ICES-144

Nanorobo ts for Mars EVA Repair

Benjamin Chu i, Lea KissnerUniversity of California, Berkeley

Copyright © 2000 Society of Automotive Engineers, Inc.

ABSTRACT

Current trends in technology indicate that nanometer-scale devices will be feasible within two decades. It islikely that NASA will attempt a manned Mars missionwithin the next few decades. Manned Mars activities willbe relatively labor-intensive, presenting significant risk ofdamage to the Marssuit. We have investigated twopossible architectures for nanotechnology applied to theproblem of damage during Mars surface activity.

Nanorobots can be used to actively repair damaged suitmaterials while an astronaut is in the field, precluding theneed to return immediately to a pressurized area.Assembler nanorobots reproduce both themselves andthe more specialized Marssuit Repair Nanorobots(MRN). MRN nanorobots operate as space-fillingpolyhedra to repair damage to a Marssuit. Both operatewith reversible mechanical logic, though only assemblersutilize chemical data storage.

INTRODUCTION

Humans will be sent to Mars to accomplish objectivesthat robotic missions cannot. "Surface exploration is thekey to the mission," requiring long periods of Marssurface activity.[1] Astronauts will be performingstrenuous activities to meet many objectives, such asdigging for samples, climbing rocks, and hiking longdistances. This will continue for 18 to 20 months, 600days nominal, under the NASA Mars ReferenceMission.[1] Wear and tear on the suits will be a problemas never before, due to a combination of strenuousactivities, damaging terrain, and duration of use. Theprotection of the astronaut in the field depends entirelyon his Marssuit. Because the probability of Marssuitdamage in the field is not negligible, we must developpossible solutions to this problem.

Figure 1: Human Technical Advancement -- As history has progressedfrom the Stone Age to the 21st Century, the level of precision thathumans have been able to achieve has increased with the complexity oftheir tools and materials.

Since the Stone Age, man has gained increasing facilitywith materials. Once man had mastered stonework, hewas able to begin the refinement of ores intoincreasingly pure substances. Relatively recently, asurge in advancement resulted from the BessemerProcess for making steel. Twenty years ago, anengineer's proverbial bread and butter was aluminumand steel. Today, high strength composites such ascarbon fiber are playing an increasing role in advancedaerospace applications. The trend is apparent. As wegain facility with the manipulation of matter, what wasyesterday's advancement becomes today's staple tool.Eventually we will achieve cheap, thorough, andinexpensive control over the structure of matter. Thismeans molecular manufacturing – building objects upfrom the individual atoms and molecules. Initially thiswill result in materials for use in conventionalapplications, such as high-strength diamond fibers andbuckminster fullerene ‘buckytubes.’ As our experienceat the nanometer scale increases, we will move intonanorobotics. (Figure 1)

PROBLEM STATEMENTSFailure modes can be classified into two categories:

1. TearsThe tearing failure mode is characterized by theseparation of layers by a lengthwise scrape or cut.

Minimal loss of suit material is associated with thisfailure mode. A tear might be caused by laceration witha sharp implement such as a surgical blade, stretchingsuit material significantly past its elastic range, or byscraping on a sharp rock. Overstretching should not bea consideration for a well designed suit.

2. PuncturesA puncture is characterized by a large hole. Significantdamage is inflicted on the suit in the immediate area ofthe puncture. It is unlikely that naturally occurringMartian rocks will be able to puncture a Marssuit duringroutine surface activities. A projectile, perhapsaccidentally ‘launched’ from some machinery, mightattain sufficient velocity to puncture a suit. More likely,punctures will be self-inflicted by geologic field toolssuch as picks and chisels. The damage area may betattered, with lower structural integrity in the surroundingmaterial due to deformation caused by foreign objectentry.

3. AbrasionAbrasion will be an ever-present detriment to the suit. Acomparison is made to jeans which while tough whennew, gradually wear thin at the knees or seat area.Unlike the catastrophic failure modes already mentioned,abrasion is a gradual degradation that can eventuallylead to failure. Furthermore, failure due to abrasion canbe prevented. The proposed architecture must addressthe problem of abrasion.

It is of further utility that we define two stages of failure.Primary failure, which can be likened to medical cases inwhich death is a possibility, is damage that extends tothe pressure-retaining layer. Gas loss is the chiefconcern in primary failure. Of less danger, butcommanding immediate attention nonetheless, aresecondary failures. These failures define the class ofdamages that do not penetrate the pressure-retaininglayer. Gas loss is not significant, as the pressurebladder remains intact.

Biological containment will be virtually impossible for amanned mission, due to nonzero suit leakage and otherfactors. Thus biological contamination will not be viewedas a problem, but rather as a consequence of sendinghumans to Mars.

REQUIREMENTSThe repair solution must either allow the astronaut tocontinue working, or provide enough time to return to thepressurized habitat safely. The astronaut must bealerted of any breaches that occur, so that a rationaldecision can be made early on.

Any system that is sent to Mars must be able to functionin the Martian environment. A successful nanoscalesolution must withstand the detriment of thermal noiseand maintain positional accuracy in the range of Martiantemperatures. Dust is also a primary concern formechanical systems.

In order for nanorobots to be economically feasible, theymust incorporate some level of self-replication. Theinherent danger in self-replicating systems is thepossibility of replication without bound.[2] So, it isnecessary to precisely control any replication thatoccurs.

To minimize the time until such a repair system ispractical, it is necessary to initially design a systemutilizing a comparatively low level of nanoscaletechnologies. However, as experimentation increasesour knowledge and manufacturing capabilities, this mayno longer be necessary.

RESULTSHarsh Martian conditions pose many problems toconventional mechanical systems. Dust can clogbearings and mechanisms as well as cause wear andtear. Average Martian temperatures of 223K at theequator and 143K at the poles can pose problems formany systems, affecting fluid viscosity and decreasingthe elasticity of materials.[3] For molecular-scalesystems, however, decreasing temperature merelyreduces thermal noise, or the positional uncertainty thatis caused by molecular vibration. The equipartitiontheorem gives each energy term in a system at thermalequilibrium a mean value of ½kBT where kB is theBoltzmann constant and T is the absolutetemperature.[4] The maximum positional variancesquared is thus kBT/k where k is the stiffness (springconstant) in N/m.[5] The proportionality of positionalvariance to temperature indicates that a lowertemperature increases the accuracy of nanometer-scalemechanical devices. The decreased temperaturerelative to Earth will serve to increase the accuracy ofany molecular positional device.

