1 © 2006 Intel Corporation

Collective ActuationJason Campbell and Babu Pillai

Intel Research Pittsburgh

2

Seth Copen Goldstein#

Carlos Guestrin#

Casey Helfrich#

James Hoburg#

Peter Lee#

Mustafa Emre Karagozler#

Brian T. Kirby#

James Kuffner#

Matt Mason#

Bill Messner#

Todd C. Mowry*#

#ClaytronicsCarnegie Mellon University

Burak Aksak#

Johnathan Aldrich#

Simon Baker#

Preethi Bhat#

Randy Bryant#

Jason Campbell*

Michael DeRosa*#

Ashish Deshpande*

Stano Funiak*#

Phillip Gibbons*

Lily Mummert*

Illah Nourbakhsh#

Padmanabhan Pillai*

Ram Ramachandran*#

Greg Reshko#

Benjamin Rister*#

Srinivasan Seshan#

Metin Sitti#

Sidd Srinivasa*

Rahul Sukthankar*#

Michael Weller#

*Dynamic Physical RenderingIntel Research Pittsburgh

DPR & Claytronics Teams

3

Background: Intel Lab at Carnegie Mellon

! Located on the 4th floor of the “Collaborative Innovation Center” (CIC) building

4

Background: DPR (Intel)& Claytronics (CMU)

! Our focus is on shape-changing ensembles! Envision sub-millimeter modules,

used in groups of 104 to 108 units

Long-term project goals:! Scalable software architecture and tools

for millions of cooperating agents! Hardware design (concepts) suitable for integrated

photolithographic + self-assembly manufacture

Video: CMU Entertainment Technology Center

6

Other Applications

• 3D Visualization & interface (medical, etc.) .

• Product design, computer-assisted sculpting

• New forms of telepresence-based human-human communication

• Shape-shifting antennas

• Variable form-factorcomputing devices

• Malleable user interfaces

• 3D facsimile sampling and reproduction

7

Some Aspects of Shape Control

! Stretchable/shrinkable “lattices”! Linear actuators, even with spherical modules! Larger forces than those possible

from a pair of modules alone! ~Millions of cooperating modules

– Must reduce overall control complexity– Need to deal with failures and variability locally

! Likely trade off spatial resolution (module size) vs. increase strength of each module’s actuators

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Mesoscale prototype catoms

! Cylindrical (~5cm = 2 inch across)! Electromagnetic actuators/latches

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Electromagnetic Rolling Demo

10

hexagonalpentagonal octagonal

Physical Manipulation Cast as a Software Problem: “Collective Actuation”

Compose groups of catoms where the outside dimensions change via internal rolling

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Related Work

! Parallel Manipulators [Luntz97] [Böhringer]! Atron chains [Christensen06]! Rolling locomotion for chain-style MRRs [Atron,

Polybot, Superbot]

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Kinematics of Module Rolling

! Treat one module as static, the other as moving

! Center of the moving module traces a circle centered on the static module

! Points outside the center of the moving module trace epitrochoids (or epicycloids for d=r)

epicycloid (d=r) eiptrochoid (d<r)

r

b = (2,0)0

bθ

a = (0,0)

kissing point

θ

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Motion model: Rolling circular modules

r

b = (2,0)0

bθ

a = (0,0)

kissing point

θ

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Actuator locations

l

depthkissing point

actuator pair

θc

r

b = (2,0)0

bθ

a = (0,0)

kissing point

θ

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Path of one actuator relative to the other

l

depthing point

actuator pair

θc

r

b = (2,0)0

bθ

a = (0,0)

kissing point

θ

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Epicycloid & Epitrochoid(depth=0) (depth>0)

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Epicycloid & Epitrochoid(act. depth=0) (act. depth>0)

-3 -2 -1 1 2 3angle

1

2

3

4intermagnet distance

-3 -2 -1 1 2 3angle

1

2

3

4intermagnet distance

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A sinusoidal approximation is close, even for out of phase actuators

-90 90 180 270 360rotation angle

1

2

3

4distance between actuators

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Based on the intercatom geometries, we get a varying “lever arm”

(i.e., mechanical advantage)

0.25 0.5 0.75 1 1.25 1.5angle HradL0.5

1

1.5

2

2.5intermagnet distance

0.25 0.5 0.75 1 1.25 1.5angle HradL0.25

0.50.75

11.251.5

1.752

dlêdtheta

distancebetween actuators

mechanical advantage

0 angle 180

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Combining the effects of lever arm and force law (inverse square, etc.)

