Improving Method for Computation of Improving Method for Computation of Grasp Quality Metric Grasp Quality Metric Using Minimal Breaking Force on Objects Using Minimal Breaking Force on Objects Mana Borwornpadungkitti Advisor: Asst. Prof. Nattee Niparnan, Ph.D.
Outline 1) Introduction 2) Our Improvements 3) Evaluation 4) Conclusion 2
Outline 1)Introduction Background knowledge Related works 2) Our Improvements 3) Evaluation 4) Conclusion 3
Grasp Synthesis Generate and test Grasp quality measure 4
Grasp Quality Measure Robustness Task External disturbance resistance 5
Outline 1) Introduction Background knowledge Related works 2) Our Improvements 3) Evaluation 4) Conclusion 6
Wrench ● force and torque – R 3 ( R 2 + R ) in 2D – R 6 ( R 3 + R 3 ) in 3D ● Wrench space - set of wrenches 7
Useful Wrench Spaces ● Grasp Wrench Space (GWS) ● Object Wrench space (OWS) 8
Useful Wrench Spaces ● Grasp Wrench Space (GWS) – Set of wrenches generated from unit contact forces of grasp ● Object Wrench space (OWS) 9
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ε metric [Ferrari and Canny 92] ● Magnitude of smallest wrench that the grasp cannot withstand ● Minimum distance from origin to boundary of grasp wrench space 11
ε metric - drawbacks ● Mixed force and torque unit ● Depend on reference frame and scale 12
Useful Wrench Spaces ● Grasp Wrench Space (GWS) – Set of wrenches generated from unit contact forces of grasp ● Object Wrench space (OWS) – Set of wrenches generated from distribution of unit forces acting on object surface 13
Object Wrench Space Usually approximated 14
Judge Grasp by its Contacts? 15
GWS / OWS 16
GWS / OWS 17
GWS / OWS 18
Propose Minimum summation of magnitude of forces acting on the object that break the grasp 19
Advantages ● Using object as input ● Force unit ● Invariant of reference frame and scale 20
Outline 1) Introduction Background knowledge Related works 2) Our Improvements 3) Evaluation 4) Conclusion 21
Related Works ● Borst et al. ; ICRA04 ● Strandberg and Wahlberg; TRO06 ● Wen and Wu; JZUS-C12 ● Jeong and Cheong; ROB12 22
Related Works ● Borst et al. ; ICRA04 - Approximate OWS, incomplete ● Strandberg and Wahlberg; TRO06 ● Wen and Wu; JZUS-C12 ● Jeong and Cheong; ROB12 23
Related Works ● Borst et al. ; ICRA04 - Approximate OWS, incomplete ● Strandberg and Wahlberg; TRO06 - Discretize force direction, incomplete ● Wen and Wu; JZUS-C12 ● Jeong and Cheong; ROB12 24
Related Works ● Borst et al. ; ICRA04 - Approximate OWS, incomplete ● Strandberg and Wahlberg; TRO06 - Discretize force direction, incomplete ● Wen and Wu; JZUS-C12 - Ray shooting, faster and more complete ● Jeong and Cheong; ROB12 25
Related Works ● Borst et al. ; ICRA04 - Approximate OWS, incomplete ● Strandberg and Wahlberg; TRO06 - Discretize force direction, incomplete ● Wen and Wu; JZUS-C12 - Ray shooting, faster and more complete ● Jeong and Cheong; ROB12 - Complete in simplifjed problem, slow 26
Timeline Borst et al. ICRA04 Strandberg and Wahlberg Jeong and Cheong TRO06 ROB12 Wen and Wu Thesis JZUS-C12 27
Minimal Breaking Force ● Equivalent to maximum scale of OWS inside GWS GWS Scaled OWS OWS 28
[Strandberg and Wahlberg; TRO06] ● Approximate OWS by Discretized force direction ● Result in surface in force space 29
[Wen and Wu; JZUS-C12] ● Improvement to [Strandberg and Wahlberg; TRO06] ● Use ray shooting to calculate GWS - OWS intersection 30
Drawbacks ● Slow ● Inaccurate 31
Drawback - slow [Wen and Wu; JZUS-C12] 2.69 sec ; MATLAB on 3.16 GHz desktop computer ● 32
Drawback - inaccurate [Strandberg and Wahlberg; TRO06] ● [Wen and Wu; JZUS-C12] ● 33
Objective ● Algorithm to calculate minimum force on object that break the grasp ● Input: Grasp – Object model – ● Output: Minimum breaking force (magnitude, position, and direction) – ● Speedup ● Accuracy 34
Outline 1) Introduction 2)Our Improvements OWS fjlter No discretized direction 3) Evaluation 4) Conclusion 35
Our Improvements Focus on Two improvements Efficiency OWS filter – – Accuracy No discretized direction – – 36
Our Improvements Focus on Two improvements Efficiency OWS filter – – Accuracy Efficiency only – ● Filtering criteria ● No discretized direction – 37
