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Uncertainty in Grasping and Feeding. Frank van der Stappen Utrecht University Shanghai, China, May 9, 2011. Outline. Algorithmic Automation Grasping: finger misplacements Feeding: pose variations Inaccurate manipulators and imprecise parts. RISC: 15 Years Ago. - PowerPoint PPT Presentation
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Uncertainty in Grasping and Feeding
Frank van der Stappen
Utrecht University
Shanghai, China, May 9, 2011
Outline
• Algorithmic Automation
• Grasping: finger misplacements
• Feeding: pose variations
• Inaccurate manipulators and imprecise parts
RISC: 15 Years Ago
‘Simplicity in the factory’ [Whitney 86] instead of ‘ungodly complex robot hands’ [Tanzer & Simon 90]
Reduced Intricacy in Sensing and Control [Canny &
Goldberg 94]:• simple ‘planable’ physical actions, by• simple, reliable hardware components• simple or even no sensors
Algorithmic Automation
• Complete,• efficient, and• provably correct planning algorithms
using • geometry,• data structures, and• modeling and
simulation
planner
Outline
• Algorithmic Automation
• Grasping: finger misplacements
• Feeding: pose variations
• Inaccurate manipulators and imprecise parts
Grasp Analysis
• Form Closure: Analysis of Instantaneous Velocities [1870s]
• Force Closure: Analysis of Forces and Moments [1970s]
– 4 fingers sufficient for most 2D parts– 7 fingers sufficient for most 3D parts
• 2nd Order Immobility: Analysis in Configuration Space [1990s]
– 3 fingers sufficient for most 2D parts– 4 fingers sufficient for most 3D parts
Wrench Analysis
Force closure: wrenches w1,…,wk induced by fingers should be able to resist any external wrench [Lakshminarayana 1978], so
w1,…,wk form a positive basis for wrench space, so
convex hull of w1,…,wk has O in its interior.
w1
w2
w3w4
Computing the Grasps or Fixtures
• Four points along four edges
4a,3a,2a,1a edges
4321 )a,a,a,a(FC :Output
4321 a and ,a,a,a on points with grasps ofset
complexity )1(O
n edges
Output-Sensitive Grasp Synthesis
• Naïve:
• Output-sensitive:
)a,a,a,a(FC compute do )a,a,a,a( allfor 43214321
)a,a,a,a(FC compute do )P(Q)a,a,a,a( allfor 43214321 })a,a,a,a(FC|)a,a,a,a{()P(Q compute 43214321 )n(O 2
)Kn(O 2
)1(O)n(O 4 x )n(O 4=
)K(O|))P(Q(|O )1(O )K(Ox =
Algorithmic Approach
2D
2D
2D
nn
n²
? n²
naive: n combinations
4smart: ± n operations
2
data structure
Finger Misplacement
• Algorithm reports continuous set of all four-finger grasps
• Some grasps are very sensitive to finger mispacements
• Postprocessing step in ‘configuration space’ of all grasps: [Ponce et al 1995, vdS et al 2000]
– determine grasp that minimizes sensivity to finger misplacement
– select the grasps that allow for a given misplacement of all fingers
Independent Grasp Regions in 2D
• Identify combinations of regions on part boundary that allow for independent finger placements [Nguyen 1988].
w1
w2
w3w4
Insensitivity to Finger Misplacements
• Place fingers at the centers of the independent grasp regions: allowed misplacement is computable.
Independent Grasp Regions in 3D
• Given a rectilinear polyhedron, identify all combinations of 7 patches that admit independent finger placement.
Boundary is subdivided into n patches of size ε x ε to guarantee allowed misplacement of ε/2.
εε
Different Algorithmic Challenges
• Red-blue containments and crossings instead of red-blue intersections
Caging
• Rigid motion of the fingers
Caging
• Rigid motion of the fingers forces part to move along
Caging
• Fingers cage a part if there exists no motion that takes
the part from its current placement to a remote placement without colliding with a finger.
