This slides present a research on 3D multifingered caging, a geometrical method to capture an object by a robotic multifingered hand.

1. 3D Multifingered Caging:
Basic Formulation and Planning
*Satoshi MAKITA and Yusuke MAEDA
(Yokohama National University, JAPAN)
1. What is “caging”? “3D multifingered caging”?
2. Definition of caging
3. Sufficient conditions for caging
4. Planning method (based on RRT)
5. Results
6. Conclusion
The 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems
22/Sep./2008 – 26/Sep./2008 @ Nice, FRANCE

2. 2
What is “Caging”?
• Geometrical method of object constraining
– An object is surrounded by robots, and inescapable from
a “cage”
– Constraining by Position-controlled robots
– Easy transportation with keeping cage formation
object
position-controlled
mobile robot

3. 3
Multifingered Caging
• Previous Work
– [Rimon 1996]
– [Pipattanasomporn 2007]
Only 2D (or 2D-based 3D) caging with circular
fingertips
object
position-controlled
circular fingertip

4. 4
3D Multifingered Caging
An object cannot escape from the
“cage” of robot hand

5. 5
Grasping vs. Caging
Grasping Caging
Control Force Control Position Control
Information Many Only shape
D.O.F. of Robot
Hand
Generally High Low d.o.f. is
enough
Position and
Orientation of
Object
Fixed Movable to some
extent...
Considering constraining margin that allows errors
of modeling and/or position control

6. 6
Objective
• 3D multifingered caging
– Formulate definition of caging
– Derive sufficient conditions for caging
– Plan robot hand motion for caging using RRT

7. 7
Definition of Caging
Caging = Constraining an object in a
closed region by robots
Impossible
to escape
[In the Real World] [In the Object C-Space]
Free C-Space
C-Obstacle
Object Configuration: qobj
Impossible
to escape

8. 8
Difficulty to Formulate Caging
Problem
• Many variations of 3D multifingered caging
• Complexity of closed caging region
– (6-dimensional configuration space)
Derive sufficient conditions for caging
(Instead of the necessary and sufficient condition)
[Typical cases (simple shape)]
• Sphere
• Disk
• Ring-like object

9. 9
Assumptions
• Symmetrical robot hand
– Same number of joints for each
finger
– Revolute joint
– Cylinder finger
– Regular polygonal palm
– Each finger attached to each
vertex
– Same vector of joint variables for
each finger

10. 10
Sufficient Conditions: Caging a
Sphere
• Sphere
– Radius: rsphere
• Robot hand
– N fingers
– Length of the jth body of finger: lj
Sphere cannot escape from every face among robot
fingers
– Trapezoid face between finger bodies
– Polygonal face composed of fingertips

11. 11
Sufficient Conditions: Caging a
Sphere
• Trapezoid face between bodies of robot finger
(dj: distance between jth joints)
• Polygonal face composed of fingertips
(rc: distance between fingertip and center axis)

12. 12
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

13. 13
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

14. 14
Sufficient Conditions: Caging a
Ring-like Object
• Ring-like object (c.f. Torus)
– Thickness: dring
• Robot hand
– 2 fingers
A ring-like object cannot escape between fingertips

15. 15
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

16. 16
Planning Method
• Based on “Rapidly-exploring Random Trees (RRT)”
[LaValle 1998]
– RRT: Path planner using random sampling
• Collision detection between robots and an object
(also obstacles)
– Using PQP (A Proximity Query Package)
• Plan a configuration path of robot hand from the
initial state to a goal state
– Goal state: Satisfying sufficient conditions for caging

17. 17
Result: Caging a Sphere
– Planning time: 0.414 CPU seconds (on average)
(Linux PC – CPU Pentium4 – 3.2GHz)

18. 18
Result: Caging a Disk
– Planning time: 1.185 CPU seconds (on average)

19. 19
Result: Caging a Ring-like Object
– Planning time: 0.294 CPU seconds (on average)

20. 20
Conclusion
• Formulate problem of 3D multifingered caging
– Formulate definition of 3D multifingered caging
– Derive sufficient conditions for caging of some typical
cases
• Sphere
• Disk
• Ring-like object
• Complex-shaped object
• Construct planner of 3D multifingered caging
– RRT-based
– With collision detection