Adaptive Sampling for Environmental Robotics

Transcription

1 Adaptive Sampling fo Envionmental Robotics Mohammad Rahimi,, Richad Pon, William J. Kaise, Gauav S. Sukhatme, Deboah Estin and Mani Sivastava Cente fo Embedded Netwoked Sensing, UCLA, Los Angeles, CA Depatment of Compute Science, UCLA, Los Angeles, CA Depatment of Electical Engineeing, UCLA, Los Angeles, CA Depatment of Compute Science, USC, Los Angeles, CA Abstact The capabilities and distibuted natue of netwoked sensos ae uniquely suited to the chaacteization of distibuted phenomena in the natual envionment. Howeve, envionmental chaacteization by fixed distibuted sensos encountes challenges in complex envionments. In this pape we descibe Netwoked Infomechanical Systems (NIMS), a new distibuted, obotic senso methodology developed fo applications including chaacteization of envionmental stuctue and phenomena. NIMS exploits deployed infastuctue that povides the benefits of pecise motion, aeial suspension, and low enegy sustainable opeations in complex envionments. NIMS nodes may exploe a thee-dimensional envionment and enable the deployment of senso nodes at divese locations and viewing pespectives. NIMS chaacteization of phenomena in a thee dimensional space must now conside the selection of senso sampling points in both time and space. Thus, we intoduce a new appoach of mobile node adaptive sampling with the objective of minimizing eo between the actual and econstucted spatiotempoal behavio of envionmental vaiables while minimizing equied motion. In this appoach, the NIMS node fist exploes as an agent, gatheing a statistical desciption of phenomena using a nested statified andom sampling appoach. By iteatively inceasing sampling esolution, guided adaptively by the measuement esults themselves, this NIMS sampling enables econstuction of phenomena with a systematic method fo balancing accuacy with sampling esouce cost in time and motion. This adaptive sampling method is descibed analytically and also tested with simulated envionmental data. Expeimental evaluations of adaptive sampling algoithms have also been completed. Specifically, NIMS expeimental systems have been developed fo monitoing of spatiotempoal vaiation of atmospheic climate phenomena. A NIMS system has been deployed at a field biology station to map phenomena in a 50m width and 50m span tansect in a foest envionment. In addition, deployments have occued in testbed envionments allowing additional detailed chaacteization of sampling algoithms. Envionmental vaiable mapping of tempeatue, humidity, and sola illumination have been acquied and used to evaluate the adaptive sampling methods epoted hee. These new methods have been shown to povide a significant advance fo efficient mapping of spatially distibuted phenomena by NIMS envionmental obotics. Keywods-component; Netwoked Infomechanical Systems (NIMS); Envionmental Robotics, Senso Netwoks; Adaptive Sampling; Statistics and Geostatistics. Figue 2. A schematic view of the Netwoked Infomechanical Systems (NIMS) concept shows mobile nodes suspended on cable infastuctue. This also shows the NIMS capability fo sensing, communicating, and tanspoting senso nodes thoughout a theedimensional volume. The NIMS infastuctue, shown hee enables pecise physical econfiguation in an envionment that would othewise be intactable fo navigation by conventional means. I. INTRODUCTION AND MOTIVATION Autonomous and compehensive envionmental monitoing obotics pesents sevee challenges fo detection, location, and tacking of phenomena in the midst of unpedictably evolving envionmental chaacteistics. Since phenomena may appea as single o multiple events and may migate within the envionment, it is equied that sensing be spatiotempoally distibuted. Also, in ode to extact desied infomation egading phenomena, it is geneally equied that multiple senso modalities be bought to bea at the same point in space and time. Futhe, the econstuction of phenomena fom senso sampling equies knowledge of the sensing channel popagation chaacteistics. Even moe impotantly, the pesence of obstacles to sensing may entiely obscue events. UCLA Cente fo Embedded Netwoked Sensing, Technical Repot 29, Novembe Unde submission to The 2004 IEEE Intenational Confeence on Robotics and Automation (ICRA)

