robotics seminar [email protected] ismcl ri scs1 scaling issues in robotics: strength, range, and...

Robotics Seminar 20050422 [email protected] ISMCL RI SCS 1

scaling issues in robotics:strength, range, and

communication limits on big and small robots

robotics institute seminar2005 april 22

mel siegelintelligent sensors measurement & control lab

the robotics institute – school of computer sciencecarnegie mellon university – pittsburgh pa 15213


what’s the point?


• Galileo knew “big is weak, small is strong”• you know big vehicles have greater range

than small vehicles• these are scaling issues

– four-year-olds know house cats from tigers by perceiving the proportions, e.g., leg diameter to height, that are determined by absolute size

• but the robotics community doesn’t pay much attention to the immutable physical constraints on the range and operating time of the mini-, micro-, and nano-robots we are talking about building and deploying


• if you want to travel a long distance/time/etc– AND IF you have to carry your own food/fuel/etc

• then you need a BIG animal/boat/airplane/robot

• which is inconsistent with a swarm/horde of SMALL ones

• making it quantitative is usually simple:– energy carried ~ h 3 (h = linear dimension)– operating time ~ h 3/P (P = baseline power)– operating range ~ h 3 v/P (v = speed)– often P ~ h 2 v, so range ~ h and time ~ h/v

• challenge is to figure P for each application


http://hypertextbook.com/physics/matter/energy-chemical/

1 MJ/kg = 1 kJ/g= (1/4.2) kcal/g= (1/4.2) food-cal/g

carbs: 4 food-cal/gfats: 9 food-cal/ggasoline: 10 food-cal/g

what if I were to use a high explosive, e.g., TNT, to fuel my robot?





http://www.batteryuniversity.com/print-partone-3.htm

1 W-hour = 3600 W-second = 3600 J

MJ/kg 0.16 0.29

0.220.43

0.110.18

0.400.58

0.360.47

0.29

note: comparison with liquid fuel is not always entirelyfair, because electrical energy is much higher effective

temperature (1 eV ~ 11,000 K), hence much lowerentropy ... but for heating, incandescent lighting, orturning motors the energy/energy comparison is fair

http://www.batteryuniversity.com/print-partone-3.htm


• proposals for mini-, micro-, and nano-robot applications almost never realistically consider issues of range and running time

• key limitation can be avoided by foraging in an energy-rich environment, e.g., soup– where robots can forage for vs. carry energy– however we’re not yet good at extracting it

• (I’ll mention some groups that are working on it)

– energy does not have to be chemical• scavenged RF, thermal, ..., energy


by the way, it’s nothing new ...

• strength: Galileo explained “small is strong, big is weak”, i.e., why big structures are prone to collapse under their own weight– soon & extensively applied to bioenergetics,

i.e., horses “eat like birds” and birds “eat like horses”

• energy: I. K. Brunel ended debate about adequacy of steamship range by showing useful range feasible with plausible size– led to era of enormous ships, e.g., “Great X ”


what are the details?


we’ll discuss details ...• ... about strength

– poppa, momma, and baby bears:what 5-year-old kids know that roboticists don’t

• ... about energy– deriving relationships and making numbers:

poppa, momma, and baby vacuum cleaners

• ... about systems– the need to be big and small simultaneously

• small so you can have enormous swarms of them• big so they can communicate cheaply and efficiently


strength


Galileo’s Two New Sciences

• Sagredo: “... if a large machine be constructed in such a way that its parts bear to one another the same ratio as in a smaller one, and if the smaller is sufficiently strong ... the larger also should be able to withstand any severe and destructive tests to which it may be subjected ...”

• Salviati (Galileo): “... the mere fact that it is matter makes the larger machine built of the same material not so strong ... the larger the machine the greater its weakness ... who does not know that a horse falling from a height of three or four cubits will break his bones, while a dog falling from the same height or a cat from a height of eight or ten cubits will suffer no injury? ...”


don’t get too big for your bridges!


gravity sets their proportions ...


and theirs ...


but not theirs ...

• their eyes are your best hint to their size• mechanics, optics, sensing, chemistry,

etc, all scale separately


and not (yet) theirs either ...


don’t miss the forest for the trees!

