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A robot trajectory programming method using multi-camera systems SILVIO GIANCOLA DAVIDE CHIARION REMO SALA MESA2014 SENIGALLIA 11/09/2014 2 Introduction Study of a need : Tiles decoration SUMMARY Hand made Serigraphy Introduction

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SLIDE 1

A robot trajectory programming method using multi-camera systems

SILVIO GIANCOLA DAVIDE CHIARION REMO SALA

MESA2014 – SENIGALLIA – 11/09/2014

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SLIDE 2

A robot trajectory programming method using multi-camera systems

Introduction

2 SUMMARY

  • Introduction
  • Tool Identification
  • Trajectory Smoothing
  • Metrologic Analysis
  • Application
  • Conclusion

Study of a need : Tiles decoration Innovative decoration process? Ø Use of anthropomorphic robot for the tile painting Robot programming method? Ø Paintbrush trajectory registration

Hand made Serigraphy Advantages Authenticity and unicity High quality product Fast method High quantity Inconvenient Poor quantity Necessity of a qualified person Poor value Printed

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SLIDE 3

A robot trajectory programming method using multi-camera systems

Tool Identification

3 SUMMARY

  • Introduction
  • Tool Identification

– Stereoscopic System – Point Cloud Indexing – Rigid Body Registration

  • Trajectory Smoothing
  • Metrologic Analysis
  • Application
  • Conclusion

NON INTRUSIVE PRECISION OCCLUSION LIGHT CONDITION AMBIGUITY

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SLIDE 4

A robot trajectory programming method using multi-camera systems

Tool Identification

4 SUMMARY

  • Introduction
  • Tool Identification

– Stereoscopic System – Point Cloud Indexing – Rigid Body Registration

  • Trajectory Smoothing
  • Metrologic Analysis
  • Application
  • Conclusion

OCCLUSION LIGHT CONDITION AMBIGUITY

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SLIDE 5

A robot trajectory programming method using multi-camera systems

Tool Identification

5 SUMMARY

  • Introduction
  • Tool Identification

– Stereoscopic System – Point Cloud Indexing – Rigid Body Registration

  • Trajectory Smoothing
  • Metrologic Analysis
  • Application
  • Conclusion
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SLIDE 6

A robot trajectory programming method using multi-camera systems

Tool Identification

6 SUMMARY

  • Introduction
  • Tool Identification

– Stereoscopic System – Point Cloud Indexing – Rigid Body Registration

  • Trajectory Smoothing
  • Metrologic Analysis
  • Application
  • Conclusion

Stereoscopic system

§ Based on 2 cameras

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SLIDE 7

A robot trajectory programming method using multi-camera systems

Tool Identification

7 SUMMARY

  • Introduction
  • Tool Identification

– Stereoscopic System – Point Cloud Indexing – Rigid Body Registration

  • Trajectory Smoothing
  • Metrologic Analysis
  • Application
  • Conclusion

Trinocular stereoscopy

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SLIDE 8

A robot trajectory programming method using multi-camera systems

Tool Identification

8 SUMMARY

  • Introduction
  • Tool Identification

– Stereoscopic System – Point Cloud Indexing – Rigid Body Registration

  • Trajectory Smoothing
  • Metrologic Analysis
  • Application
  • Conclusion

Trajectory Acquisition from Trinocular Vision System

§ Point Cloud Indexing § Rigid Body Registration § Trajectory Smoothing

4 3 1 2 1 2 3 4

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SLIDE 9

A robot trajectory programming method using multi-camera systems

Tool Identification

9 SUMMARY

  • Introduction
  • Tool Identification

– Stereoscopic System – Point Cloud Indexing – Rigid Body Registration

  • Trajectory Smoothing
  • Metrologic Analysis
  • Application
  • Conclusion

Point Cloud Ordering

§ Experimental method using distances matrix § Ex:

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SLIDE 10

A robot trajectory programming method using multi-camera systems

Tool Identification

10 SUMMARY

  • Introduction
  • Tool Identification

– Stereoscopic System – Point Cloud Indexing – Rigid Body Registration

  • Trajectory Smoothing
  • Metrologic Analysis
  • Application
  • Conclusion

Point Cloud Ordering – Algorithm

§ If n is the number of marker, we split the n x n matrix in n rows. Be rowi the ith row. § For each rowi, we define an empty 2 x n array named indi, linked to the ith row. § For each element dij of rowi, its value is matched to a correspondent value dkl of the

  • model. The rows and columns indexes (k and l) are then saved in the columns of

indi.

§ For each indi, we define isol the largest occurrence of an index in this matrix. § If all the element of indi is 0, then a marker is missing. § Else, the largest occurrence of an index different to 0 returns the correct index

  • f i.
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SLIDE 11

A robot trajectory programming method using multi-camera systems

Tool Identification

11 SUMMARY

  • Introduction
  • Tool Identification

– Stereoscopic System – Point Cloud Indexing – Rigid Body Registration

  • Trajectory Smoothing
  • Metrologic Analysis
  • Application
  • Conclusion

Point Cloud Ordering – Example

§ ind1 = 0

1 1 1 3 5 2 0 , the 1st marker corresponds to the 1st one

§ ind2 = 3

3 3 1 5 2 0 , the 2nd marker corresponds to the 3rd one

§ ind3 = 5

5 5 1 3 2 0 , the 3rd marker corresponds to the 5th one

§ ind4 = 2

2 2 1 3 5 0 , the 4th marker corresponds to the 2nd one

§ ind5 = 0

0 , a marker is missing (the 4th).

