[PPT] - On the Efficient Computation of Independent Contact Regions for PowerPoint Presentation

SLIDE 1

On the Efficient Computation of Independent Contact Regions for Force Closure Grasps

Robert Krug, Dimitar Dimitrov, Krzysztof Charusta and Boyko Iliev

Learning Systems Lab Center for Applied Autonomous Sensor Systems Örebro University, Sweden

robert.krug@oru.se

Robert Krug IROS 2010 1 / 21

SLIDE 2

Independent Contact Regions (ICR)

Impossible to position the fingers of a grasping device precisely at the desired contact locations

Robert Krug IROS 2010 2 / 21

SLIDE 3

Independent Contact Regions (ICR)

Impossible to position the fingers of a grasping device precisely at the desired contact locations Representation of a grasp as a set of regions Each region is associated with

ne finger

Robert Krug IROS 2010 2 / 21

SLIDE 4

Independent Contact Regions (ICR)

Impossible to position the fingers of a grasping device precisely at the desired contact locations Representation of a grasp as a set of regions Each region is associated with

ne finger

If each finger is placed within its respective region . . . . . . certain grasp properties are preserved

Robert Krug IROS 2010 2 / 21

SLIDE 5

Independent Contact Regions (ICR)

Impossible to position the fingers of a grasping device precisely at the desired contact locations Representation of a grasp as a set of regions Each region is associated with

ne finger

If each finger is placed within its respective region . . . . . . certain grasp properties are preserved

Robert Krug IROS 2010 2 / 21

SLIDE 6

Independent Contact Regions (ICR)

Impossible to position the fingers of a grasping device precisely at the desired contact locations Representation of a grasp as a set of regions Each region is associated with

ne finger

If each finger is placed within its respective region . . . . . . certain grasp properties are preserved

Robert Krug IROS 2010 2 / 21

SLIDE 7

Independent Contact Regions (ICR)

Impossible to position the fingers of a grasping device precisely at the desired contact locations Representation of a grasp as a set of regions Each region is associated with

ne finger

If each finger is placed within its respective region . . . . . . certain grasp properties are preserved

Robert Krug IROS 2010 2 / 21

SLIDE 8

Outline

1

Motivation

2

Concept Preliminaries Grasp Wrench Space Task Wrench Space Visibility - Convex Hulls Admissible Wrenches

3

The Algorithm: Step - by - Step

4

Benchmark

5

Contributions & Outlook

Robert Krug IROS 2010 3 / 21

SLIDE 9

Motivation

Outline

1

Motivation

2

Concept Preliminaries Grasp Wrench Space Task Wrench Space Visibility - Convex Hulls Admissible Wrenches

3

The Algorithm: Step - by - Step

4

Benchmark

5

Contributions & Outlook

Robert Krug IROS 2010 4 / 21

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Motivation

In general such regions are not unique ⇒ the computation methods reflect application/assumptions.

Robert Krug IROS 2010 5 / 21

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Motivation

In general such regions are not unique ⇒ the computation methods reflect application/assumptions. Our approach is based on geometric reasoning [Pollard, 1994] Efficient algorithm for ICR-computation on discretized objects

Robert Krug IROS 2010 5 / 21

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Motivation

In general such regions are not unique ⇒ the computation methods reflect application/assumptions. Our approach is based on geometric reasoning [Pollard, 1994] Efficient algorithm for ICR-computation on discretized objects Given a prototype force-closure grasp

Robert Krug IROS 2010 5 / 21

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Concept

Outline

1

Motivation

2

Concept Preliminaries Grasp Wrench Space Task Wrench Space Visibility - Convex Hulls Admissible Wrenches

3

The Algorithm: Step - by - Step

4

Benchmark

5

Contributions & Outlook

Robert Krug IROS 2010 6 / 21

SLIDE 14

Concept Preliminaries

Preliminaries

Grasp → set of contact points G = [ p1, ··· ,pN ]T Grasp contact forces fs are bounded

Robert Krug IROS 2010 7 / 21

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Concept Preliminaries

Preliminaries

Grasp → set of contact points G = [ p1, ··· ,pN ]T Grasp contact forces fs are bounded Mapping of contact forces ⇒ contact wrenches

τs = (ps ×f s), ws = f s τs

Robert Krug

IROS 2010 7 / 21

SLIDE 16

Concept Preliminaries

Preliminaries

Grasp → set of contact points G = [ p1, ··· ,pN ]T Grasp contact forces fs are bounded Mapping of contact forces ⇒ contact wrenches

τs = (ps ×f s), ws = f s τs

Planar grasp ⇒ 3D - wrench space

3D grasp ⇒ 6D - wrench space

Robert Krug IROS 2010 7 / 21

SLIDE 17

Concept Grasp Wrench Space

Grasp Wrench Space (GWS)

Hypothetical 2D - contact wrenches for a 4-fingered frictionless grasp

Robert Krug IROS 2010 8 / 21

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Concept Grasp Wrench Space

Grasp Wrench Space (GWS)

Hypothetical 2D - contact wrenches for a 4-fingered frictionless grasp A disturbance wrench like this . . .

