Robot Grasp Planning using Parallel
Sampling to Estimate Uncertainty in
Pose, Shape, and Mechanics
Melissa Goldstein
Edward Lee
Frank Ong
Josh Goldberg
Lelai Zhou
Ben Kehoe
Ken Goldberg
UC Berkeley
Willow Garage PR2
•
•
•
•
•
•
Mobile Base
Cameras, Lidar
2 Arms
Backdrivable for Safety
Low Precision
2 Parallel-Jaw Grippers
Holding: Rigid parts
• Contact Mechanics: Number of
contacts
–
–
–
–
–
[Reuleaux, 1876], [Somoff, 1900]
[Mishra, Schwarz, Sharir, 1987],
[Nguyen, 1988]
[Markenscoff, Papadimitriou, 1990]
[Han, Trinkle, Li, 1999]
• Immobility, 2nd Order Form Closure
– [Rimon, Burdick, 1995, 1998]
– [Ponce, Burdick, Rimon, 1995]
[Mason, 2001]
Holding: Rigid parts
• Summaries of results
– [Bicchi, Kumar, 2000]
– [Mason, 2001]
• Grasp Regions
– [van der Stappen et al,
-
+
+
2002]
• Caging Grasps
– [Rimon, Blake, 1999] [van
der Stappen 2009],
[Rodriguez, Mason 2010]
+
+
-
Parallel-Jaw Grip Points (1999)
Related Work: Mason’s Rule
• Line of pushing and the edges of the
friction cone “vote” to determine which way
the object will rotate
• We want the workpiece
to rotate in a direction that
will result in alignment
with the gripper edge
Matthew T. Mason, Mechanics of Robotic Manipulation, MIT Press: Cambridge, MA. 2001.
Stable Push Grasps
• Stable push grasps (SPGs) satisfy the
following conditions after the gripper
contacts the workpiece and continues
pushing:
– The workpiece purely rotates about the
contact point (no slipping)
– The workpiece rotates toward stability on the
gripper face (becomes aligned with the
gripper)
– The second gripper achieves force closure
Problem Statement
• Assume:
– Part on Worksurface
– Planar Projections of Part and Gripper
– Planar, Quasi-static Motion
• Given:
–
–
–
–
Nominal 2D Polygonal Part
Center of mass
Shape, Center of Mass
Lower Bound on Friction
• Uncertainty in:
– Relative Pose
– Center of mass
– Shape
Problem Statement
• Perturbations in:
– Relative Pose
– Center of mass
– Shape
– Push Motion
Approach: Stable Push Grasps
•
•
•
•
•
Position Jaws
Make Initial contact with Vertex of Jaw 1
Stable Push with Jaw 1 to Align Edges
Close Gripper
Contact with Jaw 2
Failure Modes
1. First gripper misses workpiece
Failure Modes
2. Gripper contacts outside friction cone (slip)
Failure Modes
3. Gripper contacts with too large an angle for
the workpiece to maintain sticking after
some rotation
Failure Modes
4. Gripper contacts on wrong side of friction
cone (rotation)
Max Contact Angle
Center of Mass
Inverse Friction
Cone
f: Allowable angle
z
x
0
First Gripper
d
2d
Maximal allowed phi
Angle (in degrees)
Maximal value of f for each point on the
edge within the inverse friction cone
30
f = arctan(m - x/z)
20
10
0
-10
-20
-30
0
0
0.2
x
0.4
0.6
0.8
1
1.2
1.4
1.6
Friction Cone for one side of the workpiece
d
1.8
2
2d
Note: The C-space plot
includes all constraints
except ensuring that force
closure is attained by the
second gripper.
Sampling Vertex Positions
• Sample: Part Vertices
and CG within
uncertainty zones
(500 samples)
• Sample Relative Pose
– 50x50 grid
• Sample Line of
Pushing
– 0.5 degrees
• Evaluate if SPG
• Color by % SPG
% SPG = 98%
% SPG = 74%
Number of points
Rotated Square
Successes (% of 500 Samples)
Knight
Sampling Edge Normals
• Sample: Part Edge
Normals and CG
within uncertainty
zones (500 samples)
• Sample Relative Pose
– 50x50 grid
• Sample Line of
Pushing
– 0.5 degrees
• Evaluate if SPG
• Color by % SPG
Results
% SPG = 54
Results
% SPG = 10
Results
% SPG = 36
Uncertainty May Help?
Same uncertainty about all
vertices of workpiece
Two vertices with greater
uncertainty for workpiece
Other Related Work
• Contact sensors Felip and Morales, 2009
– Robotic hand with embedded gripper,
tactile, pressure, and/or force sensors
– Sensors estimate quality of the grasp and
shape of the object to make live
improvements to the grasp
• 3D environments Nguyen 1987
– Sensors create a 3D map of the object
and environment
– Runs an algorithm on the object’s
geometry to determine a stable grasp
• Analytical Models
– Optimize the grasp quality criteria for
force closure and local object stability
Berenson, Srinivasa, Kuffner 2009
Morales, Sanz, del Pobil, Fagg 2006
BarrettHandTM with
pressure sensors
Related Work
Christopoulos and
Schrater, 2007
• Spline fitting
• Directly incorporate
uncertainty in shape
through spline geometry
• Test of force closure
Related Strategy: Task Space Regions
Dmitry Berenson et. al., “Addressing Pose Uncertainty in Manipulation Planning Using Task
Space Regions”, The International Conference on Intelligent Robots and Systems, 2009
Task Space Regions
• TSR analyze the six-dimensional space
representing possible goals for a gripper
and consider the pose uncertainty in order
to avoid potential collisions
• The rejection sampling with TSR allows to
decline if the region is impossible to
achieve the task with the uncertainty
• IKBiRRT find a C-space path to the grasp
Dmitry Berenson et. al., “Addressing Pose Uncertainty in Manipulation Planning Using Task
Space Regions”, The International Conference on Intelligent Robots and Systems, 2009
Next Steps
•
•
•
•
•
Allow Slip
Use Concavities
Consider Torque around CG
Adaptive Sampling
Parallel-Sampling in Cloud…
Cloud Computing
http://commons.wikimedia.org/wiki/File:Cloud_computing.png
Stable Push Grasps
Next Steps
• Potential Methods:
– After each 50 iterations, eliminate pointangles with less than 20% of the successes of
the most successful point
– Image segmentation: keep areas with an
average value that is “high enough,” since
relative success of areas shifts with the
sampling
Related Work: Force Closure
• Line segment between
contact points must lie within
the friction cones of the
contact points on each edge
Van-Duc Nguyen, “Constructing Force- Closure Grasps,” The International Journal
of Robotics Research, 1988; 7; 3.
Related Work: Friction Cones
If the line of pushing (lp) is within the friction cone, the
workpiece will not slip with respect to the gripper, as it is
pushed.
Matthew T. Mason, Mechanics of Robotic Manipulation,
MIT Press: Cambridge, MA. 2001.
Results
% SPG: 27%