinear Programming / Ray Shooting / Point Inclusion
Multiple grasping solution?Multiple grasping solution? Almost unobtainable until recentlyAlmost unobtainable until recently
With contact point model?With contact point model? Polygon Polygon around around 10-2010-20 faces faces Contact Point Contact Point around around 10001000 contact points contact points Much more computational extensiveMuch more computational extensive
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ChallengeChallenge
SPEED!!!SPEED!!!
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Usage of the ResultUsage of the Result
Given Task/HandGiven Task/Handenumerate solution to find the best oneenumerate solution to find the best oneO(n)O(n)
Result is associated to the objectResult is associated to the objectNormal use usually involve multiple stepNormal use usually involve multiple stepRegraspRegrasp
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Problem Statement: First DraftProblem Statement: First Draft
Given a set of contact pointsGiven a set of contact pointsFindFind
As many good grasps as possibleAs many good grasps as possible In a short timeIn a short time
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Naïve ApproachNaïve Approach
one single “one single “firm firm graspgrasp” problem” problem
Still is an active topicStill 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 ApproachNaïve Approach
Finding all solutionsFinding all solutions Combinatorial Combinatorial ProblemProblem 1000 points1000 points 4 fingers4 fingers
Must checkMust check
O(NO(N44)) Search spaceSearch space
1000
4
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Who walk along the same roadWho walk along the same road
Contact point inputContact point input Wallack Canny ‘Wallack Canny ‘9494 Brost Goldberg ‘Brost Goldberg ‘9696 Wang ‘Wang ‘0000
Multiple solutionsMultiple solutions van der Stappen ‘van der Stappen ‘0404
Multiple solutions & Contact point InputMultiple solutions & Contact point Input None...None...
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Problem DetailProblem Detail
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Grasping BasicGrasping Basic
Force ClosureForce ClosureFormal definition of firm graspFormal definition of firm grasp ““Hand can influence the object such that any Hand can influence the object such that any
external disturbance can be nullified”external disturbance can be nullified”
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Influence of a handInfluence of a hand
via contact points between a hand and an via contact points between a hand and an objectobject
Described by Described by Contact positions ( r )Contact positions ( r )Contact directions ( n )Contact directions ( n )
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Influence of a Contact PointInfluence of a Contact Point
Force (contact direction)Force (contact direction)Force vector Force vector ( f )( f )
Torque (contact position & direction)Torque (contact position & direction)Torque vector Torque vector ( r x f )( r x f )
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WrenchWrench
To combine force and torque into one To combine force and torque into one componentcomponent Easier to describe Easier to describe
Wrench = force vector concatenates with torque Wrench = force vector concatenates with torque vectorvector
w = ( f, r x f )w = ( f, r x f ) Model a contact point by a wrenchModel a contact point by a wrench
Space Space DimensionDimension
ForceForceDimensionDimension
TorqueTorqueDimensionDimension
Wrench Wrench DimensionDimension
2D2D 2D2D 1D1D 3D3D
3D3D 3D3D 3D3D 6D6D
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Wrench ExampleWrench Example
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Force Closure in terms of Force Closure in terms of WrenchesWrenches
External disturbance can also be written External disturbance can also be written as a wrenchas a wrench
Contact points can exertContact points can exertTheir respective wrenchesTheir respective wrenches
Also Also positive combinationspositive combinations of the wrenches of the wrenches
Force Closure = Force Closure = any wrenchany wrench can be can be expressed by a positive combination of expressed by a positive combination of contact point wrenchescontact point wrenches
GraspingHand
Contact Points
Forces &Torques
Wrenches
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Problem TransformationProblem Transformation
EquivalenceEquivalenceWrenches achieve Wrenches achieve force closureforce closureWrenches Wrenches positively span positively span RR66 (or R (or R33))A A Convex hullConvex hull of wrenches of wrenches contains the origincontains the origin
GraspingHand
Contact Points
Forces &Torques
Wrenches
ForceClosure?
Positively Spanning
?
The origin inside CH?
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Positively SpanningPositively Spanning
any vector can be expressed by any vector can be expressed by a positive a positive combinationcombination of given vectors of given vectors
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Point in Convex HullPoint in Convex Hull
The origin is The origin is strictly insidestrictly inside the convex hull the convex hull of contact point vectorsof contact point vectors In the In the interiorinterior of the convex hull of the convex hull
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Contact Model (Friction)Contact Model (Friction)
With frictionWith frictionOne contact point is associated with One contact point is associated with many many
wrencheswrenches
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Check PointCheck Point
Grasping problem isGrasping problem isA mathematical problemA mathematical problemA computational geometry problemA computational geometry problem
Emphasize on deriving of an efficient Emphasize on deriving of an efficient algorithm for reporting algorithm for reporting several solutionsseveral solutions from from contact point inputcontact point input
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Problem ConfigurationProblem Configuration
Object Model
Role Contact Model
Finger
Contact point
Curved object
Polygon
Optimizer
ClassifierFrictionless
Frictional
3 fingers (2D)
4 fingers (2D,3D)
2 fingers
n fingers
7 fingers (3D)
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The Problem: RevisitedThe Problem: Revisited
Input: A set of contact pointsInput: A set of contact pointsOutput: A set of grasping solutionsOutput: A set of grasping solutionsCombinatorial problemCombinatorial problem
Algorithm
ContactPoints
aswrenches Sol
SolSol
SolSol
Sol
Sol
Sol Sol
Sol
2D Frictional(3 fingers)
2D Frictionless(4 fingers)
3D Frictional(4 fingers)
3D Frictionless(7 fingers)
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How do we reach the goalHow do we reach the goal
Exploit multiple solution nature of the Exploit multiple solution nature of the problemproblemTry to use pre-computationTry to use pre-computation
Sorting, searching, suitable data structure, etc.Sorting, searching, suitable data structure, etc.
