Heterogeneous Multirobot System for Explorationand Strategic Water Sampling

Sandeep Manjanna1, Alberto Quattrini Li2, Ryan N. Smith3, Ioannis Rekleitis2 and Gregory Dudek1

Abstract— Physical sampling of water for off-site analysis isnecessary for many applications like monitoring the quality ofdrinking water in reservoirs, understanding marine ecosystems,and measuring contamination levels in fresh-water systems. Per-sistent collection of physical water samples can be improved byautomation. Robotic sampling makes it possible to strategicallycollect water samples based on real-time measurements of phys-ical and chemical properties gathered with onboard sensors.In this paper, we present a multi-robot, data-driven, water-sampling strategy, where autonomous surface vehicles planand execute water sampling using the chlorophyll density as acue for plankton-rich water samples. We use two AutonomousSurface Vehicles, one equipped with a water quality sensor andthe other equipped with a physical water-sampling apparatus.The robot with sensors acts as an explorer, measuring andbuilding a spatial map of chlorophyll density in the givenregion of interest. The robot equipped with water samplingapparatus makes decisions in real-time on where to sample thewater, based on the suggestions made by the explorer robot.We evaluate our system in simulation and on real robots inan actual drinking-water reservoir, showing the effectiveness ofthe proposed system.

I. INTRODUCTION

In this paper we propose and evaluate the design of amulti-robot system composed of two heterogeneous robots –one equipped with a sensor to measure a phenomenon, theother one equipped with a water sampling apparatus – forefficient online collection of water samples.

Collection of water samples is an essential element ofmarine science, marine biology, limnology, and related dis-ciplines. While some measurements can be made in situand in real-time, many important measurements can only beaccomplished by collecting physical samples in the domainof interest and doing the analysis at a suitable remote facility(i.e., “back in the lab”). In many cases, the selection ofsuitable sampling locations can have a large impact on thequality and accuracy of the estimation process: for exampleif pollutant extrema are being estimated. Traditional methodsfor sampling depend heavily on manual labor, are timeconsuming, and can be fraught with risks of human error.Robotic sampling systems allow scientists to collect richerand more complete data sets than would normally be possibleusing traditional manual data collection [1].

1S. Manjanna and G. Dudek are with School ofComputer Science, McGill University, Montreal, Canadamsandeep,dudek@cim.mcgill.ca

2A. Quattrini Li and I. Rekleitis are with the Department of ComputerScience and Engineering, University of South Carolina, Columbia, SC29208, USA albertoq,yiannisr@cse.sc.edu

3R.N. Smith is with Fort Lewis College, Durango, CO 81301, USA. Hewas supported by NSF MRI 1531322 and Office of Naval Research AwardN000141612634. rnsmith@fortlewis.edu

(a)

(b)

(c)

Fig. 1. Two Clearpath Heron ASVs (a), one equipped with a water qualitysensor (b), another with a water sampling apparatus (c).

In this paper, we address the problem of monitoring aregion and collecting water samples with emphasis on select-ing good sampling locations, but without a priori knowledgeof where these locations might be. This task is completedby a heterogeneous robotic team, composed of two roboticboats, an explorer that can measure variables that suggestsample utility and a sampler that can collect physical samples(Figure 1). Das et al. [2] proposed a probabilistic method fora single AUV that can monitor and sample. In our case, wedivide the task between two robots. This provides an efficienttrade off between system complexity, payload capacity, andrun time, besides improving the quality of the collectedsamples — where quality expressed as sum of measuredvalues over the samples collected.

In particular, such a task leads to two related subprob-lems: exploration and sampling. We propose an explorationstrategy for the explorer—the robot with the water qual-ity sensor—that makes real-time observations to create apreliminary map. The sampler is then informed about thepotential locations for sampling. Our method is based onthe concept of frontier-based exploration, similar to thatintroduced by Yamauchi [3] for indoor map building andexploration. In this way, the robot decides according to thelatest information and it scales well with the size of theregion, differently from common coverage approaches thatemploy a boustrophedonic coverage path [4]. Notice that theabsence of prior information on the spatial distribution of thedata of interest prevents us from using alternative powerfulselective coverage methods [5]–[8].