2 This pape descibes a new capability, Netwoked Infomechanical Systems (NIMS) combining distibuted netwoked sensing with infastuctue-enabled mobility. NIMS enables active physical econfiguation of a divese spatiotempoal distibution of senso nodes in thee dimensional envionments. NIMS infastuctue enables high pecision and eliable mobility to locate senso nodes as equied to both calibate and configue senso distibutions to the points of minimum sensing uncetainty. Howeve, this new capability is accompanied by many challenges, including the poblem of optimizing spatiotempoal senso sampling to educe esouce costs while ecoveing the most accuate econstuction of envionmental phenomena. New algoithms with analytical, simulation and expeimental esults with NIMS systems will be pesented hee. Finally, the boad ange of capabilities and applications of NIMS fo envionmental monitoing will also be discussed. Distibuted senso netwoks have demonstated feasibility fo envionmental monitoing [-3]. Howeve, expeimental and theoetical investigation of the monitoing capability detemined fom the deployment of these ealy senso netwoks has evealed the challenge of sensing uncetainty. The poblem of sensing uncetainty is inheent to envionmental monitoing since it is unchaacteized. Unexpected physical phenomena and evolving envionmental stuctues induce uncetainty in the coupling between signal souces and sensos. Futhe, since physical phenomena ae the souce of uncetainty, then physical adaptation of a senso netwok (fo example, though obotic mobility) may povide the only pactical method fo detection and eduction of uncetainty. Howeve, while mobility is equied, thee ae constaints on the fom of mobility that can povide the equied benefits fo envionmental monitoing. The stuctual complexity of natual envionments and the natue of phenomena to be studied ceate a unique set of equiements fo senso node mobility. These include: ) Mobility must pemit a wide ange of location and viewing pespectives within the space of lage thee-dimensional envionments. This equies the capability to adjust location to adapt ange between signal souces and sensos. This also equies the capability to choose viewing o sensing pespectives to enable image acquisition, fo example, in the midst of obstacles. In typical natual envionments, the pope viewing pespectives may be eached only with an ovehead, aeial pespective and may not be accessible to suface-bone obots. 2) Mobility methods must also povide pedictable and accuate senso location and pespective. Specifically, in ode to educe spatiotempoal uncetainty, it is essential to avoid navigation eos o limitations that would, in the case of conventional methods, incease uncetainty. 3) Senso mobility must also access complex teain and suface egions that may be incompatible with conventional suface vehicle navigation (o may epesent egions whee suface vehicle passage may distub the envionment in an undesied fashion). 4) Senso mobility must also be sustainable since envionmental events may evolve slowly o be infequent, yet still equie constant exploation and vigilance in ode fo detection. 5) The senso mobility system must povide a means fo enabling a logistics capability fo tanspot of senso nodes, enegy, and physical samples (fo example of atmosphee o wate esouces). 6) Finally, the mobile senso envionmental monitoing system must also suppot eliable netwok access to spatially dispesed, mobile nodes opeating in complex envionments. This netwoked capability is equied to enable the accuate coodination of sensing assets fo chaacteization of the many phenomena that ae best investigated by the simultaneous application of multiple senso devices. NIMS technology, shown in Figue, addesses the envionmental monitoing equiements above in a way that would not be diectly possible with othe obotic foms. Hee, a cableway infastuctue is shown. While many infastuctue types ae adapted fo specific applications, the geneal pupose cableway system satisfies equiements fo a boad class of envionmental monitoing equiements while intoducing only limited deployment logistics and planning cost. The cableway enables ) elevated, aeial viewing pespective, 2) accuate, epoducible motion, 3) long ange mobility in complex teain, 4) low enegy motion fo sustainable opeation, 5) logistics capability with enegy tanspot via the cable systems, and 6) node elevation fo enhancing wieless link budget elative to suface-distibuted nodes [4]. Finally, the need fo high fidelity monitoing of lage envionments will equie the simultaneous opeation of multiple NIMS nodes that exploit the infastuctue fo communication and coodination [5]. NIMS applications to envionmental monitoing ange fom fundamental science objectives