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Regrasp planning of a polygon in Regrasp planning of a polygon in the plane for a 4-fingered handthe plane for a 4-fingered hand

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OutlineOutline

IntroductionIntroductionCondition for graspingCondition for graspingSwitching graphSwitching graph Implementation and resultsImplementation and resultsConclusionConclusion

IntroductionIntroduction

RegraspRegrasp Force-closure Force-closure Equilibrium Equilibrium

Concurrent graspConcurrent grasp Parallel graspParallel grasp 2-fingered grasp2-fingered grasp

Switching graphSwitching graph

IntroductionIntroduction

Switching diagramSwitching diagram

concurrentgrasps

2-fingeredgrasps

parallelgrasps

Condition for graspingCondition for grasping

Sufficient conditionSufficient condition

a1

a3

a2

three-finger equilibrium grasp

a2

C1

C2

C3

a1

a3

“concurrent grasp”

Switching graphSwitching graph

Point in the plane can represent a set of Point in the plane can represent a set of grasps.grasps.

Independent contact regionIndependent contact region

Ea

EbEc

Ea

Eb

x0

Ec

Ea

EbEc

Fa,b,c

a

b

c

d

Switching graphSwitching graph

a,b,c a,b,d

Fa,b,c Fa,b,d

Switching graphSwitching graph

..

Fa,b,c

Fa,b,d

Fb,d,e

q1

q2Fa,b,d

q1

q2

Finger aligningFinger aligning

Switching graphSwitching graph

i

j

B A C2

2

i

2 2j

22

O(n3), n is the number of polygon’s edges.

Condition for graspingCondition for grasping

two-finger equilibrium grasp

Switching graphSwitching graph

Focus cellFocus cell

Ea

EbEb

Ea

Fa,bx0

Eb

Ea

2C

2C

( - 2 , + 2 )

Switching graphSwitching graph

Finger switchingFinger switching

Fa,c Fb,c,dq..

q

Fa,c

Ea

Ec

.q

Fb,c,d

Ec

EbEd

1

2

342

C

Switching graphSwitching graph

Finger aligningFinger aligning

Fa,b

q1 q2

Fa,b

Fb,c,d

q2

.q1

.

Eb

Ea

2C

Switching graphSwitching graph

i

2 2

j

O(n2), n is the number of polygon’s edges.

Condition for graspingCondition for grasping three-finger equilibrium grasp with parallel three-finger equilibrium grasp with parallel

contact forcescontact forces

middle

Condition for graspingCondition for grasping

PC

Condition for graspingCondition for grasping

x0

x1 x2

.

..

PC

Switching graphSwitching graph

Ea

EbEc

Eb

Ec

Set of parallel graspsSet of parallel grasps

PCPC

Switching graphSwitching graph

Finger switchingFinger switching

Ea Ed

Ec

Eb

Ec

Eb

Switching graphSwitching graph

Finger switchingFinger switching

Ea

Ec

Eb

Ec

Ed

EbEd

Switching graphSwitching graph

Finger switchingFinger switching

Ea

Eb Ec

Ed

Eb

Ec

EdEa

Switching graphSwitching graph

Finger switchingFinger switching

Ea

Eb

Fa,b

Eb

Ea

2C

Switching graphSwitching graph

Finger switchingFinger switching

Ed

Eb

Fb,d

Eb

Ea

Ec

PCPC

Fa,b

Switching graphSwitching graph

Finger switchingFinger switching

Ea

Eb Ec

Ea

Eb

Eb Ec

Switching graphSwitching graph

Finger aligningFinger aligning

Switching graphSwitching graph

i2 β

α

α+θβ+θ

β+ - θβ+ - 2θ

α + + θα + + 2θ

j

O(n3), n is the number of polygon’s edges.

Switching graphSwitching graph

a,b,d

a,b,c

b,d,f

b,e g,h

g,i,j

i,j,k

j,k,lk,l

ImplementationImplementation

Polygon objectsPolygon objects 1.8 GHz CPU1.8 GHz CPU C++ & LEDAC++ & LEDA

ResultsResults

Concurrent graspConcurrent grasp

#edges #nodes #edges #connected time(sec)

15 43 96 1 0.7

20 77 156 6 1.36

25 185 691 2 3.73

30 407 2099 1 10.75

35 550 3033 2 15.95

40 736 4580 1 28.53

ResultsResults

Parallel graspParallel grasp

#edges #nodes #edges #connected time(sec)

15 3 1 2 0

20 12 7 5 0

25 37 57 5 0.02

30 27 39 3 0.02

35 64 109 5 0.03

40 106 215 8 0.09

ResultsResults

Concurrent & 2-fingered graspConcurrent & 2-fingered grasp

#edges #nodes #edges #connected time(sec)

15 53 243 1 0.95

20 89 351 3 1.75

25 206 1415 2 5.17

30 429 3162 1 13.56

35 576 4315 2 18.53

40 773 7056 1 29.28

ResultsResults

Parallel & 2-fingered graspParallel & 2-fingered grasp

#edges #nodes #edges #connected time(sec)

15 13 55 1 0.13

20 24 101 1 0.2

25 58 436 1 0.69

30 49 390 1 0.61

35 90 714 1 1.17

40 143 1439 1 2.16

ResultsResults

All graspsAll grasps

#edges #nodes #edges #connected time(sec)

15 56 253 1 0.97

20 101 386 3 1.94

25 243 1641 2 5.48

30 456 3321 1 13.2

35 640 4704 2 20.01

40 879 7829 1 30.33

ResultsResults

Connected componentsConnected components

#edges Concurrent Parallel C&2 P&2 All

15 1 2 1 1 1

20 6 5 3 1 3

25 2 5 2 1 2

30 1 3 1 1 1

35 2 5 2 1 2

40 1 8 1 1 1

ConclusionConclusion

Regrasp planningRegrasp planningConcurrent graspConcurrent grasp2-fingered grasp2-fingered graspParallel graspParallel grasp

Dexterous manipulationDexterous manipulationOther conditions for parallel graspOther conditions for parallel graspRandom approachRandom approach

Future worksFuture works

Optimal graspOptimal grasp Independent contact regionIndependent contact regionMinimum force required for resist external Minimum force required for resist external

forceforceClosest distance between centroid of contact Closest distance between centroid of contact

points and center of masspoints and center of massOther objectsOther objects

Polyhedral objectPolyhedral objectCurved objectCurved object

Thank youThank you