We design a sampling strategy for the sampler robotwhich collaborates with the explorer robot. The samplerneeds to choose among the locations where measurementsare available so that the physical sample is also associatedwith a prior sensor measurement. The proposed strategy isa variation of the secretary hiring problem. Note that in the

scenario considered, it is not ideal to wait until the end ofexploration: first, the physical sample should be collectedclose in time to the measurement; second, in this waythe time in the field is optimized. There have been manyvariants and solutions for this problem in the field of spatialsampling [9]. Girdhar et al. propose a multi-choice hiringalgorithm [10] for making irrevocable hiring decisions froma stream of candidates. Another approach is to use multipletime windows and treat sampling within each window as aseparate secretary hiring problem as proposed by Bateni et al.in their submodular secretary algorithm [11]. We will furtherdiscuss submodular analysis of the secretary algorithm whilecomparing it to our proposed approach in Section III-B.

There is a body of existing work that is focused on usingmultiple autonomous agents to explore and map a spatialphenomenon. In [12], the authors developed a low-costmultirobot autonomous platform, and tested the proposedsystem for monitoring water quality. The work proposes adiscretization of the area and a strategy based on maximumuncertainty. Girdhar et al. demonstrated a heterogeneousmultirobot system composed of Unmanned Aerial Vehicle(UAV), Autonomous Surface Vehicle (ASV), and an AUVcovering an area of interest [13], where the interestingregions to cover is given by human operators. Many systemshave been proposed that are capable of collecting watersamples. A catamaran with a water sampling system wasproposed by Caccia et al. [14] and tested near Antarctica.Ore et al. [15] presented a UAV equipped with a watersampling apparatus. Robotic physical sampling has also beenapproached in domains other than marine robotics, such asuse of planetary robots or mining robots to collect samplesof rocks, ores, and other terrestrial samples (e.g., [16], [17]).All of these work focus more on the hardware design ofthe sampling mechanism and the autonomy capabilities toallow robots navigate environments and collect samples.Exploration techniques have a key application in addressingsearch and rescue problems [18], and gas detection [19], [20].Some methods [5], [21] assume to have a priori informationavailable so that areas can be selectively explored to increasethe reward over time. However, in our scenario, a prioriinformation is not available and is discovered online withthe explorer. Our focus is on the decision making part ofthe sampler, that is, when and where a sample should becollected.

The paper is organized as follows. The next section givesan overview of the proposed methods for the robotic team.In Section IV, we validate the proposed method both in sim-ulations and field experiments. Finally, Section V concludesthe paper discussing some of the lesson learned and outliningfuture work.

II. PROBLEM STATEMENT

Two robotic boats are deployed in a continuous two-dimensional area of interest E ⊂ R2 with a user pre-definedboundaries. We assume that such an area is obstacle-free,as in many marine science expeditions. Both of them movevia differential drive, are using GPS to localize, and they

can communicate continuously via a WiFi channel. OneASV—termed the explorer—is equipped with water qualitysensors and, as the name suggests, is assigned with thetask of exploring the region to communicate interestinglocations to sample water from. Another ASV—called thesampler—has a water sampling apparatus with k sampleunits to collect water samples to be analyzed a posterioriin a lab. As the mission evolves, the explorer selects a seriesof destination poses where to get more measurements andbuilds a more reliable model of the area, that is a map thathas low uncertainty; at the same time, the sampler receivesmeasurements from the explorer and uses this information todecide where to take a sample. The mission progresses upto the mission duration Tm, which generally depends on thespecific logistics of the mission. All k units of the watersampling apparatus should be used in such a timeframe.Even if the ultimate objective of the multirobot team is tomaximize the values of the collected samples, this processleads to two related problems addressed in this paper:

1) Exploration: explorer selects a sequence of poses Q =〈q0, q1, . . . , qn〉, with qi ∈ E , so that the model of thearea converges to the true phenomenon. Note that thisprocess can be run online, and the explorer can takedecisions as new measurements yi associated with GPSlocations xi are collected. The efficiency is determinedby traveled distance and quality of the map.

2) Sampling: based on all the measurements Y, the sam-pler selects a number of locations L, where to takephysical samples, where |L| = k and l ∈ L ⇐⇒∃yi ∈ Y|xi = l. The final objective is to maximize thesum of the values at sampled locations (

∑l∈L∗ f(l))

within the maximum duration of the mission Tm.Intuitively, the better the performance of the explorer, thebetter the performance of the sampler.

III. INFORMED STRATEGIC SAMPLING

The proposed system is based on using two robots thatcoordinate with each other to achieve the ultimate goal ofsampling. Frontier-based exploration is used by the explorer,while a variant of the secretary hiring problem is used forthe sampler. In the following, the details of both subsystemsare reported.