to public health and safety. Examples include natual envionment monitoing with equiements fo chaacteization of the atmosphee fo photosynthetic gas flux, time-lapse imaging of plant gowth and animal behavio, and sampling of wate esouces. NIMS physical sampling capabilities offe a damatic advance fo these applications by poviding a means to automate the pogammable acquisition of atmospheic gas and wate fo late chaacteization of tace concentations. NIMS may also be deployed ove wateways including ive and wetland systems. Hee NIMS offes a distibuted means fo monitoing of atmosphee, wate, and subsuface sediment all in esponse to events o model-diven schedules. NIMS devices ae applicable as well to civil infastuctues fo monitoing and inspection. In this example, NIMS devices may be deployed fo condition monitoing as well as being held in eseve and deployed apidly upon demand in esponse to emegencies and failues. A seies of new challenges accompany the development and application of NIMS fo envionmental monitoing. A pimay example lies in the accuate econstuction of distibuted envionmental phenomena, including, fo example the measuement of micoclimate dynamics. Hee, the accuate detemination of space- and time-dependent vaiables of tempeatue, wate vapo concentation, and sola illumination within the complex envionment is essential to the investigation of global change phenomena [6]. These vaiables must be sampled in a vast thee-dimensional volume while both spatial and tempoal vaiations ae unknown and initially ae unpedictable. Thus, while NIMS capabilities offe the ability to exploe lage volumes, it is now equied that sampling stategies be popely devised such that the density of sampling points is dynamically and autonomously adjusted using infomation deived fom senso systems. This equies a

3 combination of new sampling algoithms, coodinated mobility, and pope dynamic selection of senso assets. In some applications, this will also equie the coodination of multiple senso nodes. Objectives fo optimization may include the accuate econstuction of vaiable distibution o may include the optimization of accuacy associated with a vaiable set deived fom combined, distibuted measuements. II. RELATED WORK Envionmental obotic development has povided methods fo mapping, localization, and sampling of phenomena. Fo example, envionmental mapping by obotic systems includes the econstuction of a spatial model of the obot s envionment based on senso samples. Hee envionmental mapping may be chaacteized as the pesence of absence of objects that enable obot navigation and localization.[7-8] Map econstuction elies on sensing with ange findes, cameas, odometes, tactile sensos, inetial and diection sensos, and GPS. Envionmental mapping emains a challenge, paticulaly in the pesence of dynamic envionments. Robotic mapping algoithms have elied pimaily on pobabilistic as opposed to statistical appoaches. These appoaches ange fom the Bayesian filte [9] to Kalman filte [0], hidden Makov model [], to Bayesian netwok. These methods apply to mapping unknown envionments with known obotic localization o localization with known envionments. The Simultaneous Localization and Mapping (SLAM) appoach is intended to achieve both mapping and localization without pio knowledge of eithe.[2] Geostatistics povides analysis methods fo detemination of spatial vaiation and intepolation of sampled data to obtain econstuctions (maps) of phenomena. These techniques have been long used in science disciplines such soil analysis, [3] weathe mapping, [4] atmospheic science, [5] contamination studies, and geology. Also in the field of senso netwoks, eseach has yielded methods fo detemination of spatio-tempoal vaiable distibution and efficient field estimation fo fixed sensing points.[6,7] This NIMS investigation is focused on the poblem of spatiotempoal sampling of dynamic and unpedictable envionmental phenomena in thee-dimensional spaces. This equies that sampling be esponsive to not only spatial vaiation, as in Geostatistics methods, but, also to unpedictable tempoal vaiations. The exploitation of NIMS infastuctue enables pecise obotic localization, emoving an uncetainty fom the econstuction poblem. This, in tun, will enable intoduction of new sampling capabilities with coodinated mobility of individual o multiple nodes. III. ROBOTS AS STATISTICAL AGENTS The NIMS senso node motion is limited by mechanical means to a minimum esolvable unit, efeed to hee as a pixel, indicated schematically