1) 3D multifingered caging involves using multiple robot fingers to constrain an object's movement in 3D space without grasping it. 2) The document discusses different types of caging patterns (envelope, ring, waist) and develops sufficient conditions for caging common shapes like spheres, disks, rings, and dumbbells. 3) It also introduces the concept of partial caging, which aims to constrain an object as much as possible even if a robot is unable to achieve complete caging due to limitations like low degrees of freedom. Partial caging could be useful for prosthetic hands.

1. 3D Multifingered Caging
and Partial Caging
SATOSHI MAKITA
(ASSISTANT PROFESSOR,
SASEBO NATIONAL COLLEGE OF TECHNOLOGY)

2. Outline
 3D multifingered caging
 Motivation
 Classification
 Sufficient conditions
 Planning and Experiments
 Partial caging
 Motivation
 Partial caging by a prosthetic hand
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3. 3D Multifingered Caging 3

4. 3D Multifingered Caging 4

5. Motivation
- beginning of 3D caging -
 Variation of 2D caging by multiple
robots
 Caging an object by two fingertips
[Rimon 1996]
 Caging by three fingertips
[Erickson 2003][Rodriguez 2012]
 Caging a concave object
[Pipattanasomporn 2006]
 Caging manipulation by mobile robots
[Wang 2002]
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6. Motivation
- beginning of 3D caging -
 3D caging by fingertips
 More than three dimensional caging
by multiple pointed fingers
[Pipattanasomporn 2007]
-> Expansion to “real” linked robot
hands (fingers)
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7. Motivation
- beginning of 3D caging -
 Caging by a multifingered robot
hand
 Applicable to real robot hands
S. Makita and Y. Maeda: ”3D
Multifingered Caging: Basic Formulation
and Planning,” IEEE/RSJ IROS, 2697-2702,
2008.
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8. Motivation
- beginning of 3D caging -
 Related works
 Caging grasps by a humanoid robot
[Diankov 2008]
 Grasping objects with holes
[Pokorny 2013]
 Caging-based grasping
[Maeda 2012]
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9. Motivation
- beginning of 3D caging-
 Advantages
 Can be performed by position-
controlled robots
 Gap between the object and the
hand can behave some margins for
constraint
 Only geometrical information of
objects is necessary
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10. Motivation
- beginning of 3D caging-
 Demerits
 The position and orientation of objects
is not fixed
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11. Classification of caging
patterns
 Envelope-type Caging -> Sphere
 A robot hand surrounds the object
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12. Classification of caging
patterns
 Ring-type Caging -> Ring
 The fingers of the hand are inserted to
the hollow of the object
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13. Classification of caging
patterns
 Waist-type Caging -> Dumbbell
 The fingers are wound around the
constricted part of the object
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14. How to cage an object by
a hand?
 Problems
 Formulation -> Sufficient conditions
 Linked robot -> collisions
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Impossible
to escape
[In the Real World]
Free C-Space
C-Obstacle
Impossible
to escape
[In the Object C-Space]
Difficult!

15. Sufficient conditions for
caging
 Target objects
 Sphere
 Disk
 Ring
 Dumbbell
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16. Sufficient conditions
- Caging a sphere -
 Sphere cannot escape from every
face among robot fingers
 Trapezoid face between finger bodies
 Polygonal face composed of fingertips
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17. Sufficient conditions
- Caging a sphere -
 Trapezoid face between bodies of robot
finger
(dj: distance between j-th joints)
 Polygonal face composed of fingertips
(rc: distance between fingertip and center axis)
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18. Sufficient conditions
- Caging a disk -
 Disk (circular plate)
 Radius: rdisk
 Thickness: tdisk
 Robot Hand
 N fingers
Disk cannot escape between robot fingers
 Between joints or joint and fingertip
 Between fingertips
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19. Sufficient conditions
- Caging a disk -
 Between each joint and/or each
fingertip
(dijkl: Distance between jth joint of ith
finger and lth body of kth finger)
 Between fingertips
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20. Sufficient conditions
- Caging a ring -
 A ring-like object cannot escape
between fingertips
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p11
p1j
p1,L+1
p2j
p2,L+1
Sobj
p21
Finger Finger
<Sliced view>
Ring

21. Sufficient conditions
- Caging a dumbbell -
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The constricted part cannot
escape from the gap
between fingertips
The disk-shaped part cannot
escape from the ring-formed
hand
The constricted part goes
through the hollow region of
the hand

22. 22
Caging a Complex-shaped
Object
 Approximate by an inscribed simple-shaped
object
 Approximate by a combination of simple-
shaped objects
Stamp tool
-> a sphere and a disk
Using simple shapes as shape primitives

23. 3D multifingered caging
- Goal configurations -
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24. 3D multifingered caging
- Goal configurations -
 Caging a stamp (sphere and disk)
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25. 3D multifingered caging
- Motion planning -
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26. 3D multifingered caging
by an arm/hand system
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27. 3D multifingered caging
by an arm/hand system
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28. 3D multifingered caging
by an arm/hand system
 Absorbing uncertainty
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29. Caging by a prosthetic
hand (Simulation)
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30. Caging by a prosthetic
hand (in actual)
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31. Partial caging
ONGOING PROJECTS

32. Motivation
- Why “partial” caging? -
 Difficulty to achieve “complete”
caging
 Low degrees of freedom
 Relative size between the object and
the hand
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Many robots… Many fingers…

33. Motivation
- Why “partial” caging? -
 To constraint the object in the
incomplete cage as far as possible
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34. Motivation
- Why “partial” caging? -
 Related works
 Tests of partial cage quality
[Makapunyo 2013]
 Gravity caging [Jiang 2012]
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By path searching
Gravitational force

35. Partial caging by a
prosthetic hand
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36. Partial caging by a
prosthetic hand
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37. Conclusion
 3D multifingered caging
 Derivation of sufficient conditions
 Motion planning
 Introduction of partial caging
 (Complete or partial) caging for
prosthetic hands
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38. References
 http://www.sasebo.ac.jp/~makita/
 S. Makita et al.: “3D Two-Fingered Caging for Two Types of
Objects: Sufficient Conditions and Planning,” Int. J. of
Mechatronics and Automation, (to appear)
 S. Makita et al.: ”Geometrical constraint in Graping,”
IROS Workshop: Beyond Robot Grasping - Modern
Approaches for Learning Dynamic Manipulation, 2012.
 S. Makita et al.: “Motion Planning for 3D multifingered
Caging with Object Recognition using AR Picture
Markers,'' IEEE ICMA, 2158-2164, 2012.
 S. Makita and Y. Maeda: ”3D Multifingered Caging: Basic
Formulation and Planning,” IEEE/RSJ IROS, 2697-2702, 2008.
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