A. Gaussian Process Frontier-based Exploration

Starting with zero knowledge about the spatial phe-nomenon in the given region, the explorer’s objective isto select locations L∗ = [x1,x2, . . . ,xm] over time suchthat the phenomenon is mapped efficiently. Note that whilethe robot is traveling to those locations, measurementsY = [y1, y2, . . . , yt] with associated GPS locations X =[x1,x2, . . . ,xt] are collected at the frequency rate of thesensor. The goal is to optimize the time and the traveleddistance to create a good model f(x) of the phenomenonf(x).

With finite time and finite battery life of the robot, itis not feasible to take measurements at every location in

Fig. 2. Candidate locations generated by two techniques at a mission timestep. The colormap represents the variance in the spatial representation ofthe field. Red circles represent the potential candidate locations l. Blacklines show the contours. (a) Contour based location selection. (b) Fixedwindow location selection.

the region of interest E . Hence, we use Gaussian Pro-cesses (GP) [22] to model the spatial field. In particular,a phenomenon over locations W can be estimated as aposterior distribution p(f(W) | X,Y) ∼ N (µW,ΣW)fitted over a set of noisy observations Y made at loca-tions X. The mean vector µW is obtained as µW =K(W,X)cov(Y)−1Y and represents the estimate of thephenomenon, while the covariance matrix is given by ΣW =K(W,W) − K(W,X)cov(Y)−1K(W,X)T . Mean andcovariance functions should be formulated to completelydefine a GP. As done in the mainstream approach, mean isassumed to be zero, and the covariance function, denoted ask(x,x′), is a radial basis kernel (RBF):

k(x,x′) = σ2f exp

(− |x− x′|2

2l2

), (1)

where signal variance σ2f and length scale l2 are parameters

that encode amplitude and smoothness. Note that, with aGP it is possible to quantify the uncertainty of the estimatesin W by looking at the main diagonal of ΣW, also calledpredictive variance.

Our exploration technique uses a one-step look ahead,where the robot decides on a set of locations to visit atepoch m only after reaching the chosen location of epochm − 1. This technique has been extensively used in abody of work related to frontier-based mapping of indoorenvironments [3]. We propose two methods to generate a listof locations (Figure 2). One of the approaches is to considerlocations on the outer-most contour between a region withhigh variance and a region with low variance (Figure 2(a)).An easier method is to consider all the locations on a fixedplanning window centered on the current position of therobot (Figure 2(b)).

The list of new locations is added to the list of candidatelocations L, thus the algorithm chooses among all the loca-tions around the current trajectory of the explorer. The ratio-nale is that every measurement decreases the variance withina window; as such, the ASV should go to the boundary ofthat window to build an efficient representation of the spatialfield with minimum distance traveled. Candidate locationsL are then evaluated based on the predicted variance atthese locations according to the learned GP model andtheir distance from the current robot location. The location

Fig. 3. Plot showing the RMSE of the generated map along withdistance traveled by the robot. The comparison is between multiple sizedfixed windows. Error bars indicate standard deviation over five real-timesimulation trials.

Fig. 4. Plot showing the RMSE of the generated map along with distancetraveled by the robot. The comparison is between fixed window techniqueand contour based technique. Errorbars indicate standard deviation over fivereal-time simulation trials.

with highest predicted variance and least distance is chosenas the current step target. We use a normalized blendingfunction (Eq. (2)) to resolve the trade-off between distanceand variance.

l∗ = argminl∈L

(1− w(t)) ∗ d(xm, l) + w(t) ∗ v(l), (2)

where d(xm, l) = d(xm, l)/maxl∈L d(xm, l) is a normal-ized distance between the current robot position and can-didate location l; and v(l) = 1 − v(l)/maxl∈L v(l) is thenormalized variance at location l. With time, it is beneficialto explore the locations with higher variance even if theyare far from the robot’s current location. We need to weighthe variance higher as the time proceeds. Hence, we use afunction for weight w over time, giving more importance tothe variance criterion as exploration time proceeds:

w(t) = t/(t+ r), (3)

where r ≥ 0 is a constant that tunes the steepness of thecurve.

