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

Summary Motivation Related Work Problem Statement Sampling Preliminary Results Future Work

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, 2 nd Order Form Closure –[Rimon, Burdick, 1995, 1998] –[Ponce, Burdick, Rimon, 1995] [Mason, 2001]

Holding: Rigid parts Summaries of results –[Bicchi, Kumar, 2000] –[Mason, 2001] C-Spaces for closed chains –[Milgram, Trinkle, 2002] Fixturing hinged parts –[van der Stappen et al, 2002] Antipodal Points for Curved Parts –[Jia 2002] Caging Grasps – [Rimon, Blake, 1999]

Parallel-Jaw Grip Points (1999)

Related Work: Friction Cones Matthew T. Mason, Mechanics of Robotic Manipulation, MIT Press: Cambridge, MA 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.

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

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.

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 BarrettHand TM 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

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 Uncertainty in: –Relative Pose –Center of mass –Shape

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 withJaw 2

Eliminate Misses 1.First gripper misses workpiece

Eliminate Slip 2. Gripper contacts outside friction cone (slip)

Eliminate Unstable Due to Slip 4. Gripper contacts with too large an angle for the workpiece to maintain sticking after some rotation

Eliminate Unstable Rotations 3. Gripper contacts on wrong side of friction cone (rotation)

Configuration Space Center of Mass Inverse Friction Cone 0 d2d  : Allowable angle First Gripper Maximal value of  for each point on the edge within the inverse friction cone Angle (in degrees) Note: The C-space plot includes all constraints except ensuring that force closure is attained by the second gripper.  = arctan(  - x/z) x z 0 d2d x

Rotated Square Number of points Successes (% of 500 Samples) Knight

Sampling-based Approach Sample: Part Shape Vertices and CG within uncertainty zones Sample Pose Sample Line of Action Evaluate if SPG Color by % SPG

Results Probability of SPG: 0.535

Results Probability of SPG: 0.270

Results Probability of SPG: 0.090

Results Probability of SPG: 0.355

Results

Future Work Allow Slip Use Concavities Eliminate points early in the sampling process to save computation time.

Future Work Potential Methods: –After each 50 iterations, eliminate point- angles 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

Cloud Computing

Example Same uncertainty about all vertices of workpiece Two vertices with greater uncertainty for workpiece

Stable Push Grasps