SINGLE WALL CARBON NANOTUBES

Figure 3: Elastic Properties of Nanotubes – Single wall carbonnanotubes have been shown to possess extraordinary elasticity.Buckling effects are observed (arrows, left) under applied load, but thereis no permanent deformation.[6]

Different configurations of carbon yield materials ofunique characteristics. Diamond, for example has acubic lattice configuration and is the hardest materialknown to man. Carbon fiber is a staple material in theaerospace industry, due to its high strength/weight ratio.Buckminster fullerenes, or single wall carbon nanotubes(SWNT), are a class of diamondoid structures that are ofparticular interest. Carbon nanotubes have beenexperimentally tested to have an average Young’smodulus of circa 2 TPa.[6] By comparison, the Young’smodulus for carbon fiber is 0.8 TPa for relatively highpurity samples.[7] In considering the energetics ofSWNT deformation, it is useful to examine the energyrequired to bend a tube. Tibbetts’ equation for strainenergy is of the form:[8]

22

3

24 R

C

R

Ea

N

Ebend =Ω=

where E is the elastic modulus, R is the radius ofcurvature, L is the length of the cylinder, and a is arepresentative thickness of the order of the graphiteinterplanar spacing (3.35 Å). The total number of carbonatoms is given by N=2 RL/

where is the area per

carbon atom.

The results of this theoretical model indicate that theenergetics of deformation for SWNT nanotubes favorextreme elasticity. They are able withstand significantstresses without permanent deformation. Thesepredictions have been confirmed through experimentalobservation as seen in Figure 3.

The properties of carbon nanotubes indicate that theymay be useful in strong composites. A chief determiningfactor of fibrous composite stiffness is the axial ratio(length/thickness) of the constituent fibers.Manufacturers, however, desire shorter fibers for use inlow-cost injection molding processes. Because of theirinherently small size, carbon nanotubes can achieveexceptional axial ratios. Typical SWNT diameters are onthe order of 1-2 nm (10-20 atomic diameters), withexperimentally achieved lengths of thousands times the

diameter.[9] Even in the case of an axial ratio of 1000, itwould merely mean dealing with fibers on the order of10-6 m. Typical short fiber glass or carbon fiber axialratios are around 10 (length/thickness) with microndiameters. The uniform linear crystalline structure ofSWNT nanotubes (Figure 4) indicates that unlimitedlength nanotubes are theoretically possible. If ‘spoollength’ nanotubes were achieved, the application ofSWNT fibers would be extended into the realm ofcontinuous fiber composites. Graphitic carbon and glassare the most commonly used continuous fiber materials.Interwoven continuous fiber nanotube composites wouldpossess desirable characteristics, such as extremelyhigh modulus and the ability to withstand large loads inthe direction of fiber orientation.

Figure 4: Buckytube Structure – Single wall carbon nanotubes aretypically 1-2 nm in diameter, and can theoretically be any length.[9]

For the technological level of the proposed architecture,active abrasion repair is not incorporated. Instead, werely on advanced suit materials such as interwovennanotube fabrics. Theoretical models done byYakobson and Smalley indicate nanotube fabrics willhave the desirable property of inhibiting stress singularitypropagation.[10] This is just a manifestation of thefamiliar property of many matrix composites: crackdeflection along the fiber due to low interfacial strength.In the case of a nanotube fiber bundle, the interfacialbonding is due to the van der Waals force – the samecharacteristic that gives graphite its lubricity. The crackdeflection is a key feature we seek in preventingabrasions from growing into more serious damage. Apreventative measure might be to incorporatereplaceable pads into high-wear areas of the suit.These high wear areas can be determined by simulation,or by observing real geologists in the field.

Carbon nanotube materials have the potential to replacecontemporary composites in aerospace applications.High tensile strength nanotube fabrics will be strongerthan Kevlar, and should prevent Marssuit punctures inall but the most strenuous conditions. Stiff nanotubematrix composites should be much stronger than currentcarbon fiber composites, while retaining the tougheningmechanisms of crack deflection and fiber pullout.Marssuits will undoubtedly use the most advancedmaterials, and so the focus must shift to when Marssuitsfail.

NANOROBOTICSA robot is a combination of a computer and aconstructor, in the most general case a UniversalComputer (something that can calculate anythingcomputable) combined with a Universal Constructor(something that can build anything that can be built).[11,12] This combination could, in Von Neumann's theory,reproduce anything, including itself. When one shrinksthis robot to a nanometer scale, it becomes botheconomical and practical to manufacture nanorobots torepair a Marssuit.

This architecture contains two distinct types of robots:assemblers and MRN nanorobots. It is not necessary tohave designed and implemented Von Neumann'sUniversal Constructor to have practical assemblers.These assembler nanorobots need only the capability toreproduce themselves and to manufacture MRNnanorobots. Assembly takes place in a speciallyconstructed tank, which remains in the habitat,manufacturing MRN nanorobots and assemblerswhenever needed. MRN nanorobots are removed fromthe solution and added to the suit to begin their work.Though based on the same technology, these differentrobots have significant differences in design andcapabilities due to their different roles.

