Building a Universal Planar Manipulator

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Building aUniversal Planar Manipulator

• Dan Reznik
• Emil Moshkovich
• John Canny
• UC-Berkeley

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Our Main Resultwafr98,icra98

• Minimalism Flat Horizontal Plate is a Universal
  Planar Manipulator! (UPM)
• longitudinal vibrations
• sliding friction
• parallelism

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Where are we withinDistributed Manipulation?
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(No Transcript)
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Coulomb Friction(Sliding Mode)

• saturator of relative velocity (non-linear)
• above threshold of static friction

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Friction Field
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Review The Algorithm
C1
C2

• Given
• Compute
• Such that

C4
C3
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Goal of the talk

• Algorithm ok, in simulation
• Show how algorithmic requirements are being met
  in practice!

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Practical Requirements

• Generate a non-linear field
• Flexibly choose centers of rotation
• Real-time detect coins positions
• H/W S/W integration

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Problem Isynthesizing a non-lineardisplacement
field
C
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Use Pulsed Asymmetric Vibration (rotational)
P2
P1
C
Parts perceive constant, tangential force
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Pulse it d ? ?t2
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Problem IIHow do we make the table rotate about
a chosen COR?
C
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The Actuation Kinematics
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The Prototype

• 4 voice coils
• 8x8 CorianTM table

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Forward dynamics and the Real World

• Motors not the same
• Cross-talk, mechanical asymmetries
• Sensitive to M, I, and frequency.

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Back to the white board...
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Dont guess the COR measure it!
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Install Accelerometers PC Interface
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Acceleration Curve Fit
recover amplitude
integrate adjust
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Real-Time COR Recovery
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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
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Building a COR Library

• Visually steer to Cj
• Save amplitudes (X1,X2,Y1,Y2)j
• Load as needed by manipulation algm

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Problem IIIHow do we recover parts positions?

• At every step, algm needs to know Pis
• DPis given by task

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Use Vision!
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Image ? Features
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Updates Local Search
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Integrating it all1-Coin Experiment
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3
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7
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Video Snapshots
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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 parts positions
• simple image processing

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Current problems
C

• Stiction, saturation near C
• Needs more angular acceleration (tangential force)

r1
r2
sliding?
sticking?
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New Prototype

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

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Conclusions

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

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Dangers of Vibratory Manipulation
The End
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Manipulation Task Primitive
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Non-Additivity
Linear
Non-Linear
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Error ? e2