Robert Krug IROS 2010 8 / 21

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Concept Grasp Wrench Space

Grasp Wrench Space (GWS)

Hypothetical 2D - contact wrenches for a 4-fingered frictionless grasp A disturbance wrench like this . . . . . . can be countered by a convex combination of grasp wrenches

Robert Krug IROS 2010 8 / 21

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Concept Grasp Wrench Space

Grasp Wrench Space (GWS)

Hypothetical 2D - contact wrenches for a 4-fingered frictionless grasp A disturbance wrench like this . . . . . . can be countered by a convex combination of grasp wrenches All possible convex combinations

⇒ GWS

Mirror image of all resistible disturbance wrenches

Robert Krug IROS 2010 8 / 21

SLIDE 21

Concept Task Wrench Space

Task Wrench Space (TWS)

Consider a given prototype grasp . . . . . . and knowledge about possible disturbances

Robert Krug IROS 2010 9 / 21

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Concept Task Wrench Space

Task Wrench Space (TWS)

Consider a given prototype grasp . . . . . . and knowledge about possible disturbances TWS ⇒ space of wrenches to counter given disturbances

Robert Krug IROS 2010 9 / 21

SLIDE 23

Concept Task Wrench Space

Task Wrench Space (TWS)

Consider a given prototype grasp . . . . . . and knowledge about possible disturbances TWS ⇒ space of wrenches to counter given disturbances Obviously some redundancy

Robert Krug IROS 2010 9 / 21

SLIDE 24

Concept Task Wrench Space

Task Wrench Space (TWS)

Consider a given prototype grasp . . . . . . and knowledge about possible disturbances TWS ⇒ space of wrenches to counter given disturbances Obviously some redundancy

Robert Krug IROS 2010 9 / 21

SLIDE 25

Concept Task Wrench Space

Task Wrench Space (TWS)

Consider a given prototype grasp . . . . . . and knowledge about possible disturbances TWS ⇒ space of wrenches to counter given disturbances Obviously some redundancy Approximate the Task . . . . . . by shifting hyperplanes parallely

Robert Krug IROS 2010 9 / 21

SLIDE 26

Concept Visibility - Convex Hulls

Visibility

Well known from computational geometry Facet f is visible from x ⇒ x lies in the half-space of f not containing the centroid

Robert Krug IROS 2010 10 / 21

SLIDE 27

Concept Visibility - Convex Hulls

Visibility

Well known from computational geometry Facet f is visible from x ⇒ x lies in the half-space of f not containing the centroid If x1 “sees” the same facets as x . . . . . . replacement preserves the

riginal convex hull

Robert Krug IROS 2010 10 / 21

SLIDE 28

Concept Admissible Wrenches

Admissible Wrenches

Changing grasp contact points means changing grasp wrenches

Robert Krug IROS 2010 11 / 21

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Concept Admissible Wrenches

Admissible Wrenches

Changing grasp contact points means changing grasp wrenches Define search spaces utilizing the visibility concept

Robert Krug IROS 2010 11 / 21

SLIDE 30

Concept Admissible Wrenches

Admissible Wrenches

Changing grasp contact points means changing grasp wrenches Define search spaces utilizing the visibility concept Every grasp with wrenches in each search space . . . . . . guarantees the task

Robert Krug IROS 2010 11 / 21

SLIDE 31

Concept Admissible Wrenches

Admissible Wrenches

Changing grasp contact points means changing grasp wrenches Define search spaces utilizing the visibility concept Every grasp with wrenches in each search space . . . . . . guarantees the task

Robert Krug IROS 2010 11 / 21

SLIDE 32

Concept Admissible Wrenches

Admissible Wrenches

Changing grasp contact points means changing grasp wrenches Define search spaces utilizing the visibility concept Every grasp with wrenches in each search space . . . . . . guarantees the task