The system of assembler nanorobots utilizes abroadcast architecture (Figure 5), both to decreasecomplexity and increase safety.[5] Each “molecularconstructor,” or assembler, has a very limited onboardcomputer, limited mostly to interpreting and applyinginstructions broadcast from a macroscopic computer. Itis far more practical to perform the complex calculationsnecessary to build nanorobots of many precisely placedmolecules in a macroscopic computer. To move thistask to the assembler would require far greaterprocessing power and storage capability than will bepractical for some time to come. This architecture alsoenforces the most basic possible safety precaution:protection against undue replication. As each assemblerhas only enough capability to decode and carry out theinstructions transmitted to it, it cannot start replicatingwithout bound. This simple precaution can prevent the“extraordinary accident” of runaway replication.[13]

Figure 5: Broadcast Architecture – In a broadcast architecture, manymolecular constructors are under the complete control of a singlemacroscopic computer.[5]

Instructions can be transmitted in a variety of ways, butthe simplest and most practical for our purposes utilizesthe liquid environment of the assembly tank. Themacroscopic computer can transmit informationacoustically.[1] Each assembler can be equipped with apressure sensor and the rise and fall in pressure can beinterpreted as instructions. Though chemical signals,like those used in biological organisms, are possible, theslowness and sensor complexity required for thisscheme is prohibitive.

This liquid environment not only allows communication,but practical dissemination of needed molecules to theassemblers. Energy and raw materials are suspendedin the “feedstock” liquid.[2] Fuels can be added forenergy, and easily manufactured ‘parts’ reduce thecomplication of assembly. These ‘parts’ are actuallymolecules that can be easily linked together by theassembler, and thus are ideal building materials.Wastes can be disposed of easily into the feedstock. Bydesigning the assemblers to rely on this feedstock, weadd another measure of safety to our design.[14]

Assembler robots are far more flexible in theircapabilities than their MRN nanorobot counterparts.MRN nanorobots are specialized robots, made to finddamage in the suit, recognize it, and repair it.Assemblers have a manipulator that can be turned to awide variety of tasks, making the extreme safetyprecautions a necessary part of their design. The MRNnanorobots have only one task, and so its instructionscan be programmed into the design and checked beforethey are deployed. Should a MRN nanorobot’s logic bedamaged, it becomes as useless and harmless due toits limited capabilities. This is an acceptable outcome,as it cannot harm the astronaut. It is impractical toattempt to communicate with the nanorobots in anycase, as they lack a suitable medium for signaltransmission.

In a liquid medium, pressure or chemical signals can besent to a large number of nanorobots at once. However,sending these sorts of messages through a mixture ofgas and other nanorobots is not practical. Themovement of the astronaut will destroy pressure signals.Chemicals have no medium to travel though. Extremelyweak electrical signals could be passed through a thinlayer bonded to the suit’s inner layer. However, MRNnanorobots that are not in contact with this layer cannotreceive the signals. Signals can be passed from robot torobot using any of these means during contact. Due tothe extreme complexity of controlling this sort of adistributed network and the essential unpredictability ofsignal transmission, this proposed architecture does notincorporate these capabilities. The system will functionwithout it, and requires a lower level of technology,decreasing the time needed before it is possible.

We shall take a strategic approach to the designrequirements of Marssuit Repair Nanorobots. When the

suit is damaged, the nanorobots should converge uponthe affected area and begin repair, much like our ownbiological repair system. The method in which they‘attack’ the damage must be fast and efficient. Becauseof the time constraints, a molecular level reconstructionof the suit material is unfeasible. Temporary repairsolutions are attractive if they are fast. The logicalnanorobotic approach is to utilize fast-movingnanorobots to fill up the breach. This can beaccomplished with nanorobots in the form of space-fillingpolyhedra (SFP). (Figure 6) SFP nanorobots quicklyseal breaches by interlocking with one another insuccessive waves until the damage is sealed.

Figure 6: Space-Filling Polyhedral Nanorobots – Space-filling polyhedralnanorobots rapidly converge upon damaged areas and seal them

Virtually every robot ever constructed has been made upof four common components.[15] These general designprinciples carry over as well into the molecular scale,and provide general guidelines for organization. Amanipulator is “a collection of mechanical linkagesconnected by joints to form an open-loop kinematicchain” used for any manipulation or movement by therobot.[15] Sensors convey information about the statusof the manipulator or any number of outside conditions.The controller is the ‘brain’ of the robot, sequencing andinterpreting data from the sensors to control themanipulator. The power-conversion unit providesenergy to the system.

MANIPULATORIn order to operate effectively at the atomic scale,scientists require methods for manipulating the atomicworld. Chemists have been operating at the atomicscale for centuries, but deliberate placement ofmolecules to specific sites has only been achievedrecently. Today’s method of atomic manipulationrequires extensive laboratory equipment such as atomicforce microscopes (AFM). This is laborious, andeconomic production of large quantities of tailoredatomic constructions is unfeasible by this method. If weare to achieve efficient control of atomic levelconstructions, we must have ‘hands’ that are equivalentin scale.

Intrinsic to any successful manipulation tool is highpositional accuracy. Nanometer positional devices willnecessarily be stiff in order to combat the detrimentaleffects of thermal noise. They must also achieve arequired positional range. For atomic construction, amanipulator must have six degrees of freedom. Merkle’sanalysis of six degrees of freedom positional devicesgives a reasonable analysis of possible manipulatorconfigurations.[16] His conclusions indicate that serialdevices (multiple joint arms) are inferior to the paralleldevices that utilize extending struts for positionaldetermination. Among parallel devices, the Stewartplatform (Figure 7) is of interest because of its simplicity.

The Stewart platform consists of a tool-holdingmechanism with a triangular base and six movablestruts. For nanorobotic purposes, the tip of the Stewartplatform serves as a versatile nest site where variable-affinity molecular ‘tools’ can be affixed. An excellentaspect of the Stewart platform is that the struts needonly support tension and compressive forces, as thebending moments are negligible due to the constraints ofthe design.

Figure 7: The Stewart Platform – The Stewart platform has six 100 nmlength struts, which provide six degrees of positional freedom to themanipulator tip.

If Stewart platforms are to be used on Mars, theirproperties must be examined. To specify the minimumdiameter of the struts, a numerical exercise is useful.