in Figue 2. Pixels epesent the uppe bound on spatial sampling fequency. Exhaustive sampling of the envionment at all pixels may geneally be pohibitively expensive in time and esouce cost. Indeed, fo many Suveillance Aea NIMS Shuttle Node Senso Node Figue 2. A schematic view of a typical NIMS natual envionment deployment is shown. The NIMS Senso Node may ise and fall vetically and popagate hoizontally though the Patol Aea. The allowed measuement sites, pixels, ae indicated by points in the suveillance aea. Sensed vaiables including atmospheic tempeatue, wate vapo density, sola illumination, and othes vey in space and time. Sampling must follow a policy that enables econstuction of envionmental data with an estimated degee of accuacy that may be specified in advance of sampling. examples, an attempt to sample at highest spatial esolution may esult in an unacceptable latency with espect to visiting envionmental egions, esulting in eos in the econstuction of dynamically vaying envionmental phenomena. Thus, the development of a NIMS sampling policy is equied in ode to minimize econstuction eo fo a set of finite esouces in node mobility. Ou appoach assigns the NIMS nodes to opeate as statistical agents that ae commissioned to acquie data egading vaiable distibutions by appopiately scheduled exploation. This appoach is intended to apply to envionmental conditions whee no pio knowledge exists egading vaiable distibution. Howeve, it is also intended to be applicable to instances whee domain knowledge may be applied to supeimpose ules that focus exploation and sampling (fo example, to those egions estimated by domain knowledge to equie the highest spatiotempoal sampling ate). In the following discussion, we eview choices of sampling policies, including ou poposed policy, fo econstuction of a map of envionmental vaiables. Note that this map may be composed of a single vaiable such as the senso attibutes the obot caies (i.e. tempeatue, humidity, gas composition, o othes) o it may be a moe complex utility function such as a map of the coelation between the vaiables themselves (fo example the coelation of atmospheic gas composition and tempeatue) o coelation between images collected in multiple spectal bands. The following impotant assumptions focus ou initial ou analysis:. The econstuction of a spatiotempoal map of dynamic phenomena using a single obotic element inheently implies a contention between spatial and tempoal fidelity and system coveage. This obotic sampling system is intended to detemine its own sampling distibution based only on its measuement esults. Howeve, we conside the limit whee the ate of change of phenomena is low to the extent that it may be consideed static duing the time equied fo the NIMS

4 system to complete its sampling cycle ove those points detemined to be visited by the sampling policy. In the limit whee the sampling policy and phenomena chaacteistics esult in spase sampling, then this appoximation is valid. Howeve, examples will be exploed and new appoaches will be equied that exploit multiple obotic NIMS nodes to econstuct maps of apidly evolving phenomena in lage spaces. 2. Analysis assumes that the NIMS infastuctue enables obotic senso localization at a degee of accuacy such that motion contibuted negligible sensing uncetainty. (This is eadily achieved with pesent NIMS achitectues that exploit odomete measuements fo motion along fixed cables.) 3. Fo the pesent investigation, it is futhe assumed that no sensing eos ae pesent and that the phenomena undestudy ae spatiotempoally continuous. While these assumptions ae boadly applicable, in the futue, these assumptions will be lifted. Specifically, NIMS will be applied to in situ calibation of sensos and instuments, the detection of sensing uncetainty, and the adaptation of the NIMS system to enhance sensing pefomance. IV. SAMPLING POLICY Adaptive sampling policies investigated in the past include: A. Unifom (Regula o Gid) Sampling Unifom sampling methods acquie measuements at unifom intevals. The pimay disadvantage of this method is, of couse, high esouce cost since in ode to achieve adequate sampling density at those egions equiing geatest density, the sampling density must be unifomly high eveywhee. Secondaily, the lack o andomization in sampling intoduces a potential eo in sampling of peiodic phenomena. Acceptable Eo + - Statification Policy Mobile Sampling Estimation Eo Piecewise Estimation Map Figue 3. The NIMS sampling policy descibed hee is intended to poduce a map of an envionmental vaiable with a specified maximum acceptable eo between the econstucted (computed) map and estimated actual phenomena. Adaptation of the Statification Policy detemines the ate and location of Mobile Sampling, in esponse to an estimated eo level. seven statification stages.