Robert Krug IROS 2010 11 / 21

SLIDE 33

Concept Admissible Wrenches

Admissible Wrenches

Changing grasp contact points means changing grasp wrenches Define search spaces utilizing the visibility concept Every grasp with wrenches in each search space . . . . . . guarantees the task find wrenches inside the search spaces ⇒ corresponding contact points form the ICR

Robert Krug IROS 2010 11 / 21

SLIDE 34

The Algorithm: Step - by - Step

Outline

1

Motivation

2

Concept Preliminaries Grasp Wrench Space Task Wrench Space Visibility - Convex Hulls Admissible Wrenches

3

The Algorithm: Step - by - Step

4

Benchmark

5

Contributions & Outlook

Robert Krug IROS 2010 12 / 21

SLIDE 35

The Algorithm: Step - by - Step

Step 1: Defining the wrench spaces

EXAMPLE: Discretized Ellipse

Robert Krug IROS 2010 13 / 21

SLIDE 36

The Algorithm: Step - by - Step

Step 1: Defining the wrench spaces

EXAMPLE: Discretized Ellipse Initial grasp G = [ p1, ··· ,p3 ]T

Robert Krug IROS 2010 13 / 21

SLIDE 37

The Algorithm: Step - by - Step

Step 1: Defining the wrench spaces

EXAMPLE: Discretized Ellipse Initial grasp G = [ p1, ··· ,p3 ]T Grasp contact forces are bounded . . . . . . and lie inside a L-sided polyhedral cone ⇒ |ft| ≤ µfn

Robert Krug IROS 2010 13 / 21

SLIDE 38

The Algorithm: Step - by - Step

Step 1: Defining the wrench spaces

EXAMPLE: Discretized Ellipse Initial grasp G = [ p1, ··· ,p3 ]T Grasp contact forces are bounded . . . . . . and lie inside a L-sided polyhedral cone ⇒ |ft| ≤ µfn Convex hull over those wrenches

⇒ GWS

Robert Krug IROS 2010 13 / 21

SLIDE 39

The Algorithm: Step - by - Step

Step 1: Defining the wrench spaces

EXAMPLE: Discretized Ellipse Initial grasp G = [ p1, ··· ,p3 ]T Grasp contact forces are bounded . . . . . . and lie inside a L-sided polyhedral cone ⇒ |ft| ≤ µfn Convex hull over those wrenches

⇒ GWS

In this example: TWS ⇒ sphere

Robert Krug IROS 2010 13 / 21

SLIDE 40

The Algorithm: Step - by - Step

Step 2: Computation of search spaces

Robert Krug IROS 2010 14 / 21

SLIDE 41

The Algorithm: Step - by - Step

Step 2: Computation of search spaces

Consider region C1

Robert Krug IROS 2010 14 / 21

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The Algorithm: Step - by - Step

Step 2: Computation of search spaces

Consider region C1 Right now, just p1 ∈ C1 . . . . . . with two corresponding wrenches

Robert Krug IROS 2010 14 / 21

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The Algorithm: Step - by - Step

Step 2: Computation of search spaces

Each vertex of the GWS ⇒ associated search space

Robert Krug IROS 2010 14 / 21

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The Algorithm: Step - by - Step

Step 2: Computation of search spaces

Each vertex of the GWS ⇒ associated search space Recall concept of Visibility Wrenches in search space . . . . . . can replace original grasp wrenches

Robert Krug IROS 2010 14 / 21

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The Algorithm: Step - by - Step

Step 2: Computation of search spaces

Shift hyperplanes belonging to current vertex parallely . . . . . . tangent to the TWS

Robert Krug IROS 2010 15 / 21

SLIDE 46

The Algorithm: Step - by - Step

Step 2: Computation of search spaces

Shift hyperplanes belonging to current vertex parallely . . . . . . tangent to the TWS Build intersection of exterior half-spaces

Robert Krug IROS 2010 15 / 21

SLIDE 47

The Algorithm: Step - by - Step

Step 2: Computation of search spaces

Shift hyperplanes belonging to current vertex parallely . . . . . . tangent to the TWS Build intersection of exterior half-spaces For the second wrench belonging to p1 . . .