Stretching stiffness is given by:

LErkstretch2π=

where E is Young’s modulus (2 1012 Pascals for SWNTnanotubes), L is the length of the strut in meters, andkstretch is the equivalent spring constant, k. By equatingspring energy and thermodynamic energy for a smalldisplacement along a rod axis, it is found that

Positional variance = 2 = kBT / k (4.1)

where is the mean displacement. By substitution,

Positional variance = 2 = kBTL /(πr2E) (4.2)

or, in terms of the minimum diameter to meet positionalrequirements,

Diameter = 2r = 2kBTL /(π 2E)]1/2 (4.3)

The numerical values used are:

L = 10-7 m (100 nm)

Positional variance (choose 1/10 of an atomic diameter):

2 = (0.1 Å)2 = 10-22 m

E = 2 1012 Pa (Young’s modulus for carbonnanotubes)

kBT = 3 10-21 J (using Mars’ mean equatorialtemperature, 223K)

By substitution into Equation 4.3, the minimum strutdiameter is found to be 1.4 nm. Single wall carbonnanotubes are precisely applicable as struts. In fact,SWNT nanotubes are the only viable molecular structurethat has all the properties we seek. Macroscopicactuator bodies are usually constructed from aluminumor steel. For the same reasons (simplicity and strength),the ‘monoelemental polymer’ structure of SWNTnanotubes make them a good choice. Because ofcarbon nanotubes’ hollow cylindrical nature and highmodulus, they are uniquely suited to acting as linearactuators. Nested nanotube actuators can be driven bypressure differences. (Figure 8) By varying the internalpressure with feedstock molecules, the nanotube strutcan be made to extend or retract.

The effective seal of properly nested carbon nanotubes3.35 Å due to the van der Waals radii between theconstituent carbon atoms in the nanotubes. Van derWaals repulsive forces serve as a barrier to particles,and so the problem of leakage is negligible. With properpressure differentials between the actuator reservoir andthe external environment, different magnitudes of forcecan be exerted and translated into movement throughthe Stewart platform tip. An assembler can utilize amatrix of Stewart platforms in order to create moreassemblers.

Figure 8: Molecular Actuator – A carbon nanotube nested in an openbuckytube can serve as a molecular actuator.

The assembler operates essentially like a factory. Adiamondoid wall encloses the ‘factory floor,’ which iseither a vacuum or filled with inert gas. Each Stewartplatform acts as a tool. If assembly were to take placeexposed to the feedstock, it would limit the effectivenessof the Stewart platform. Exact construction would bedifficult, if not impossible as molecules in the feedstockreacted with the molecular tool at the platform’s tip. Thisenclosing wall also insulates the molecular actuatorsfrom the effects of change in external pressure.

One can think of MRN nanorobots as an active adhesivesealant. When a breach occurs, the robots literallytumble end-over-end to form a protective seal. Inessence, space-filling polyhedra are equivalent tobiological platelets. The mode of locomotion ischaracterized by repeated pivots about common edges,as the polyhedra are identical geometric structures.[17]An effective layer of these polyhedral nanorobots will bepresent in the Marssuit, so that time is not wasted intraveling to damaged areas. The first nanorobots arriveat the damaged area quickly, because they are directlyadjacent to the damage. By either chemical ormechanical signal, the front line of nanorobots issignaled to anchor to the remaining suit material. Thisanchoring might be done with a tailored chemicalreaction, forming a chemical bond with the suit and thuspermanently anchoring the MRN.

By mechanical design, the nanorobots are capable oflatching on to each other. As the repair progresses, thenanorobots begin to layer upon one another until theyhave formed a barrier around the damage. Tears shouldpresent little difficulty as the interlocking polyhedra can‘bridge’ a small rip with minimal locomotion. Puncturesare challenging due to possible outgassing, which wouldhinder the convergence of the nanorobots. Withsufficiently strong mechanisms, a violently outgassingbreach might be sealed, but a more elegant solution ispreferable. By orienting the polyhedra such that theyattach to the underside (facing the surface) of theMarssuit, successive waves of nanorobots can approachthe previously established edge and then ‘hang on.’ Forexample, consider a circular puncture. As the SFP

nanorobots repaired the hole, one would see the breachclose in concentric circles.

Gas leakage is undoubtedly the most pressing concernin the event of suit damage. The MRN nanorobots’primary function is to seal the breach and thereforeprevent rapid gas loss. Without going into detailedstatistical mechanics, several arguments will suffice toplace an upper bound on gas loss. Assuming that thenanorobots are cubic in shape and is ∆ (arbitrary units)on a side, the effective area presented to an incidentmolecule is ∆2. A likely choice for a wall material is thegraphene sheet, which serves as a large potential(electrostatic, etc.) barrier to incident molecules. Thegas loss through the MRN faces will be negligiblecompared to through the interfacial gaps. Let us nowassume that the interfacial gap width is σ = ∆ / 100. Forinstance, a 50 nm gap (5000 nm MRN) is room aplentyfor a variety of nanotube latching mechanisms. For alarge number of nanorobots tessellating over a breach,the number of gaps per MRN approaches two. Then,neglecting the corner effects, the effective area for gasflow is reduced by a factor of 2σ∆ / ( ∆2 + 2σ∆ ) = 1/51.About 2% of the initial area is available for leakage.Now consider that a 1 mm layer of nanorobots of ∆ =5,000 nm will have about 200 layers of MRNs. In thelocality of a puncture the repair will probably be thickerthan one millimeter, further attenuating the leakage. Thespecifics of the attenuation have to do with the ‘lattice’configuration of the nanorobots. For the cubicnanorobots there is a straight path for molecules to takesince the layers are not staggered, so we can expect arelatively low attenuation effect. Other geometries suchas the rhombic dodecahedron do not present such aclear path for molecules to escape. For the morecomplex geometries, we can expect a quasi random-walk pattern to develop. Furthermore, the interfacial gapis not just open space – it is crowded by the MRNlatching mechanisms. From this rough estimate we seethat the MRN presence significantly lowers the leak rate.We also notice that the cubic configuration turns out tobe the least desirable in terms of sealing effectiveness.