[8-9] Disadvantages of nested statified sampling have appeaed in fixed senso deployments whee the equiements on statification may vay, endeing the statification sub-optimal. Howeve, fo NIMS envionmental monitoing, the sampling policy may be continuously adapted to follow evolving equiements. V. ROBOTIC ADAPTIVE SAMPLING A. NIMS Sampling Policy We developed a Nested Statified Sampling method fo NIMS as a divide and conque algoithm (shown in Figue 3) that defines a sampling tee whee individual stata occupy leaves on this tee. Hee, Fist the complete suveillance aea unde investigation, is statified into a numbe of stata, m. Then, envionmental vaiables ae sampled in each stata with a numbe of samples popotional to the aea of the stata with: () ρ = α P S B. Random Sampling The andom sampling pocedue assues that each element in the pixel population has an equal chance of being selected. As fo unifom sampling, esouce cost is potentially pohibitive and may lead to loss of tempoal fidelity. C. Statified Random Sampling This adaptive method is well-suited to sampling in the pesence of envionmental heteogeneity. Hee, the envionment is patitioned into stata in which statistical chaacteistics of envionmental vaiables ae detemined. Random sampling may occu in each statum. This method offes the benefit that adequate sampling density is applied to those stata fo which estimation eo is high. Howeve, at the same time, those stata not equiing high density sampling ae not ove-sampled at high esouce cost. D. Nested Statified Random Sampling This adaptive method uses the statified andom sampling appoach but bases sampling density on the vaiance of measued vaiables within each statum. This method continues the statification pocess and ceates a hieachical tee of stata. It has been applied to soil analysis with up to a (2) µ = PS ρ = / α Whee, ρ is the numbe of sampling points in the cuent statum, µ is the mean of vetical and hoizontal step size in tems of pixels, P s is the numbe of pixels in the cuent statum and α is a design paamete with the statum ank indicated by. In pactice paamete α may be selected based on domain knowledge and have a linea elation with α -. Then, data is acquied in the cuent stata using (2). The vaiance of these data ae computed and, if the vaiance is found to exceed a theshold value, statification is again pefomed to poduce educed aea stata with an equivalent numbe of sample points. Iteation of this pocess continues until vaiance falls below a desied theshold. A statum is egaded as fully mapped when the vaiance of each leaf of this statum tee is obseved to fall below theshold. This pocess continues until the entie egion has been sampled with a statum ank

5 Figue 4. A contou map of elative humidity acquied by a NIMS system in an outdoo test envionment is shown. Vetical axis coesponds to vetical node elevation, with hoizontal axis indicating hoizontal displacement. Note the maximum in humidity at lowe left. Hee, the Nested Statified Sampling algoithm has been applied. The highe density of stata at lowe left is clea with a lowe density appeaing elsewhee. Lowe left zone is nea wet land with maximum humidity vaiation B. Maximum and Minimum Sampling Point If we define location of a statum inside the tee as the ank,, of that statum then the population of pixels in each of the stata is: (3) P = N S pixels P = A/ A m (4) ( ) S pixel Whee P S is the numbe of pixels in the cuent statum, N pixels is the total numbe of the pixels in the suveillance aea, A is the suveillance aea, A pixel is the size of each pixel and m is degee of statification. The maximum depth of the statification tee is: (5) m ( A/ Apixel ) Tee Log m d = Since at each step we effectively α the sampled point then the maximum numbe of sampling point is: = (6) Smax = N pixels α = Whee, S max is the maximum bound on the numbe of sampling points in the exteme case of a complete andom system. A complete andom system is a system fo which in the limit of the smallest indivisible stata (n pixels < m) the vaiance of values of all neighboing pixels exceeds the theshold vaiance). The minimum numbe of sampling points is: d tee Figue 5. The vaiogam of the data set of Figue 4 is shown