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Building a Universal Planar Manipulator

Building a Universal Planar Manipulator. Dan Reznik Emil Moshkovich John Canny UC-Berkeley. Our Main Result: [wafr98,icra98]. Minimalism: Flat Horizontal Plate is a Universal Planar Manipulator! ( UPM ) longitudinal vibrations sliding friction parallelism.

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Building a Universal Planar Manipulator

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  1. Building aUniversal Planar Manipulator Dan Reznik Emil Moshkovich John Canny UC-Berkeley

  2. Our Main Result:[wafr98,icra98] • Minimalism: Flat Horizontal Plate is a Universal Planar Manipulator! (UPM) • longitudinal vibrations • sliding friction • parallelism

  3. Where are we withinDistributed Manipulation?

  4. vp vs Coulomb Friction(Sliding Mode) • “saturator” of relative velocity (non-linear) • above threshold of static friction

  5. Friction Field

  6. d1 d2 d1 d2 d4 d3 d4 d3 Review: The Algorithm C1 C2 • Given: • Compute: • Such that: C4 C3

  7. Goal of the talk • Algorithm ok, in simulation • Show how algorithmic requirements are being met in practice!

  8. Practical Requirements • Generate a non-linear field • Flexibly choose centers of rotation • Real-time detect coins’ positions • H/W & S/W integration

  9. d d Problem I:synthesizing a non-lineardisplacement field C

  10. Use Pulsed Asymmetric Vibration (rotational) P2 P1 C Parts perceive constant, tangential force

  11. Pulse it: d  t2

  12. y x Problem II:How do we make the table rotate about a chosen COR? C

  13. The Actuation Kinematics

  14. The Prototype • 4 voice coils • 8”x8” CorianTM table

  15. Forward dynamics and the Real World • Motors not the same • Cross-talk, mechanical asymmetries • Sensitive to M, I, and frequency.

  16. Back to the white board...

  17. Don’t guess the COR: measure it!

  18. Install Accelerometers + PC Interface

  19. Acceleration Curve Fit recover amplitude integrate & adjust

  20. Real-Time COR Recovery

  21. COR Steering -2 -1 -2 +2 +1 +1 0 +1 +1 0 -1 0 -2 -1 -1 +3 +3 +2 -1 -1 0 -1 0 -1

  22. Building a COR Library • Visually steer to Cj • Save amplitudes (X1,X2,Y1,Y2)j • Load as needed by manipulation algm

  23. Problem III:How do we recover part’s positions? • At every step, algm needs to know Pi’s • DPi’s given by task

  24. Use Vision!

  25. Image  Features

  26. Updates = Local Search

  27. 2 1 Integrating it all:1-Coin Experiment 4 3 5 6 7 8

  28. Video Snapshots

  29. Summary: Problems Solved • I: Synthesize non-linear manipulation primitive • friction + asymmetric rotation • cool actuation design • II: Make the table rotate about chosen COR • install accelerometers • least-squares fit to cos(t)+(cos2t)/2 • recover amplitudes, solve simple equation • III: Recover part’s positions • simple image processing

  30. Current problems C • Stiction, saturation near C • Needs more angular acceleration (tangential force) r1 r2 sliding? sticking?

  31. New Prototype • Larger table: 15”x15” (vs. 8”x8”) • Stronger voice coils: 50 lbf (vs. 5 lbf) • More space-efficient • Sturdy aluminum base

  32. Conclusions • Novel distributed manipulator • single moving part • simple control • closer to working prototype • Applications? • Active desk • Moving people? Furniture? • Micro-scale

  33. Dangers of Vibratory Manipulation The End

  34. Manipulation Task & Primitive

  35. Non-Additivity Linear Non-Linear

  36. V U q U+V [U,V] V U Error  e2

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