If the space filling polyhedra operate as desired, we canexpect the resulting repair to be rather stiff like a scab.This is due to the space tessellation of the polyhedra,and the interlocking mechanisms. The question of brittlefracture arises when dealing with stiff materials.Because the nanorobots are built up in successivelayers, the same toughening mechanism as withnanotube fiber composites is possible. That is, anadvancing crack tip is deflected along the interfaciallayers thereby reducing the stress concentration. Also,we must not forget that the MRNs form a dynamicallyreconfigurable barrier, so that if a crack manages topropagate past several layers of nanorobots, therepairing process will repeat anew. Ideally, theastronaut should deliberately avoid subjecting such arepair to high impact loads. Normal astronaut

locomotion should not be effected by this repair, as thearea around the repair should remain flexible enough toaccommodate the ‘scab.’

Let us now deal with the problem of dust. Atmosphericdust on Mars has a size range of about 50-100 µm.[18]Most of the dust directly on the Martian surface will beequivalent or greater in size. Since we have not yetcommitted to a specific size for the MRN nanorobots letus take a conservative estimate of 5,000 nm (5 µm),which is about the size of a human red blood cell. Bythis estimate, typical Martian dust is over ten times thesize of a MRN. If a speck of dust is embedded such thatit is not dislodged by outgassing, the nanorobots havelittle choice but to build up around the impediment. Thisis likened to a nail or thorn puncturing a tire that has acommercially available gel sealant – the breach issealed despite the impediment. The same argumentapplies to larger penetrating objects as well.

Many mechanically useful nanoscale components havebeen developed that could be used to construct suchpolyhedral nanorobots. Once again, SWNT nanotubesare ideal structural members for nanometer construction.Researchers at Rice University have developed amethod by which open nanotubes can be tethered togold particles, forming useful mechanical linkages.[19]The perfection of this technique could allow us toconstruct a variety of polyhedral shaped structures.NASA researchers have modeled feasible gears fromopen nanotubes, and Merkle has simulated a viablemolecular bearing.[20, 21] The inherently voluminousfamily of polyhedrons presents an ideal enclosure formechanical logic components and fuel reserves.

SensorsNanometer-scale sensors will be difficult to design in thebeginnings of nanorobotics. Sophistication in this areawill develop with research – but this will take time. Todecrease the time and research needed to develop thisMarssuit repair system, only the simplest possiblesensor arrays are used.

To implement the broadcast architecture for theassembler nanorobots, there must be a way to receiveinstructions. A molecular actuator (Figure 8)constructed of nested SWNT nanotubes can be easilymodified for this purpose. Instead of modifying theinternal pressure to produce an external effect on theactuator, the actuator is exposed to the pressures of theassembly tank. As the pressure changes, the actuatorwill move, which can be easily transmitted to the controlsystem.

There are many different devices that sense position,from potentiometers to springs. Many of these can bescaled down effectively to the nanometer scale and usedin nanorobotics. One approach to movement of the

Stewart platform (Figure 7) is to measure every aspectof its movement. Using a standard Proportional IntegralDerivative (PID) control system, one can control theplatform very accurately. However, due to the entirelack of friction on the molecular scale, if the pneumaticsor engines to move the platform are very accurate, thesesensory capabilities are not required. When usingreasonably stiff structural elements, thermal noise willnot cause more than a fraction of an atomic diameter ofpositional error, without explicit positional sensing.[5]

The capabilities required on the MRN nanorobotare quite different than those of the assembler. MRNnanorobots need to be able to make their way towardsthe site of suit damage, and detect the damage whenthey have reached it. To reduce sensor requirements asmuch as possible, MRN nanorobots can be programmedto act like gas molecules in many respects. Consider abox with a partition through the middle. One side is filledwith gas at a certain pressure, while the other side is avacuum. If the partition is removed, the gas moleculesmove towards the area of lower concentration. BecauseMRN nanorobots move randomly about common axeswhen a certain number of faces are not in contact withother nanorobots, they move naturally towards areaswhere there are few nanorobots because they are morefree faces in that direction. Once damage occurs, therewill be a local decrease in ‘pressure’ of MRNnanorobots, which will carry them towards the damage.

Once they reach the damage, they need to be able torecognize it. How this can be implemented dependsconsiderably upon the material used. In any case, theyshould be able to sense a chemical difference betweenthe surface of the fabric and the edge of the fabric, sothey will know to bond to it. It is a more difficult problemto detect a MRN nanorobot that has bonded to the suitfabric. There are several ways of accomplishing this,including displaying the chemistry of the broken suitfabric on a face, so that other MRN nanorobots candetect it upon contact and will cease to pivot. Anothermethod is extending claws or other small extremities thatcould be sensed on contact with other MRN nanorobots.

These contact signals are inherently directional, as theMRN nanorobots will adhere to the surface on whichthey detect them. To directionalize the repair towardsthe hole as opposed to making it essentially random,MRN nanorobots can display the signal on the faceopposite to the one adhered to the previous MRNnanorobot. This way, they will repair more or lessaligned with the damage, and can meet to seal the hole.

ControlTwo basic types of logic have been designed forcomputers: mechanical and electrical. Innanocomputers, size is a major limitation. As electronscan tunnel through distances of a few nanometers, this

greatly increases the minimum size of nanoelectricdevices.[23] Mechanical logic devices can reach twonanometers before thermal noise makes them unreliableat room temperature.[24] Though nanoelectric deviceswill become feasible at some point, mechanical logic willlikely precede it and remain as compact, low-speed logicand storage.

Conventional computer architectures use an irreversiblearchitecture. This is a design in which one losesinformation during the course of a calculation, and socannot deduce the inputs from the outputs (Figure 9).However, to effect this erasure of information requiresln(2)kBT Joules of energy per bit to be dissipated asheat, where kB is the Boltzmann constant and T is theabsolute temperature.[2] Each and gate, for example,erases one bit of information. Macroscopic computersare designed to have enough airflow through them todissipate this heat, but nanocomputers will not have thisluxury. The energy dissipated as heat is lost energyfrom the system as well, requiring a greater energyinput.