in the uppe panel. The lowe panel displays the quad-level tee. Lowe ank egions of the tee coespond to high vaiance zones while highe ank egions coespond to low vaiance zones. Leaf zones may show diffeent aeas and but thei vaiance falls below a cetain theshold. The leaves can be used to ceate a contou map of the envionment. The tee also gives and estimation on the uppe bound of the vaiogam value at each ankl depending on the numbe of leaves node at that ank.. (7) S min = N pixels α S min and S max show the minimum and maximum bound on the numbe of sampling points. Note that pefomance of adaptive sampling policy in the wost case is equal to a simple andom sampling with S max samples of the population. In this case the penalty of the adaptive sampling policy is (d tee -) additional sampling sweeps. In geneal, the numbe of sampling points is equal: l = d tee q= l (8) S = N pixels Al / A) [( α ] l = q= Whee, S is the numbe of sampling points ove all leaf statums. Leaf statums ae statified sections fo which vaiance is below the vaiance theshold and hence has not been statified futhe. A l is the size of the leaf statum and l is its ank in the tee. C. Eo Estimation This system ultimately conveges to poduce a piecewise estimated map of the envionment within each statified block, epesented by the mean of that statum and its vaiance. Ou Estimation of the envionmental vaiable map is then epesented by: (9) M ˆ x y = Z L ( x, y) x, y L ˆ, q

6 Whee M ˆ is map estimation at point x,y and x, Zˆ ( x, y ) y L is the estimation of the aveage of highest ank statum (leaf statum) that contains point x,y. The mean squae oot eo of this estimation of map is then equal to: X p Y p (0) ˆ δ = ( zi, j Zˆ L ( i, j)) i= j = Whee, δˆ is the map estimation eo, X p and Y p ae the maximum numbe of pixels in X and Y axis, z i,j is the sampling pixel at point i,j and Zˆ L ( i, j) is the aveage value of the leaf statum that the pixel belongs to it. In pactice a moe sophisticated spatial mapping technique, fo example, that of Kiging[20] may be eadily used hee leading to educed estimation eo in specific applications. D. Convegence Popeties Convegence condition of this sampling algoithm depends on the spatial distibution of data. Thee ae existing techniques fo specification of sampling chaacteistics fo envionments. One such tool that has eceived much attention is the vaiogam [2]. The vaiogam eveals the andomness and stuctued aspects of the spatial dispesion of a given vaiable. The vaiogam is a plot of the aveage squae diffeence between the values of a spatial vaiable at pais of points sepaated by a lag distance vesus the lag itself (Figue 5). The empiical vaiogam γ (h) is calculated as N ( h) () γ ( h) = [ y( x ) ( + ) 2 i y xi h ] 2N( h) i= whee h is the lag (in pixels) ove which γ (semivaiance) is measued, N is the numbe of obsevations used in the estimate of γ(h), and y is the value of the vaiable of inteest at the spatial position xi. The value y(xi + h) is the vaiable value at lag h fom x. This calculation is then epeated fo diffeent intevals of h. The empiical vaiogam descibes the oveall spatial patten of sample data. This adaptive sampling appoach is sensitive to vaiogam value and adapts sampling density of the phenomenon in accodance with vaiance. It samples the envionment at high lag values and based on vaiance of the infomation, statifies the envionment leading to lowe lag distances and povides an estimate of the vaiance at these less lowe lag distances. In pactice, fo most phenomena, the vaiogam monotonically deceases fom highe lag distance towad lowe lag distance. In those cases this sampling appoach conveges towad a statified tee. Thee ae some ae cases in which the vaiogam of a phenomenon may exhibit tempoal fluctuation o peiodicity. Spatial peiodicity may occu in the envionment (fo example as a esult of cultivation and land management. In such cases the vaiogam displays a local minimum point nea the vaiance Rank Rank2 Rank3 Rank4 Rank5 Constant 00 (4) Linea (6) 0 0 Squae 0 50 (2) (28) Cubic 0 50 (2) (8) 37.5 (96) Random (6) 75 (92) Nomalized Sample Density Level Linea Squae Law Cubic Law Map Suface Chaacteistic Random Figue 6. The uppe images display chaacteistic map suface topogaphies whee the vetical axis epesents an envionmental vaiable value and the hoizontal axes epesent the spatial coodinates associated with NIMS node motion. Fom left: A level suface, linea, squae, cubic and andom suface ae shown. The table shows the pecentage of the aea coveed