We evaluated both the techniques to generate a set ofcandidate locations mentioned in Figure 2 using a simulatedworld with chlorophyll measurements. The details about thesimulations will be discussed later in Section IV-A. We builta representation of the world as the robot was traveling andcollecting measurements. Figures 3 and 4 show the root mean

squared error (RMSE) of the phenomenon model f(x) withthe ground truth f(x) plotted against the distance traveled.Figure 3 presents a comparison between different sized fixedwindows and Figure 4 presents a comparison between fixedwindow and contour-based candidate selection methods. Thecontour-based method travels longer distances to improve thequality of the map, thus compromising the minimum distancecriterion. Because of its good performance, we will discussthe fixed window candidate selection technique in the rest ofthis paper.

B. Look-back Selective Sampling

The explorer robot, while exploring the region to build themodel, communicates the potential candidates for samplingwater based on its observations. Then, it is the sampler’s taskto maintain a list of these candidate locations and strategi-cally decide on k locations where to collect water samplesfrom—recall that k is the maximum number of samples thatcan be collected. There are at least two approaches thatone can think of for this scenario: the first one is to startmaking decisions as soon as candidate suggestions comefrom the explorer; the second is to wait until the explorerhas completely mapped the scalar field and then use allthe candidate locations to pick k locations. However, in ourapplication of sampling water from the surface of the waterbody, based on its current properties, it is very important thatthe water-quality measurement (using water-quality sensoron the explorer robot) and the physical water sample aregathered temporally close to each other. This is because ofthe dynamic behavior of the phenomenon that we are tryingto capture. Hence, in this paper we discuss a technique tocollect physical samples in parallel with the explorer andachieve a good sampling score by collecting samples withinthe peaks hotspots in the spatial field.

As formalized in Section II, given M measurements—i.e., candidate sampling positions—we need to choose ksample locations that optimize the quality of the final result.Since we are looking at simultaneous decision making alongwith the explorer, there is a need for optimal stoppingcriteria—in other words, when the sampler decides to useone of the remaining water sampling units to collect aphysical sample. This problem has similarities with theclassic Secretary Problem that uses optimal stopping theory.The basic form of the secretary problem has n applicantswho are interviewed in random order, and a decision is tobe made immediately after every interview. Once rejected, anapplicant cannot be recalled. So, the problem is to choosean optimal stopping rule to maximize the probability ofselecting the best candidate. Our problem is a variant of thisproblem as we need to choose k sample points instead of justone. Moreover, we have an advantage: the robot can lookback and choose an old candidate if it is the best locationto sample water from. In our case, we want to maximizethe sum of the values at sampled locations (

∑l∈L∗ f(l))

with a minimum distance constraint (Td). The threshold Tdprevents acquisition of spatially neighboring samples. Thevalue for Td is application specific and also depends on the

possible error in robot localization. We still need a stoppingrule to make our decision. Hence, we use a variant of thesecretary problem algorithm that suggests we reject first n

ecandidates and then stopping at the first candidate with ahigher ranking than all the ones evaluated until now. In thisway, the probability of success is maximized and is 1/e [23].In our case, we need to choose k samples, hence the stoppingthreshold becomes n

ke .

Algorithm 1 Look-back Selective Sampling AlgorithmInput: Number of water sampling units k

Measurements frequency in Hz, fMission duration in s, TmDistance threshold in m, Td

Output: List of selected candidates L∗ where sampler shouldtake samples

1: τ = Tm∗fk . Total maximum number of measurements

for each water sampling unit2: L = ∅ . List of candidates suggested by the explorer3: L∗ = ∅ . List of selected candidates4: Cc = 0 . Current candidate counter5: found = false . Flag to identify sample chosen withinτ

6: repeat7: l = receiveMeasurementFromExplorer()8: Cc = Cc + 19: if ( Distance(l, L∗) > Td ) then

10: L = L ∪ l11: end if12: if Cc == τ/e then13: ymax = maxl∈L yl . yl: measured value in l14: else if Cc > τ/e then15: if yl > ymax then16: l∗ = l17: found = true18: else if Cc == τ then . Time slot expired for k19: l∗ = argmaxl∈L yl20: found = true21: end if22: if found == true then23: goToAndSample(l∗)24: L∗ = L∗ ∪ l∗25: remove l∗ and its neighbors within Td fromL

26: Cc = 027: found = false28: end if29: end if30: until |L∗| ≥ k

Kleinberg suggested an algorithm [25] that works bysplitting the candidates in two roughly half intervals chosenrandomly using a binomial distribution B(n, 12 ). Then, thealgorithm proceeds by recursively applying the classic secre-tary algorithm. The submodular secretary algorithm proposedby Bateni, et al. [11] provides a mechanism for selecting a set

90 m

100

m

(a) (b) (c)

