scaling issues in robotics: strength, range, and communication limits on big and small robots

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scaling issues in roboticsstrength, range, and
communication limits on big and small robots
mel siegelintelligent sensors measurement
control labthe robotics institute school of
computer sciencecarnegie mellon university
pittsburgh pa 15213
robotics institute seminar2005 april 22
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• whats the point?

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• Galileo knew big is weak, small is strong
• you know big vehicles have greater rangethan
  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 doesnt 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

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• 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

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1 MJ/kg 1 kJ/g (1/4.2) kcal/g (1/4.2)
food-cal/g carbs 4 food-cal/g fats 9
food-cal/g gasoline 10 food-cal/g what if I
were to use a high explosive, e.g., TNT, to fuel
my robot?
http//hypertextbook.com/physics/matter/energy-che
mical/
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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 effectivetemperature (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.h
tm
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• 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 were not yet good at extracting it
• (Ill mention some groups that are working on it)
• energy does not have to be chemical
• scavenged RF, thermal, ..., energy

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by the way, its 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

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• what are the details?

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well discuss details ...

• ... about strength
• poppa, momma, and baby bearswhat 5-year-old
  kids know that roboticists dont
• ... about energy
• deriving relationships and making numberspoppa,
  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

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strength
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Galileos 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? ...

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dont get too big for your bridges!
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dont get too big for your bridges!
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gravity sets their proportions ...
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and theirs ...
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and theirs ...
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but not theirs ...

• their eyes are your best hint to their size
• mechanics, optics, sensing, chemistry, etc, all
  scale separately

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and not (yet) theirs either ...
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and not (yet) theirs either ...
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dont 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 animals 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

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• 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

data from U.S. National Park Service
http//www.nps.gov/seki/shrm_pic.htm
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energy
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• 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

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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 timein 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)

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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 Maxwells Demon
• extract energy from thermal gradients (legal)
• ... from thermal fluctuations (maybe not legal)

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other power-requirement scenarios
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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 hif moving is cheap vs.
  keeping warm

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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

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• 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

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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

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geometrically-similarrobotic vacuum cleanersof
different size
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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

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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 F model collects only 0.1 as much
  dirt as the 30 cm F model, whereas you probably
  expected 10

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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

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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

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systems
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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)

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scale issues for communication

• if you have N sensor node devices available then
  each will sample volume Vatm / N(Vatm volume
  of the earths 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)

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• n ? Ptransmit ? (? transmitter on time)
• Ptransmit ? h 3 and ? hso n h 4
• signalnoise n/?n 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 )

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system scale issues

• different environments ? different gotcha-s
• space, oceans, extreme temperatures, etc
• havent 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

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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

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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, Theres Plenty of Room at the
  Bottom an Invitation to Enter a New Field of
  Physics, http//www.zyvex.com/nanotech/feynman.htm
  l

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thanks for listening ...

• my contact information
• mel siegel mws_at_cmu.edu
• 1 412 268 8742 office/lab
• http//www-2.cs.cmu.edu/mws

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