Our Improvements Focus on Two improvements Efficiency OWS filter – – Accuracy Efficiency only – ● Filtering criteria ● No discretized direction – Both efficiency and accuracy ● Novel method ● 38
Outline 1) Introduction 2) Our Improvements OWS fjlter No discretized direction 3) Evaluation 4) Conclusion 39
Minimal Breaking Force ● Is same as maximum scale of OWS inside GWS ● Comes from single force ● Acts on object vertex , for polyhedral object [Strandberg and Wahlberg; TRO06] 40
Proposition Intersection point between minimum scaled compact set A and another compact convex set B is member of vertices of convex hull of A GWS B OWS' A' A vertex ● A → OWS ● B → GWS 41
Improvement Only vertices of convex hull of OWS instead of entire OWS 6 wrenches instead of 10 wrenches 42
OWS filter - Complexity O(|V f | log m) per force direction ● V f : feasible vertices in this direction ● m : number of vertices of convex hull O(d|V f | log m) overall ● d : number of force direction 43
Outline 1) Introduction 2) Our Improvements OWS fjlter No discretized direction 3) Evaluation 4) Conclusion 44
OWS Calculation [Strandberg and Wahlberg 06] ● [Wen and Wu 12] ● Both discretize disturbance force direction No discretized direction 45
No Discretized Direction ● Extended from [Strandberg and Wahlberg 06] ● i : Force Direction ● j : Vertex concave ● k : hyperplane 46
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Corollary ● Optimal disturbance force direction for fixed object vertex and GWS hyperplane ● No discretized direction by iterating over all object vertex and GWS hyperplane 48
No Discretized Direction - Complexity O(|V||H|) ● V : object vertices ● H : GWS hyperplanes 49
Outline 1) Introduction 2) Our Improvements 3)Evaluation OWS fjlter No discretized direction 4) Conclusion 50
Evaluation ● Compare our method with [1] Strandberg and Wahlberg 06 – [2] Wen and Wu 12 – ● Octave on 3.16 GHz Core i7 ● Metrics Speed – Accuracy – 51
Settings μ ● Robot: 0.3 (~ 16.7°) – Disturbance: 1.5 (~ 56.3°) – Friction cone approximated by 8-sided pyramid ● Discretize direction using vertices of geodesic dome ● freq = 1 to 9 – 52
Objects - Basic ● Box : 6 facets ● Sphere : 720 facets 53
Objects - KIT ● Three objects from KIT object models database ● Three level of detail (# facet) ● 800 ● 5k ● 25k 54
Grasps - Basic ● Three grasps with different number of contact points – Four – Five – Six 55
Grasps - KIT ● Three grasps using the BarrettHand in different parts of each object – Bottom – Middle – Top 56
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Outline 1) Introduction 2) Our Improvements 3) Evaluation OWS fjlter No discretized direction 4) Conclusion 58
0.267 0.223 0.654 0.538 1.09 0.538 59
a b c g h i d e f 60
Speedup - Basic ● SW [Strandberg and Wahlberg; TRO06] • WW [Wen and Wu; JZUS-C12] Speedup = T old Object Grasp SW WW Box four 0.73 0.62 T new five 0.98 0.67 six 1.00 0.74 Sphere four 0.88 1.23 five 1.19 1.55 six 1.00 1.49 61
Speedup - KIT ● SW [Strandberg and Wahlberg; TRO06] • WW [Wen and Wu; JZUS-C12] 17.4 e 0.9 62
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Outline 1) Introduction 2) Our Improvements 3) Evaluation OWS fjlter No discretized direction 4) Conclusion 64
No Discretized Direction Black , green , and blue line represent BW , SW9 , and SW3 , respectively 65
No Discretized Direction Black , green , and blue line represent BW , SW9 , and SW3 , respectively 66
No Discretized Direction Black , green , and blue line represent BW , SW9 , and SW3 , respectively 67
No Discretized Direction Black , green , and blue line represent BW , SW9 , and SW3 , respectively 68
No Discretized Direction Black , green , and blue line represent BW , SW9 , and SW3 , respectively 69
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Outline 1) Introduction 2) Our Improvements 3) Evaluation 4)Conclusion 75
Conclusion ● Computation of a minimal magnitude of force acting on object that break the grasp ● Speed up calculation time – examining only vertices of convex hull of OWS ● Improve accuracy – calculating optimal disturbance force direction 76
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