A Minimalist Planar Manipulator

Dan S. Reznik & Prof. John Canny

UC-Berkeley

June, 2000

The art of design:versatility vs. simplicity

Actuator arrays

Minimal art

involved a pure

and clear

demonstration of

sculpture in its

barest form. The

materials they

used were often

simple items like

Styrofoam,

firebricks, or light

bulbs. They used

recognizable

geometric shapes

to represent form

and style in their

work.

Minimalism

1 horizontal, rigid plate enough?

(x,y,)

Talk outline

• 1d part feeding

• System details

• Extending to 2d manipulation– “it’s possible”

• Refining 2d method– “local” fields

• Demo, summary

1d Parts Feeding

)sgn( ps vvmgf

vs

vp

1 2 3 4 5 6

-1

-0.5

0.5

Asymmetry

1 2 3 4 5 6

-1.5

-1

-0.5

0.5

cosHwtL- 1

2cosH2 wtLBang-bang

62%56%mg

mg

Coulomb Pump

5 10 15 20 25 30

-1.5

-1

-0.5

0.5

Equilibrium

50 100 150 200

0.1

0.2

0.3

0.4

0.5

0.6

veq

1 2 3 4 5 6

-1.5

-1

-0.5

0.5

Viscosity

f (v-veq)

Straight-Line Feeding

Circular Feeding

Anything Goes

Interesting Apps

• Novel “tangible” UI’s– Force feedback (viscosity is free)– Active desk

• Fancy product displays– Rotate wine bottles

• Fluid-based micro manipulation

The System

50 lbfvoice coils

Teklam1” H/C

NewportOptical Table

B/W camera

Table Dynamics

2121

21

21

YYXX

YYf

XXf

z

y

x

PC Interface

videocapture

A/D

signalgeneration

Image Processing

• Plate edges

• Coin positions– Initial– tracking

Accelerometers

COR calibration

cor

x1,y1

x2,y2

Signal Generation

• 2 PIC16c76– PC downloads

waveform samples– 4 d/a: pwm out– Phase precision

From 1d feedingto

2d parallel manipulation

Force vs. Amplitude

1 2 3 4 5 6

-3

-2

-1

1

24%

Rotation Fields

Force vs Radius

0.2 0.4 0.6 0.8 1 1.2 1.4

0.2

0.4

0.6

0.8

1

1.2

1.4

peak velocity

force/cycle

radius

Non-Rigid Flow

Pulse it: vpart 0

Pulsed Rotation

Measured DisplacementsC

Velocity Field Family

Cx , Cy , k

Velocity: closed under sum

Force: not closed!

Sum Families

MCP

CPk

M

j j

jj 3

)(dim

1

3)(dim1

M

jjj CPk

Sum Families: fixed centers

MCP

CPk

M

j j

jj

1

)(dim

1)(dim1

M

jjj CPk

Parallel Manipulation

N parts => 2N constraints

Our Idea

• Horizontal Plate: 3 dof• Task: move N-parts• Propose: Sum 2N rotations!

– Satisfy 2N constraints

Sum Concatenation

q’ = (U+V) q = V U q + O(2)

q

q’

V

U

(U+V)

O(2)

Concatenate Rotations

P1

P1’P2

P2’

C2 C1

C4C3

Sequence Rotations (1)

C1

Sequence Rotations (2)

C2

Sequence Rotations (3)

C3

Sequence Rotations (4)

C4

Simulation

Cross Talk

C4

“Local” Field

C-C

f1+f2

1f

Radial Jamming

“Local” Field

Localized Forces Video

Local Field Affordances

• Reduces cross talk

• Round-robin + vision feedback

• Faster execution– N parts => N pulses– Blend

• Robustness, robustness, robustness!

Bowtie

(vhs)

Sorter

Inertial Flow

U

L

/viscous

inertialRe

UL

U

viscous

Uinertial 2

Force: not closed!

3D Underwater Manipulation

f1+f2

h2o

Summary

• Motivation: minimalism

• 1d feeding, asymmetry

• 2d feeding, non-closure of force fields

• Local fields: diagonalization

• Implementation and results

How do we stack up?

Dofs/control compl.

programmability

Thank you!