If the current placement lies in a bounded component of free configuration space then the part is caged.
Outline
• Algorithmic Automation
• Grasping: finger misplacements
• Feeding: pose variations
• Inaccurate manipulators and imprecise parts
Part Feeding
• Feeders based on various actions: push, squeeze, topple, pull, tap, roll, vibrate, wobble, drop, …
Parts Feede
r
Feeding with Fences
• Every 2-dimensional part can be oriented by fences over a conveyor belt.
• Shortest fence design efficiently computable [Berretty, Goldberg, Overmars, vdS 98].
www.durafeed.com
Vibratory Bowl Feeders
• Parts vibrate upward along a helical track.
• Obstacles force wrongly oriented parts back to the bottom of the bowl.
• Design of obstacles.
Algorithmic Trap Design
• Filtering traps for vibratory bowl feeders
• Combination of rejection functionality of traps and reorientation functionality of fences
Blades
Blades
Assumptions
• Parts– identical polyhedra– quasi-static motion– singulated
• Zero friction• No toppling• Locally linear track
Part Reorientation and Rejection
• Reorientation: track pose to blade pose– Blade angle– Blade height
• Rejection: blade pose− Blade width
Modeling
blade angle
blade width wblade height
h
INPUTPolyhedral part P & Center of mass C
OUTPUT
Set of blades b(,h,w) feeding P
ALGORITHM
Blade Space
Blade width
Blade height
Blade angle
hw
• Point represents a blade• Surfaces subdivide space
Critical Surface
Blade width
Blade height
Blade angle
• Critical surface for every initial pose, consisting of patches (one per possible reorientation)– Above surface: part in that pose falls– Below surface: part in that pose survives
S
Critical Arrangement
Blade width
Blade angle
• B is a blade that feeds P1
• Valid solutions: points above all but one surface: 1-level
P1
P2
P3
B
Blade height
Physical Experiments
pose I
blade
track wall
• Discrepancies with prediction by model– Part motion– Part model– Part variations
Uncertainty in Reorientation
Uncertainty in Reorientation
pose A
pose B
Height
Uncertainty in Reorientation
pose I
Angle
Width
Patches of initial part pose I’s critical surface correspond to final part poses
patch Bpatch A
Angle
h=H
Consider cross-section at blade height h
Uncertainty in Reorientation
Height
Width
Angle
Width
blade
Model predicts that the blade reorients the part to pose A after which it is rejected but the experiments shows that it occasionally gets fed in pose B
Uncertainty in Reorientation
patch B
patch A
Alter Patches
width
patch A patch B
angle
w
Pose B may be fed by the blade
width
angle
Adjust width of the patch
Uncertainty in Reorientation
patch A patch B
Outline
• Algorithmic Automation
• Grasping: finger misplacements
• Feeding: pose variations
• Inaccurate manipulators and imprecise parts
Uncertainty
• Determine manipulation plans that work despite given variations in – part shape– manipulator actions
• Analysis• Existence• Synthesis
Imperfect Parts
• For a given task and a family of shapes, plan actions that accomplish the task for any shape in the family
Inaccurate Manipulators
• For a given part, task, and a range of perturbations of any possible action, plan actions such that even the perturbed versions of the actions in the plan accomplish the task
AMPLIFI
New project: Algorithms for manipulation planning with imperfect parts and inaccurate manipulators
Open PhD position, funded by NWO:• MSc degree in computer science or mathematics• interest in (and preferably background) in algorithms design• interest in applications in Robotics and Automation.
Thank You!
Papers available from http://people.cs.uu.nl/frankst/
Joint work with: Mark Overmars, Ken Goldberg, Elon Rimon, Mark de Berg, Xavier Goaoc, Chantal Wentink, Robert-Paul Berretty, Jae-Sook Cheong, Onno Goemans, Mostafa Vahedi, Heinrich Kruger, Herman Haverkort, Anthony Lewandowski, Marshall Anderson, Gordon Smith