𝑒13 𝑒15 𝑒12 𝑌 𝑒31 𝑒35 𝑒32 𝑌 𝑒51 𝑒53 𝑒52 𝑌 𝑒21 𝑒23 𝑒25 𝑌 𝑌 𝑌 𝑌 𝑌

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SLIDE 12

A robot trajectory programming method using multi-camera systems

Tool Identification

12 SUMMARY

  • Introduction
  • Tool Identification

– Stereoscopic System – Point Cloud Indexing – Rigid Body Registration

  • Trajectory Smoothing
  • Metrologic Analysis
  • Application
  • Conclusion

Rigid Body Registration

§ Find Rotation and Translation of a point cloud respect to a model

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SLIDE 13

A robot trajectory programming method using multi-camera systems

Tool Identification

13 SUMMARY

  • Introduction
  • Tool Identification

– Stereoscopic System – Point Cloud Indexing – Rigid Body Registration

  • Trajectory Smoothing
  • Metrologic Analysis
  • Application
  • Conclusion

Rigid Body Registration

§ Find Rotation Translation and Scaling of a point cloud respect to a model § Singular Value Decomposition (SVD) § 𝑁 = ∑

𝑠

,

  • ∗ 𝑠

,/ = 𝑉 ∗ 𝑇 ∗ 𝑊 3 ,45

, w𝑗𝑢ℎ 𝑠

,

  • and 𝑠

, the deviation of points of a cloud respect to its barycenter

§ 𝑆𝑝𝑢𝑏𝑢𝑗𝑝𝑜 = 𝑉 ∗

1 1 𝑡𝑗𝑕𝑜 𝑒𝑓𝑢 𝑉 ∗ 𝑊/ ∗ 𝑊/

§ 𝑈𝑠𝑏𝑜𝑡𝑚𝑏𝑢𝑗𝑝𝑜 = 𝑞̂- − 𝑆𝑝𝑢𝑏𝑢𝑗𝑝𝑜 ∗ 𝑞̂

w𝑗𝑢ℎ 𝑞̂-𝑓𝑢 𝑞̂ the barycenter of the point clouds

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SLIDE 14

A robot trajectory programming method using multi-camera systems

Trajectory Smoothing

14 SUMMARY

  • Introduction
  • Tool Identification
  • Trajectory Smoothing
  • Metrologic Analysis
  • Application
  • Conclusion

Filtering and Interpolations :

§ Cubic / Spline interpolation § Bézier Curves interpolations § B-Spline interpolations (NURBS) § Low Pass filter

Tests :

§ Sinus Following § White Noise reduction § Sinus and White Noise Combination § Acquired Data

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SLIDE 15

A robot trajectory programming method using multi-camera systems

Trajectory Smoothing

15 SUMMARY

  • Introduction
  • Tool Identification
  • Trajectory Smoothing
  • Metrologic Analysis
  • Application
  • Conclusion

Sinusoids White noise Combination Acquired data Cubic / Spline

++

  • Bézier curves
  • ++
  • B-Spline (NURBS)

+ + + +

Low Pass

+ + + +

Results :

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SLIDE 16

A robot trajectory programming method using multi-camera systems

Trajectory Smoothing

16 SUMMARY

  • Introduction
  • Tool Identification
  • Trajectory Smoothing
  • Metrologic Analysis
  • Application
  • Conclusion

Amplitude Spectrum of an acquisition:

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SLIDE 17

A robot trajectory programming method using multi-camera systems

Metrologic Analysis

17 SUMMARY

  • Introduction
  • Tool Identification
  • Trajectory Smoothing
  • Metrologic Analysis
  • Application
  • Conclusion

Metrologic Analysis

  • Accuracy (AP) : proximity of

measurement results to the true value

  • Repeatibility (RP) : precision of the

measurement

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SLIDE 18

A robot trajectory programming method using multi-camera systems

Metrologic Analysis

18 SUMMARY

  • Introduction
  • Tool Identification
  • Trajectory Smoothing
  • Metrologic Analysis
  • Application
  • Conclusion

Metrologic Analysis

§ Repeatability § Analysis of the reconstruction of a marker at the origin position § Statistical study (gaussian) § Results § Uncertainty respect to the axis : § X axis : 0,21 mm § Y axis : 0,05 mm § Z axis : 0,15 mm

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SLIDE 19

A robot trajectory programming method using multi-camera systems

Metrologic Analysis

19 SUMMARY

  • Introduction
  • Tool Identification
  • Trajectory Smoothing
  • Metrologic Analysis
  • Application
  • Conclusion

Metrologic Analysis

§ Accuracy § Trajectory analysis among the coordinate system axis § Use of the Rigid Registration algorithm on the point cloud defining the

trajectory

§ Results § Error among X camera axis: 0.7 mm § Error among Y camera axis: 1.2 mm § Error among Z camera axis: 3.7 mm

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SLIDE 20

A robot trajectory programming method using multi-camera systems

Application

20 SUMMARY

  • Introduction
  • Tool Identification
  • Trajectory Smoothing
  • Metrologic Analysis
  • Application
  • Conclusion

Application

§ Model of the robot : ABB IRB 120

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SLIDE 21

A robot trajectory programming method using multi-camera systems

Application

21 SUMMARY

  • Introduction
  • Tool Identification
  • Trajectory Smoothing
  • Metrologic Analysis
  • Application
  • Conclusion

Application

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SLIDE 22

A robot trajectory programming method using multi-camera systems

Conclusion

22 SUMMARY

  • Introduction
  • Tool Identification
  • Trajectory Smoothing
  • Metrologic Analysis
  • Application
  • Conclusion

Conclusion

§ Feasibility OK § Precision < 0.3 mm § Accuracy to improve with

correct registration between the 2 setups