The solution to this problem is simply not to erase anyinformation – to make the calculation reversible. Oncethe calculation is run, store the result and then run thecalculation in reverse to ready the computer for anothertask. A reversible computer can be run with as littleenergy as desired, simply by running calculations moreslowly to reduce friction, as the ln(2)kBT limit does notapply.[24] There is probably some practical limit due tofriction and molecular interaction, but this certainly liesfar below the thermodynamic barrier.

A B Output A B Output1 1 1 1 1 11 0 0 1 0 10 1 0 0 1 10 0 0 0 0 0

A B C D A B C D1 1 1 1 1 1 1 11 0 0 1 1 0 1 00 1 0 1 0 1 1 00 0 0 0 0 0 0 0

Figure 9: Conventional and Reversible Logic Gates – Conventional logicgates (top) dissipate energy because they discard information. Forexample, if the output of an and gate is 0, there is no way to deducedefinitely what the input was. Reversible logic gates (bottom) do notdiscard the unneeded bits (output D) and thus can be run reversibly, withminimal energy loss.

A mechanically equivalent macroscopic logicdevice is a simple spring. Arbitrarily, the stretched stateis defined as 1, and the compressed state as 0. While inits equilibrium state, the spring conveys no information.To represent a bit of information in the spring, one hasto invest ½ kx2 Joules, where k is the spring constantand x the displacement from equilibrium. In anirreversible architecture, once the bit has served its partin a calculation, it is erased. This is equivalent to thespring being released. As no spring is perfect, theoscillatory behavior will decay towards the equilibriumposition. The ½ kx2 invested in storing the informationwill be lost to friction, the second term in Equation 4.4.

Motion of a damped (frictional) spring:

02

2

=++ kxdt

dxb

dt

xdm (4.4)

However, if one restores the spring without releasing it,allowing the –kx force from the spring to pull it back, theenergy can be recovered. As this is not a perfectsystem, the frictional second term in Equation 4.4 doesnot allow the storage or recovery to be perfectlyreversible. However, the frictional term b is proportionalto dx/dt, or velocity. Therefore, reducing the speed atwhich the spring moves can reduce the energy lost tofriction to any arbitrary level.

Several different types of mechanical reversible logichave been proposed. Drexler proposed "rod logic,"where interlocking gates and knobs on rods performBoolean logical operations reversibly.[25] (Figure 10)Merkle has proposed a scheme with bistable computingelements pulled by springs.[22] DeMara has developeda system with helical latches, reset springs, and rodassemblies.[26] Each of these forms of logicaloperations is a practical solution, and we shall not givepreference to any of these schemes at this point.

Figure 10: Rod Logic – This and gate is an example of Drexler’s rodlogic. If both lower rods are in the 1 position (left), then the probe knobspass through the gates when driven. This can be interpreted as a 1. Ifboth lower rods are not in the 1 position (right), the probe knobs cannotpass through the gates, and the upper rod cannot move. This can beinterpreted as a 0. Gates or other probe knobs can be attached to otherfaces of the rods, enabling this and gate to operate as part of a largercomputer.

Like the four components that make up a robot, fivecomponents make up a computer: input, output,memory, datapath, and control.[25] Sensor data is input,as instructions to the manipulator are output. Memorycontains data and programs. Control directs thedatapath, I/O, and memory. The datapath is the actualcalculation mechanism.

Input is read directly from the sensors. If we are usingmechanical logic, it is simple for the sensors to setmechanical devices to be read directly by the computer.This would involve a loss of at least ln(2)kBT per bit, butwould be insignificant compared to the workings of theentire nanocomputer. Output can be handled in this wayas well, by setting mechanical devices. These can stopmotors or pneumatics, or restrict the motion of parts ofthe manipulator as needed. If needed, these can beoperated reversibly in the manner of shared reversiblemechanical memory, but the small number of bitsneeded for this uncomplicated manipulator render thisunnecessary.[20]

Main memory can be implemented with latch rods orhelices.[20, 24] If operated irreversibly, main memorywould have to be kept extremely small because of theln(2)kBT Joule energy dissipation. Though thenanocomputers on both the assemblers and MRN

nanorobots are quite simple, limiting main memory inthis way would unnecessarily decrease the capabilitiesof these nanorobots and necessitate a completeredesign for any other model. Instead, operatingmemory reversibly can solve these problems and scaleto more complex architectures as well. Once theinformation is computed and stored in main memory, to‘erase’ the information, one simply recomputes theanswer in memory. Then, the mechanical main memorylatches can be released. This differs fundamentally fromsimply writing over the information, and thus losing it,because it is done reversibly and thus with as littleenergy loss as is required.[20]

Secondary storage is not required on MRN nanorobots,but to reduce the complexity of assembler calculations,we choose to add secondary memory to the assemblers.A feasible chemical storage involves using Hydrogenand Fluorine atoms at specified places along a polymerto represent the state 1 or 0. A probe molecule, mostfeasibly (CH3)3PO, can be used like the head on a diskdrive to read the state of the polymer and its embeddeddata.[26] As the entire computational task of theassembler is to interpret instructions from themacroscopic broadcasting computer, there is no need towrite to secondary storage. The polymer can befabricated, complete with data, during assembly. Thispolymer functions quite like a punched paper tape in anold mainframe. The data cannot be written except forwhen it is originally made, making it read-only memory.A head passes over it sequentially to determine whethereach particular position represents the state 1 or 0.

The datapath is constructed with reversible mechanicallogic. The calculations must temporarily storeintermediate values in order to reverse the computationand avoid losing information and the associated energydissipation.

Control is handled quite differently in the assembler andthe MRN nanorobot for reasons of safety. Theassembler utilizes the broadcast architecture describedearlier, with a macroscopic computer directing theactions of molecular assemblers. To enforce this model,control is tightly regulated in the assemblers. They haveonly just enough capability to receive an instruction frominput and translate it into output instructions to themanipulator. There are a very limited set of instructionsthat control can utilize, so that a mistake in manufacturecannot lead to an "extraordinary accident." If anassembler is manufactured incorrectly, it cannot functionwithout external instructions, and the worst-casescenario is the creation of flawed MRN nanorobots orassemblers that will be useless and harmless as well. Itis far more probable that a flawed assembler will ceaseto function at all.