Robert Krug IROS 2010 15 / 21

SLIDE 48

The Algorithm: Step - by - Step

Step 3: Evaluation of viable contact points

Test neighboring contact points for ICR-inclusion

Robert Krug IROS 2010 16 / 21

SLIDE 49

The Algorithm: Step - by - Step

Step 3: Evaluation of viable contact points

Test neighboring contact points for ICR-inclusion Check if corresponding primitive wrenches are admissible

Robert Krug IROS 2010 16 / 21

SLIDE 50

The Algorithm: Step - by - Step

Step 3: Evaluation of viable contact points

Test neighboring contact points for ICR-inclusion Check if corresponding primitive wrenches are admissible Either by solving a LP . . . . . . or via dot products with the hyperplane normals

Robert Krug IROS 2010 16 / 21

SLIDE 51

The Algorithm: Step - by - Step

Step 3: Evaluation of viable contact points

Test neighboring contact points for ICR-inclusion Check if corresponding primitive wrenches are admissible Either by solving a LP . . . . . . or via dot products with the hyperplane normals New GWS preserves the Task

Robert Krug IROS 2010 16 / 21

SLIDE 52

The Algorithm: Step - by - Step

Step 3: Evaluation of viable contact points

Test neighboring contact points for ICR-inclusion Check if corresponding primitive wrenches are admissible Either by solving a LP . . . . . . or via dot products with the hyperplane normals New GWS preserves the Task Independent evaluation of each contact region

Robert Krug IROS 2010 16 / 21

SLIDE 53

The Algorithm: Step - by - Step

Step 3: Evaluation of viable contact points

Test neighboring contact points for ICR-inclusion Check if corresponding primitive wrenches are admissible Either by solving a LP . . . . . . or via dot products with the hyperplane normals New GWS preserves the Task Independent evaluation of each contact region The final ICR

Robert Krug IROS 2010 16 / 21

SLIDE 54

Benchmark

Outline

1

Motivation

2

Concept Preliminaries Grasp Wrench Space Task Wrench Space Visibility - Convex Hulls Admissible Wrenches

3

The Algorithm: Step - by - Step

4

Benchmark

5

Contributions & Outlook

Robert Krug IROS 2010 17 / 21

SLIDE 55

Benchmark

Numerical Results

Test-PC: Core 2 Duo 2.9-GHz 1000 random 4-hard fingered grasps . . . . . . on the model of a cup

Model comprises 2911 vertexes / 5822 triangles

Robert Krug IROS 2010 18 / 21

SLIDE 56

Benchmark

Numerical Results

Test-PC: Core 2 Duo 2.9-GHz 1000 random 4-hard fingered grasps . . . . . . on the model of a cup Friction cone discretization L = 8

→ tmean = 0.17s

Model comprises 2911 vertexes / 5822 triangles

Robert Krug IROS 2010 18 / 21

SLIDE 57

Contributions & Outlook

Outline

1

Motivation

2

Concept Preliminaries Grasp Wrench Space Task Wrench Space Visibility - Convex Hulls Admissible Wrenches

3

The Algorithm: Step - by - Step

4

Benchmark

5

Contributions & Outlook

Robert Krug IROS 2010 19 / 21

SLIDE 58

Contributions & Outlook

Contributions: Efficient algorithm, parallelizable in the number of grasp contact points

Robert Krug IROS 2010 20 / 21

SLIDE 59

Contributions & Outlook

Contributions: Efficient algorithm, parallelizable in the number of grasp contact points Allows for arbitrary object geometries . . . . . . with frictionless, frictional and soft-finger point contact models

Robert Krug IROS 2010 20 / 21

SLIDE 60

Contributions & Outlook

Contributions: Efficient algorithm, parallelizable in the number of grasp contact points Allows for arbitrary object geometries . . . . . . with frictionless, frictional and soft-finger point contact models Incorporation of a bounded disturbance wrench set

Robert Krug IROS 2010 20 / 21

SLIDE 61

Contributions & Outlook

Contributions: Efficient algorithm, parallelizable in the number of grasp contact points Allows for arbitrary object geometries . . . . . . with frictionless, frictional and soft-finger point contact models Incorporation of a bounded disturbance wrench set Future Work:

⇒ Sensitivity analysis on real-world data

Robert Krug IROS 2010 20 / 21

SLIDE 62

References

Nguyen, V.-D. (1986). Constructing force-closure grasps. In Robotics and Automation. Proceedings. 1986 IEEE International Conference

n, volume 3, pages 1368 – 1373.

Pollard, N. S. (1994). Parallel methods for synthesizing whole-hand grasps from generalized prototypes. PhD thesis, MIT, Dept. of Electrical Engineering and Computer Science. Pollard, N. S. (2004). Closure and quality equivalence for efficient synthesis of grasps from examples. International Journal of Robotics Research, 23(6):595–614. Roa, M. A. and Suárez, R. (2009). Computation of independent contact regions for grasping 3-d objects. IEEE Transactions on Robotics, 25:839–850.

Robert Krug IROS 2010 21 / 21