7.5 15 22.5 30 37.5 45degrees rolled

0.5

1normalized force

red = inverse cubeblack = inverse squareblue = inverse semilog

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Composing multiple actuators

90 180rolling angle HdegL0.2

0.40.60.8

1relative force

actuator spacing = 25°, d=5%, inverse square law,only one pair of actuators is active at any given time

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mean vs peak force over varying interactuator angles

20 40 60 80 100interactuator angle

0.5

1average force

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Quantifying actuator forcein our unitless analysis

2d

r

fm

fmax

“unit” force

max force

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Math (see the paper for details)

θθ−

=θ

θθ

=cosr2sinr2

ddb

sinr2cosr2

b

φφ−+−φ−+φ−

=

φ−+φ−

φ−+φ−−=

sin)cos)1(1(2)cos)1(1)((cos2

2sin)1(sin22cos)1(cos2)1(

drdr

rdrrdrrd

l

φ−+= cos)22(2 rrdrl

φ−=φ

sin)1(2 drdd l

−−

−=

−−⋅

−=⋅=

θθθθ

θθθθθ

θ cossin

1)csc(

)sin()1(21

cos2sin2

ddrrr

dd

ddb

ddb c

cll

θ−θ

−θ−θ−−θ−θ

==γ

γ

cossin

1))cos()22(2)(csc(

ddrr

ddbq ccll

mcc

mL fdrr

dfq

f γθ−θ−−θ−θθ−−

=

•

=

))cos()22(2)(csc(cos)1(3

10

1232

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Lifting force for an octagonal cell

octagonal

left sideactuator pairs working

interfaces

stationaryinterface

non-workinginterface

12

3

fL

rollinginterfaces

4

56

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Lifting force for an octagonal cell

octagonal

left sideactuator pairs working

interfaces

stationaryinterface

non-workinginterface

12

3

fL

rollinginterfaces

4

56

mcc

mL fdrr

dfq

f γθ−θ−−θ−θθ−−

=

•

=

))cos()22(2)(csc(cos)1(3

10

1232

27

Lifting force for an octagonal cell

octagonal

left sideactuator pairs working

interfaces

stationaryinterface

non-workinginterface

12

3

fL

rollinginterfaces

4

56

mcc

mL fdrr

dfq

f γθ−θ−−θ−θθ−−

=

•

=

))cos()22(2)(csc(cos)1(3

10

1232

20 40 60 80degrees rolled

5101520253035

lifting force

fmax

(d=10%, inverse square law)

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Lifting force for an octagonal cell

20 40 60 80degrees rolled

5101520253035

lifting force

fmax

82 84 86 88 90degrees rolled

50100150200250300

lifting force

fmax

10 fmax

d=10%, inverse square law

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Experiment: Self-Articulating Structures

1 4

2 3

567

89

10

each servo motordrives one gear

interface

other interfacesare unpowered

pinned links constrain orientation(equivalent to an additional motor held stationary)

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Experiment: Self-Articulating Structures

0.00

10.00

20.00

30.00

40.00

50.00

1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00

extension

min

out

side

rad

ius

0.00

10.00

20.00

30.00

40.00

50.00

1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00

min

out

side

radi

usno

rmal

ized

by

thic

knes

s

tightest curvature achieved vs extension

curvature normalized to beam thickness

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Experiment: Force Test Cell

cell supportsa measuredweight viaa pulley

ammeter tracks servo torque1

4

2

3

5

6

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Experiment: Force Test Cell

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Experiment: Force Test Cell

cell supportsa measuredweight viaa pulley

ammeter tracks servo torque1

4

2

3

5

6

0

0.01

0.02

0.03

30 45 60 75 90α

N*m

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Pinned gears + Servos

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3D Simulation

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Control Complexity / Bandwidth Observations

! Reduced DOF: Collective Actuation cells offer a reduced degree-of-freedom means of commanding the structure

! Potential for Aggregation: Depending upon the shape, adjacent cells may be combined into single logical entities for control purposes

! Scalability: Arrays of cells can control large structures with control complexity proportional to the number of desired degrees of freedom in the shape

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What works

! Kinematic Simulation: octohedral & hexahedral cells in 2D; octohedral in 3D

! Kinematic Prototypes: Pinned 2D cells using toothed gears & servos

! Force-at-distance Driven Prototypes: Magnetically-retained/driven 2D versions using permanent magnets (illustrate force curves around fixed operating points)

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Selected Unsolved Problems

! Stability of rolling modules, particularly in 3D

! Hardware: Robustness of our current force-at-distance actuators is low – so far our electromagnet prototypes don’t work sufficiently reliably to test this technique

! Distributed Control Algorithm(see future work by Ram Ravichandran)

! Dynamics

! Exploit nonuniform failure modes:It is possible to predict which bonds will break when a cell is overloaded – use this property to strengthen cells or detect and respond to failures

39 © 2006 Intel Corporation