The control systems of MRN nanorobots are handledmuch in the manner of early computers, such asBabbage’s Analytical Engine and other computers

preceding the stored program concept.[11, 27] Beforethe stored program concept, all computers were eitherconstructed for one particular task, or reprogrammedlaboriously by rewiring the entire computer or basicallyreconstructing the entire mechanical computer. For thesake of both simplicity and safety, we choose toconstruct the MRN nanorobots the same way. Theyhave no need for more than one task and so do not evenneed the option of reprogramming. In this way, they arenot able to do anything more than their originalprogramming.

MRN nanorobots should be tested before they arereleased into a suit. However, the worst-case scenariofor a flawed MRN nanorobot is that it fails to repair ahole in the suit. As there are billions of other MRNnanorobots in the suit for exactly that purpose, the otherones will seal the hole, moving around the flawed one asan unmoving pivot.

These nanorobots cannot ‘evolve’ into a robot withcapabilities the original does not have. The assemblersand MRN nanorobots are designed in such a way thatany mistake in their fabrication simply flaws thembeyond repair. As there are no useful forms that a‘mutation’ can take, they cannot ‘evolve.’ Experimentsshow that computer programs virtually always simply failto work if they are ‘mutated,’ and "unless they arespecially designed, replicators directed bynanocomputers will share this handicap."[14]

Power ConversionThe first problem in power conversion is separating thefuel from the other molecules in the externalenvironment. Drexler has proposed a "sorting rotor."[25](Figure 11) This rotor is embedded in the diamondoidwall in such a way that as the cam turns, a portion of therim will cycle from the outside environment to the inside.Around the rim of this rotor are variable-affinity bindingsites for the desired molecule. These sites are controlledso that when they are exposed to the outer environmenttheir affinity for the desired molecule is high, and whenthey are turned to the inside their affinity is low. Apossible way to eliminate affinity while turned to theinside is simply to mechanically push a rod into thebinding site, physically precluding occupancy.[29]Binding sites should have an extremely low affinity for allother molecules in the feedstock mixture. In this way, asection of the rim will turn to the external reservoir,adjust the binding sites for high affinity, and bind to thedesired molecules. Once the cam has turned them tothe internal reservoir, the binding sites are adjusted forlow affinity for the desired molecule, and it unbinds andremains in the internal reservoir. By using several ofthese in a "cascade," the purity of the desired moleculein the final inner reservoir is extremely high, and themolecule can be presented in any orientation desired.

Figure 11: Sorting Rotor – Variable affinity binding sites on a rotor makeit possible to separate fuel and other molecules out of the feedstock.Operated in reverse, they can dispose of wastes.[23]

Many molecules can serve as fuel. They can either beone-use molecules like hydrocarbons, or reusable fuelslike Adenine Triphosphate (ATP). ATP is the energystorage unit used by the cells in animals. Threephosphate molecules are loosely bonded to the rest ofthe molecule, and breaking these bonds releases amanageable amount of energy, unlike the combustion ofhydrocarbons. The ATP molecule, stripped of one ormore of its phosphates, returns to have them re-addedand more energy stored. This is a practical fuel modelfor nanorobotics because it releases manageableamounts of energy and the waste can be easilyconverted back into fuel by enzymes in the feedstock.

Waste removal can be handled in the same manner asfuel separation, except in reverse. Another rotor’sbinding sites can have high affinity for the wastemolecules that result from the assembly process. Whenthe cam rotates the sites to the external reservoir, theaffinity of the sites for the waste molecules can bereduced, possibly by mechanically forcing a rod into thesite. The waste molecules will disassociate from thebinding sites and join the feedstock. To prevent thefeedstock from becoming too high of a concentration ofwaste molecules, a filtration system can removeimpurities and waste molecules. This can be achieved ina number of ways, including another set of rotors withvariable-affinity binding sites. Wastes can be removedpermanently from the feedstock, or used as raw materialto make new molecules for the assemblers.

While this is quite practical for the assemblernanorobots, there is no feedstock to transport fuelmolecules to the MRN nanorobots. It is possible tosimply assemble the MRN nanorobots with a reservoirmuch like a fuel tank. Before the construction of this tankis completed, the assembler can simply fill it with fuelmolecules. There are a few problems with this approach,however. The first is waste – if we supply the MRNnanorobot with enough fuel molecules for an extendedstay in the suit, many of these molecules will not beused. Once a MRN nanorobot repairs damage to thesuit, it simply becomes a part of the suit and essentiallydead. It has no need for fuel in this state. Perhaps as a

part of the repair process, it could open its fuel tank andlet the molecules float free. This would only benefit MRNnanorobots in the immediate area, however, and manyof the molecules will probably escape through thebreach without being collected. If the MRN nanorobothas only enough fuel for a limited amount of activity, itmust be removed to make room for other MRNnanorobots after its fuel has expired. Perhaps the layerthe MRN nanorobots are to repair could be exchangedfor a new one with fresh MRN nanorobots periodically orafter extreme damage. The nanorobots could beequipped with a sensor for a certain chemical signal thatwill not occur in the suit naturally. This chemical signal isinterpreted as an instruction to detach from the suit.They then become essentially dust which can be rinsedoff the layer and replaced with fully fueled MRNnanorobots. It is more elegant to refuel the MRNnanorobots, but not strictly necessary. Once washedinto the tank, the assemblers could be instructed by themacroscopic computer to open up the fuel tank and fill itagain. After refueling, MRN nanorobots can again bereturned to the suit. Without the feedstock to removewaste molecules, MRN nanorobots have to store theirwastes on board. Another tank similar to the fuel tank,with easy access for the assemblers to empty it, couldbe added to the MRN nanorobots to store wastes.

Suit Integration

To obtain information about the operation of the MRNnanorobots, there must be some communicationbetween the nanorobotic system and the rest of the suit.It is neither necessary nor desirable for an individualMRN to hold any information about its environment, butmerely to move in accordance with its programming.Systems consisting of many objects with a simplebehavior can exhibit a desirable "emergent behavior" ifthe simple behavior is carefully chosen. By putting theunderstanding of this emergent behavior in the suitrather in the individual MRN, we reduce complexity inthe nanorobots, which are by far the mosttechnologically difficult portion of the system.