• Galileo recognized weight ~ h 3, capacity of leg to support it ~ d 2 (d = leg diameter), so d ~ h 3/2 ... we recognize an animal’s absolute size by observing d relative to h

• “Notice that the principle of proportionally of larger diameter supporting-structures for larger animals also applies to plants. A giant sequoia, such as those found in Sequoia and Yosemite National Parks, is a very tall tree. It has a massive, large diameter trunk while smaller trees have relatively small diameter trunks.”Thomas J. Herbert, Department of Biology, University of Miami, Coral Gables, FL:

http://www.bio.miami.edu/tom/bil160/bil160goods/17_scaling.html

http://www.bio.miami.edu/tom/bil160/bil160goods/17_scaling.html


• but a tree is not an animal: it is “all leg”!

• weight ~ d 2 h (d = diameter, h = height)

• load bearing capacity ~ d 2

• so h is limited by material not diameter

sequoia tree diameter/height vs height

0.08

0.09

0.1

0.11

0.12

0.13

0.14

0.15

0.16

200 210 220 230 240 250 260 270 280 290

height (feet)

dia

me

ter/

he

igh

t ra

tio data from U.S.

National Park Service http://www.nps.gov/seki/shrm_pic.htm

http://www.nps.gov/seki/shrm_pic.htm

http://www.nps.gov/seki/shrm_pic.htm


energy


• a mobile machine of characteristic dimension h can carry energy ~ h 3

• how long will it run? how far will it go?– tmax ~ h 3/P, rmax ~ h 3 v/P (P = power)

• it depends on many details, but a goodfirst guess is minimum power Pmin ~ h 2v

– so maximum running time tmax ~ h/v

– and maximum range dmax ~ h

• so a few big airplanes are used for the long-haul routes, and you worry about swallowing small germs, not about breathing them


step length / step time• what is the implied numerical factor?

– step length is proportional to h– step time is proportional to h/v– all vehicles have the same range in steps– all vehicles have the same running time

in step times– for baseline power ~ h 2 v, i.e., drag limited

• the implied numerical factor is the number of steps in the fuel tank of the particular vehicle design (independent of scale)


a few plausible solutions ...

• beam me calories, Scottie– collect natural or beamed-in light, RF, etc

• do what microbes do– extract chemical energy from the environment

• do what birds do– extract wind energy from thermal updrafts

• build a Maxwell’s Demon– extract energy from thermal gradients (legal)– ... from thermal fluctuations (maybe not legal)


other power-requirement scenarios


maximum survival time• heat loss rate ~ body surface area

• so P ~ h 2 tmax ~ h

• small mammals in cold climate must eat their own body weight several times daily

• this is a good model for, e.g., a planetary rover whose main energy expenditure is to keep itself – and its batteries – warm enough to function properly

• rmax = v tmax ~ v h

if moving is cheap vs. keeping warm


maximum speed• families of geometrically similar animals

all have the same top (sprint) speed– a consequence of (almost) all life having

(almost) the same basic muscle elements, connected in series to achieve required length, and in parallel to achieve required strength

• robots can overcome this limitation of (most) animals by using accumulators – springs, capacitors, inductors – to tank-up on energy slowly and release it rapidly into a load of lower impedance


• note that this applies to sprinting• ultimate limit to sprint speed is

when tension snaps the muscle or tears its attachment to the bone

• energy-efficient “cruising” or “loping” motion involves pendulous motion of the limbs– fnatural ~ h -½, vcruising ~ h fnatural ~ h 1/2

– on other planets fnatural ~ (g/h)½,

so vcruising ~ (gh)½


maximum jumping height• expend all your stored energy to jump

as high as you can once• stored energy ~ h 3

• mass ~ h 3

• m g H ~ h 3 g H ~ h 3 H = constant• it is well known in biomechanics that

“all geometrically similar animals jump to the same height”

• heights above centers-of-mass, of course


geometrically-similarrobotic vacuum cleaners

of different size


imagine families of ...• geometrically similar vacuum cleaners ...