by diffeent leaf anks (leaf numbes) fo each of those functions. It is clea that as non-lineaity inceases the statification pocess shifts fom low anks leaves to highe ank leaves. The lowe gaph shows the dependence of sampling density on the chaacteistics fo these typical sufaces. Hee, sampling density is nomalized with espect to the maximum sampling density of 2500 points fo this system. theshold, complicating the seach fo an optimal sampling solution. A method that may avoid the effects of such local minimum include the poactive exploation of continued statification even afte algoithm convegence is obseved E. Motion Policy Fo this investigation, it is assumed that the NIMS node system has eithe been povided with an obstacle map (limiting its ange of motion) o this obstacle map has been discoveed though use of depth sensos. The motion policy of the NIMS node is othogonal to its sampling policy. A obot may suppot a wide ange of sampling policies including the adaptive sampling policy in a aste scan fashion. In the case of the adaptive policy the sampling step size scales linealy with location in the sampling tee. Adding the assumption of the pesence of any tempoal vaiability duing the map fame time, highlights the impotance of a motion policy since this is equied fo minimizing distotion of measuements in distibuted locations. The aste scanning method used fo the expeiments epoted hee follow a comb patten, elying on vetical excusions of

7 Figue 7. At left is a panoamic view of the expeimentally deployed NIMS node system at the Wind Rive Canopy Cane Reseach Facility nea Cason, Washington (the NIMS installation is in the egion of the highlighted box). The span fo this deployed installation is 50m and the height above the foest floo suface is also 50m. The NIMS node infastuctue cable is suspended between two tall tees. The cente image displays an ovehead view of the NIMS node. Hee it is suspended at a height of 50m above the foest floo. Note that senso systems ae suspended fom the node at an autonomously adjustable height. This pemits the NIMS senso node system to sample data in boad and deep vetical plane within the envionment. At ight, the NIMS node is shown in a detail view. Hee, its imaging system is seen. the NIMS measuement node ove the entie measuement ange followed by hoizontal steps. VI. SIMULATION RESULTS Sampling efficiency in this appoach depends on the natue of the vaiable map suface. While this sampling method finds the minimum numbe of equied sample points to achieve a desied accuacy in econstucted data, the advantages of this appoach ae geatest fo systems that display spatially localized vaiance. Of couse, fo envionments displaying a high vaiance the density of sample points may always be high. This has been investigated in simulation. We have evaluated sampling algoithm esponse to epesentative suface shapes. These include a ) unifom, level suface, 2) a suface displaying a linea slope in height, 3) a suface displaying a squae law chaacteistic, 4) a suface displaying a cubic law chaacteistic, 4) and a suface displaying a andom suface height vaiation. In all these simulations the suveillance aea was pixels, the span of the signal was between zeo and one and the theshold vaiance was 8% of the full span of the signal. This means that in ou simulation, adaptive sampling policy guaantees a piecewise eo estimation in which, estimated eo bounded to the theshold vaiance. We have investigated the effect of inceasing nonlineaity fo the same eo on the numbe of sampling points while estimation of eo is bounded to vaiance theshold. Figue 6 shows the effect of this map chaacteistic on the statification pocess. As the map chaacteistic inceases in ode, as expected, the density of sampling points inceases fom 500 samples to 2375 samples in the case of andom distibution. The maximum theoetical bound on numbe of samples in this case (based on equations 5 and 8 above) is 2500 fo a simple andom sampling policy. VII. NIMS DEPLOYMENT We have deployed a NIMS system fo investigation of micoclimate dynamics phenomena with measuement of atmospheic tempeatue, humidity, and sola illumination (measued in the Photosynthetically Active Radiation (PAR) spectal band. In addition to local deployments nea ou facilities an expeimental deployment has also been completed at the Wind Rive Canopy Cane Reseach Facility [22] nea Cason, Washington, located in the Wind Rive Expeimental Foest. The NIMS deployment included a complete system with NIMS senso nodes (caying both vetical and hoizontal mobility), sola cell enegy havesting with sustainable opeation, batteies, powe tansfe system, and sensos including an image and micoclimate dynamics senso systems. This node spanned a 50m wide tansect that was 50m deep in a egion between tees (Figue 7). VIII. FUTURE WORK Each of the many NIMS envionmental obotics applications will ely on adaptive sampling methods that include those descibed hee. Examples of futue development include: Systems and algoithms that pemit accuate econstuction of data in the pesence of apid tempoal vaiation of envionmental vaiables. Methods combining mobile and fixed senso nodes that may emain at a location o be adaptively elocated, on demand, by the NIMS system. Coodinated sampling algoithms linking multiple mobile and fixed devices. Hee, the challenge of meeting sampling demands in space and time will be patially elaxed by the availability of multiple assets that may be popely distibuted. Using moe accuate piecewise linea tee estimation of a phenomena. Estimation of leaf aea can be eplaced by highe ode estimatos at each statum [23] to incease sampling efficiency especially as nonlinealy of the phenomena inceases. Finally, while the sampling method epoted hee elies on a poactive exploation of the envionment (followed by the execution of an optimized sampling policy) othe sampling methods will be developed that ae eactive to events. These sampling methods and NIMS node systems ae being pepaed fo futhe long tem deployments (multiple seasons) and expeimental investigations of

8 envionmental phenomena at the James San Jacinto Mountains Reseve.[24] IX. CONCLUSION In this pape, we have descibed the new Netwoked Infomechanical (NIMS) methodology that pemits the intensive and extensive exploation of envionments with mobile, obotic senso systems. This envionmental obotic technology has pomising potential fo monitoing of natual envionments, uban envionments, and indoo facilities. Its applications include scientific investigation, public health monitoing, chaacteization and tacking of envionmental contamination and emediation pogess, as well as applications in commece. NIMS offes the unique chaacteistics of pecise mobility in complex envionments with low enegy, sustainable tanspot. A paticulaly impotant objective fo NIMS monitoing is the spatiotempoal mapping of envionmental vaiables. Hee, the objective is to enable a econstuction of envionmental vaiables in a full thee-dimensional space. This meets with the challenge of computing pope sampling density in ode to minimize eo in econstuction. This pape has descibed an adaptive sampling method that exploits the NIMS system to poactively exploe the envionment and simultaneously develop a spatially vaying map of sampling density with the objective of allowing accuate vaiable map econstuction. This, in tun, enables data econstuction while minimizing equied mobility, theeby educing esouce costs associated with investigation. An analytical desciption of this sampling method has been pesented along with simulation esults. Finally, expeimental measuements confim the applicability of this technique to envionmental obotics applications including micoclimate monitoing. ACKNOWLEDGMENT The authos would like to thank membes of the NIMS team specifically Duo Steven Liu, Chistophe Lucas, Rachel Scollans, and Lisa Shiachi, fo thei wok on the expeimental deployment of the NIMS system. We also would like to thank D. Michael Hamilton fo his advice and guidance. We futhe acknowledge Mak Hansen fo his comments and suggestions. Finally, we also wish to acknowledge suppot by the Wind Rive Canopy Cane eseach team including Ken Bible, Mak Ceighton, Jey Fanklin, Rick Meinze, and David Shaw. REFERENCES [] [2] Pottie, G.J., and Kaise, W.J., Wieless Integated Netwok Sensos, Communications of the ACM, vol. 43, pp. 5-58, [3] Estin, D., Pottie, G.J., Sivastava, M., Instumenting the wold with wieless senso netwoks, ICASSP 200, Salt Lake City, May 7-, 200 [4] Sohabi, K., Maniquez, B., and Pottie, G.J., Nea gound wideband channel measuement in MHz", IEEE VTC Sping '99, Houston, TX May 6-20, 999. [5] Mataic,M.J., Sukhatme,G.S., and Ostegaad, D., Multi-obot Task Allocation in Uncetain Envionments, Autonomous Robots (to appea). [6] Ozanne, C.M.P., Anhuf, D., Boulte, S.L., Kelle, M., Kitching, R.L., Köne, C., Meinze, F.C., Mitchell, A.W., Nakashizuka, T., Silva Dias, P.L., Stok, N.E., Wight, S.J., Yoshimua, M. 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