Problem reformulationProblem reformulationReduce dimension of wrench spaceReduce dimension of wrench space
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Work PlanWork Plan Study the works in the related fieldsStudy the works in the related fields Preliminary works on a heuristic algorithm Preliminary works on a heuristic algorithm Study a reformulation of the problemStudy a reformulation of the problem In-depth study of grasp planning algorithmsIn-depth study of grasp planning algorithms Perform extensive comparison of various Perform extensive comparison of various
grasping conditiongrasping condition Develop algorithmsDevelop algorithms ComparisonComparison Publish a journal articlePublish a journal article Prepare and engage in a thesis defensePrepare and engage in a thesis defense
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Recent WorksRecent Works Fast Computation of 4-Fingered Force-Closure Grasps from Surface PointsFast Computation of 4-Fingered Force-Closure Grasps from Surface Points. .
Proc. of the IEEE/RSJ International Conf. on Intelligent Robots and Proc. of the IEEE/RSJ International Conf. on Intelligent Robots and Systems, pp 3692-3697, 2004. Systems, pp 3692-3697, 2004.
Regrasp Planning of Four-Fingered Hand for Parallel Grasp of a Polygonal Regrasp Planning of Four-Fingered Hand for Parallel Grasp of a Polygonal Object.Object. Proc. of the IEEE International Conf. on Robotics and Automation, Proc. of the IEEE International Conf. on Robotics and Automation, pp 791-796, 2005. pp 791-796, 2005.
A Heuristic Approach for Computing Frictionless Force-Closure Grasps of A Heuristic Approach for Computing Frictionless Force-Closure Grasps of 2D Objects2D Objects from Contact Point Set. Proc. of the IEEE International from Contact Point Set. Proc. of the IEEE International Conference on Robotics, Automation and Mechatronics, 2006 Conference on Robotics, Automation and Mechatronics, 2006
Planning Optimal Force-Closure Grasps for Curved Objects by Genetic Planning Optimal Force-Closure Grasps for Curved Objects by Genetic Algorithm.Algorithm. Proc. of the IEEE International Conference on Robotics, Proc. of the IEEE International Conference on Robotics, Automation and Mechatronics, 2006 Automation and Mechatronics, 2006
4-Fingered Force-Closure Grasps from Surface Points using Genetic 4-Fingered Force-Closure Grasps from Surface Points using Genetic Algorithm .Algorithm . Proc. of the IEEE International Conference on Robotics, Proc. of the IEEE International Conference on Robotics, Automation and Mechatronics, 2006 Automation and Mechatronics, 2006
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ObjectiveObjective
To develop efficient algorithms that report To develop efficient algorithms that report several force closure grasps from a set of several force closure grasps from a set of finite contact pointsfinite contact points
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Scope of the ResearchScope of the Research
Considers force closure grasping in both Considers force closure grasping in both 2D and 3D in friction and frictionless case2D and 3D in friction and frictionless case
Derived algorithms must work faster than Derived algorithms must work faster than an enumerative approach that uses the an enumerative approach that uses the fastest computationfastest computation
Performance measurement can be either Performance measurement can be either an actual running time (in case of a an actual running time (in case of a heuristic algorithm) or a complexity heuristic algorithm) or a complexity analysis (in case of a complete algorithm)analysis (in case of a complete algorithm)
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Scope of the ResearchScope 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 ContributionExpected Contribution
Having algorithms that report several force Having algorithms that report several force closure grasps from a set of discrete closure grasps from a set of discrete contact points.contact points.
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Thank YouThank You
Comments are heartily welcomedComments are heartily welcomed
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Coulomb FrictionCoulomb Friction
fn
ft = ufN
a = tan-1(u)
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DLR HandDLR Hand
Sensor per each fingerSensor per each finger 3 joint position sensors:3 joint position sensors: 3 joint torque sensors:3 joint torque sensors: 3 motor position/speed 3 motor position/speed
sensors: sensors: 1 six-dimensional 1 six-dimensional fingerfinger tiptip
force torque force torque sensorsensor:: 3 motor temperature 3 motor temperature
sensors: sensors: 3 sensors for temperature 3 sensors for temperature
compensation: integrated compensation: integrated sensorssensors