– biggest for cleaning aircraft hangars ...– smallest for cleaning bathroom tile grout ...– each a linearly-scaled model of the others ...– except where the optimization criteria cannot

be achieved without changing the size of a particular component, e.g., the brush diameter

• investigate running time and range vs. size for differing optimization criteria– family characterized by its optimization

criterion


true vacuum cleaner family

• energy is spent mostly on moving air• optimization criteria: constant air

velocity at the intake, independent of the scale of the particular family member

• intake scales as h 2, P ~ h 2 tmax ~ h

• dirt collected per unit time ~ h 2

• dirt collected per refueling ~ h 3

• so the 3 cm Φ model collects only 0.1% as much dirt as the 30 cm Φ model, whereas you probably expected 10%


brush-action model• energy is spent mostly on the friction

of the brush against the floor/carpet/etc

• width of brush ~ h• front-back extent of brush in contact

with floor independent of scale• rotational speed independent of scale• forward velocity independent of scale• P ~ h tmax ~ h 2

• dirt collected per refueling also ~ h 3, but for different combination of factors


wall-cleaning family• aim is to clean walls vs. floor• dirt load small: energy spent climbing• energy requirement same as in the

jumping problem, but speed is constant vs. decreasing linear ramp

• H independent of scale• dirt collected ~ h• consistent with (probable) expectation


systems


a system can bebig and small at the same

time• e.g., a large network of small sensing nodes

– Global Environmental Monitoring System (GEMS)– data to initialize global weather model codes– foresee supercomputers that can do 1010 nodes– 1 node / km3 over globe to 20 km altitude– nodes must be very small

• small sensible residence time in atmosphere• 1010 * (1 mm3) = 10 m3 ~ 3 tons of finished Si

– significant fraction of world production capacity (I think)


scale issues for communication

• if you have N sensor node devices available then each will sample volume Vatm / N(Vatm = volume of the earth’s atmosphere)

• R ~ N -1/3 (R = distance between nodes)• if total mass of all nodes is limited to M

then h 3 ~ M/N h ~ N -1/3

• so in this model h ~ R

• Preceive ~ Ptransmit h 2/R 2 if ≈ h

• Ptransmit ~ -1 dn/dt (n = no. of photons)


• n ~ Ptransmit ( = transmitter on time)

• Ptransmit ~ h 3 and ≈ hso n ~ h 4

• signal:noise = n/Δn = n½ ~ h 2 ~ N -2/3

• so in a scenario where the fundamental constraint is the total weight of silicon you are allowed to use, more data are (obviously) obtained as it is divided into more individual sensor nodes, but the signal-to-noise ratio for each sensor node then decreases as N -2/3 (communicating at ≈ h ~ N -1/3 )


system scale issues• different environments different

gotcha-s– space, oceans, extreme temperatures, etc

• haven’t considered advantageous shapes– e.g., filaments vs. spheres for “sailing”– shape could change with operational mode

• communication efficiency– small size inefficient antenna for long

wavelengths high energy cost / photon– important additional reason to exploit shape


principal conclusions• if you want to travel a long

distance/time/etc– and you have to carry your own food/fuel/etc

• you need a BIG animal/boat/airplane/robot/etc

• inconsistent with a fleet/horde/etc of SMALL ones

• making it quantitative is usually simple:– energy carried ~ h 3 (h = linear dimension)– operating time ~ h 3/P (P = baseline power)– operating range ~ h 3 v/P (v = speed)

– often P ~ h 2v so range ~ h and tmax ~ h/v

• challenge is to figure P for each application


interesting references ...• C. J. Pennycuick, Newton Rules Biology: A

physical approach to biological problems, Oxford University Press, 1992

• Dialogues Concerning Two New Sciences, translated by Henry Crew and Alfonso di Salvio, Prometheus Books, 1991. ISBN 0879757078. Identified as “the classic source in English, published in 1914” on the websitehttp://www.fact-index.com/t/tw/two_new_sciences.html

• Richard P. Feynman, There’s Plenty of Room at the Bottom: an Invitation to Enter a New Field of Physics, http://www.zyvex.com/nanotech/feynman.html

http://www.fact-index.com/t/tw/two_new_sciences.html

http://www.zyvex.com/nanotech/feynman.html

http://www.zyvex.com/nanotech/feynman.html


thanks for listening ...• my contact information:

mel siegel [email protected]+1 412 268 8742 office/lab

http://www-2.cs.cmu.edu/~mws

mailto:[email protected]

http://www-2.cs.cmu.edu/~mws

robotics seminar [email protected] ismcl ri scs1 scaling issues in robotics: strength, range, and...

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