A Minimalist Planar Manipulator
Dan S. Reznik & Prof. John Canny
UC-Berkeley
June, 2000
The art of design:
versatility vs. simplicity
Actuator arrays
Minimalism
1 horizontal, rigid plate enough?
(x,y,q)
Talk outline
• 1d part feeding
• System details
• Extending to 2d manipulation
– “it’s possible”
• Refining 2d method
– “local” fields
• Demo, summary
1d Parts Feeding
vp
vs
f mg sgn(vs v p )
L L
HH
Asymmetry
1
Bang-bang cos w t - cos 2 wt
2
0.5 0.5
+mg
56% 62%
1 2 3 4 5 6 1 2 3 4 5 6
mg
-0.5 -0.5
-1 -1
-1.5
Coulomb Pump
0.5
5 10 15 20 25 30
-0.5
-1
-1.5
Equilibrium
0.6
0.5 veq
0.4
0.3
0.2
0.1
50 100 150 200
Viscosity
f a (v-veq)
0.5
1 2 3 4 5 6
-0.5
-1
-1.5
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
B/W camera
Teklam
1” H/C
50 lbf
voice coils
Newport
Optical Table
Table Dynamics
fx X1 + X 2
fy Y1 + Y2
z X 1 X 2 + Y1 Y2
PC Interface
video
capture
A/D
signal
generation
Image Processing
• Plate edges
• Coin positions
– Initial
– tracking
Accelerometers
COR calibration
x1,y1
cor
x2,y2
Signal Generation
• 2 PIC16c76
– PC downloads
waveform samples
– 4 d/a: pwm out
– Phase precision
From 1d feeding
to
2d parallel manipulation
Force vs. Amplitude
1
1 2 3 4 5 6
-1
24%
-2
-3
Rotation Fields
Force vs Radius
peak velocity
1.4
1.2
1 force/cycle
0.8
0.6
0.4
0.2
0.2 0.4 0.6 0.8 1 1.2 1.4
radius
Non-Rigid Flow
Pulse it: vpart 0
Pulsed Rotation
Measured Displacements
C
Velocity Field Family
Cx , Cy , k
Velocity: closed under sum
Force: not closed!
Sum Families
M
dim k j ( P C j ) 3
j 1
M (P C j )
dim k j 3M
j 1
P Cj
Sum Families: fixed centers
M
dim k j ( P C j ) 1
j 1
M (P C j )
dim k j M
j 1
P Cj
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)
U
V
(U+V)
q
O(2)
q’
Concatenate Rotations
C C1
2
P2
’
P1
P
P1 ’ 2
C C
3 4
Sequence Rotations (1)
C1
Sequence Rotations (2)
C
2
Sequence Rotations (3)
C
3
Sequence Rotations (4)
C
4
Simulation
Cross Talk
C
4
“Local” Field
-C C
Radial Jamming
f1+f2
f1
“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
inertial UL inertial U 2
Re
viscous / viscous U
Force: not closed!
3D Underwater Manipulation
h2o
f1+f2
Summary
• Motivation: minimalism
• 1d feeding, asymmetry
• 2d feeding, non-closure of force fields
• Local fields: diagonalization
• Implementation and results
How do we stack up?
programmability
Dofs/control compl.
Thank you!