Simple communications can be achieved by addinganother molecular actuator to each face of an MRNwhich mates with a simple detector which can bepushed inwards by the actuator. We define thereception of a signal as when one of the detectors of anMRN is depressed a single time. A signal is propagatedby actuating the molecular actuators of the other fivefaces, or some subset of these including the faceopposite to the one on which the signal was received. Ifthe received signal is propagated with a probability p(0.5 < p < 1), we will see a diminishing signalpropagating roughly outwards from a source, withsmaller signal waves washing back. Adding a smallrefractory period to the response will ensure that thesignal will propagate little, if at all, in any but the radial

direction. The probability of propagation includes suchfactors as having broken nanorobots in the system, whocannot pass on a signal, as well as foreign mattertrapped in a matrix of MRN nanorobots, which will notpropagate the signal. These signals do not need to beinterpreted by the nanorobots they pass through, butsimply passed on.

By embedding ‘listening stations’ in the fabric of the suit,these signals can be put to use. The MRN nanorobotsthat are adjacent to the fabric of the suit are propagatingsignals into it as part of their normal propagationprocess, and a simple receiver can capture the signalsand send them back to the main suit processor foranalysis. A listening station should be as large asseveral MRNs, so as not to be rendered vulnerable tobeing covered by a broken nanorobot and therebyhaving its signals blocked. By analyzing the signalsreaching different locations, we can infer what ishappening in different locations in the suit.

A signal is produced at the end of every move by anMRN. Normally, only a few MRN nanorobots will bemoving at any one time, and these the farthest from thefabric surface. The signals captured by the listeningstation under these conditions will be relativelyinfrequent, as the signals degrade over time anddistance and there are not a large number of them beingproduced. However, during the initial moments of a ripvirtually all of the nanorobots in the area of the rip will bemobilized, putting out a very large number of signals,which are easily distinguishable from the signal receivedunder normal conditions. Since a signal degrades overdistance, those listening posts that are very close to therip will receive far more signal pulses than those fartheraway. By using a system of triangulation based onsignal duty cycle, the suit can infer the severity andlocation of damage.

CONCLUSIONS

Carbon nanotube materials can be used in many placeswhere a light, strong material is required. The elasticproperties and high tensile strength of nanotube fabricsmakes for an ideal material in Marssuit construction.The toughening effect of crack deflection furtheraugments the utility of nanotube matrix composites.

Used in combination, assemblers and MRN nanorobotscompose a practical system for actively repairingMarssuit damage. Assemblers work within a feedstockenvironment, rich with fuel molecules and the rawmaterials with which to construct copies of boththemselves and MRN nanorobots. A broadcastarchitecture sends signals from a central computer to

each assembler through the liquid medium of thefeedstock, ensuring safety and reducing thecomputational requirements of assemblers. Inside their‘factory floor’ – either vacuum or inert gas – are an arrayof Stewart platforms constructed with molecular strutsand SWNT nanotubes. Sensors include possiblepositional sensors to determine the position of theStewart platforms, and a molecular actuator built ofnested SWNT nanotubes to receive broadcastinstructions. Fuel and raw materials are separated fromthe feedstock by a Drexler sorting rotor, and wastesremoved in the same way.

MRN nanorobots act as space-filling polyhedra to repairthe damage to a Marssuit. To reduce the need forsensors, they move in a random fashion like gasmolecules. A local decrease in ‘pressure’ of nanorobotswill carry them towards the damage, which they senseon contact with chemical sensors. Unable to receive fueland dispose of wastes in the feedstock, they carry tankswith fuel molecules and wastes. If they are to berecycled, the assemblers can open the tanks, removethe wastes, and replenish the fuel.

Both types of nanorobots will utilize mechanicalreversible logic. This will dramatically reduce bothenergy expenditure and heat dissipation, which isdifficult on a molecular scale and could damage ordisable the nanorobots. Assemblers will also have read-only chemical memory, implemented with a modifiedpolymer and a chemical probe.

New materials such as SWNT nanotube compositeshave the potential of providing superior strength/weightratios. Theoretical predictions and experimentalobservation indicate that carbon nanotubes have goodelastic characteristics. Although nanotube compositeshave not yet been experimentally observed, we can infertheir properties by comparison with similar materialssuch as carbon fiber or fiberglass. If the observedmicroscopic properties of nanotubes extend tomacroscopic matrix composites, we can expect a newclass of tough nanotube composites.

This system of assembler and MRN nanorobots utilizesa comparatively low level of nanoscale technology,which will make it feasible at the very beginning of ourdevelopment of nanotechnology. MRN nanorobots willbe able to seal damage to a Marssuit, allowing anastronaut time to return to the Mars habitat.

Decreased temperatures serve to increase the accuracyof positional devices, though they such devices can workin fairly high temperatures as well without excessivethermal variance. Dust, which can clog and disablemacroscopic mechanical devices, has little effect on thefunction of MRNs. Assemblers, by building boththemselves and MRN nanorobots, make the largenumber of MRN nanorobots economically feasible. Thiscapability cannot become a danger, however, due to the

broadcast architecture and dependence on thefeedstock. Nanorobotics thus can be used safely andeffectively to actively repair Marssuit damage.

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CONTACT

http://www.nanorobotics.org/

Benjamin Chui – bchui@nanorobotics.org

Lea Kissner – chialea@nanorobotics.org

DEFINITIONS, ACRONYMS, ABBR EVIATIONS

Å: angstrom (10-10 meters)AFM: atomic force microscopekB: Boltzmann’s ConstantMRN: Mars Repair Nanorobotnm: nanometer (10-9 meters)PID: proportional integral derivativePLSS: portable life support systemSFP: space-filling polyhedraSWNT, bucky tube: single walled carbon nanotubeTPa: 1012 Pascals (N/m2)