Fig. 5. (a) Gazebo simulation for the ASV [24] used in our experiments. (b) Simulated chlorophyll density map overlaid on top of the water surface.The colorbar shows the simulated chlorophyll density. (c) Part of the Lake Nighthorse, Durango used for running simulation experiments.

of candidates with the top sum of individual rating of candi-dates. This algorithm could be a good fit for our problem ofmaking online decision about the water sampling. However,the submodular algorithm splits the samples uniformly intok equal windows and the samples from one window arenot considered while making a decision for another window.We would like to have an option to look back into all thewindows while making the decision. This is because, in ourapplication, we are not bound by the trajectory followed bythe explorer. The sampler robot is free to go back and visitany old measured location if it does not find any eligiblecandidate as the time proceeds. Hence, we propose a look-back selective sampling technique, where the robot appendsnew candidates into a list and use the list to look back ifthere are no eligible candidate within the time threshold. Thepseudo-code for our approach is presented in Algorithm 1.

Line 1 divides the maximum number of measurementover the mission in k uniform time slots. Line 9 check ifa new measurement taken at location l is far enough fromcurrent selected sampling locations. Line 12 is the secretaryproblem threshold to get optimal probability. Line 15 makesan irrevocable decision, following the secretary problemalgorithm. However, if the time slot for a water samplingunit expires (Line 18), then the sampler samples from thelocation where ymax was found. The rationale is that givenk water sampling units, Tm should not be spent all for oneof them.

IV. EXPERIMENTAL RESULTS AND DISCUSSION

We evaluated the system in both simulation and in thefield on real robots. The simulation environment allows usto report extensive repeatable controlled measurements ofperformance using realistic data with perfect ground truth.The field deployment lets us observe the performance andfeasibility of our approach in practice and confirm its utilityand usability. Three different setups are used in this paperto extensively evaluate the proposed system: 1. Simulatedrobots exploring and sampling from a synthetically createdworld, 2. Real world data (chlorophyll concentration in theflood plains of Amazon) is used to create a world forsimulated robots, and 3. deployment of two robotic boatsin a reservoir to map the chlorophyll density distribution inthe reservoir and collect water samples rich in chlorophyllcontent.

Fig. 6. Chlorophyll concentration dataset used for validating our ex-periments : (a) Flood plains of Amazon river. Considered region is ap-proximately (2 km× 2 km) (b) Chlorophyll concentration (mg/m3) mapgenerated from MODIS reflectance values [27].

A. Simulations

Gazebo [24] with an autonomous surface vehicle (ASV)plugin [26] that simulates a physically realistic ClearpathHeron robotic boat (Figure 5(a)) is used in our experimentsdue to its capabilities of simulating the vehicle dynamics toreasonable precision. A ROS node was created to simulate awater quality sensor, returning measurements at given GPSlocations, according to some data source. Two environmentsare used for our simulations, one with synthetic data, theother one with actual data.

The synthetic world, along with the simulator, are shownin Figure 5. In particular, Figure 5(b) shows synthetic datasimulating a chlorophyll density field overlaid on top ofthe water surface. To generate such data, we used multi-Gaussian models to imitate the chlorophyll dense regionsand its diffusion on the water surface. GPS data from aregion (100m× 90m) in Lake Nighthorse, Durango, CO(shown in Figure 5(c)) is used as the underlying localizationfor our simulations. We performed five repetitions for eachof the experiments in real-time simulation (one trial lastingapproximately 2.5 hours).

The real setup in our simulations uses the chlorophyllconcentration (mg/m3) map, at the flood plains of Amazon,generated from MODIS reflectance values [27]. We chose abounded region of size (2 km× 2 km; see Figure 6(a)) fromthis dataset to build an environment for the simulated ASV.The spatial field from this dataset is presented in Figure 6(b).

We evaluate our system by initially comparing and testingboth the components (explorer and sampler) separately andthen we present results from the whole system coordinatingtowards the collection of water samples with high utility

(a) (b) (c)

90 m10

0 m

Fig. 7. Trajectories planned and traversed (Yellow lines) by the ASVaccording to: (a) Planning window based GP-frontier explorer. (b) Globalmaximum variance search. (c) Lawnmower coverage.

measured in terms of sampling score (mentioned later in Eq.(5)).

1) Evaluating the explorer: To estimate the utility of ourexploration algorithm, we measure its performance over timeand compare this to alternative state of the art approaches.Note that most methods assure good data as time (or distancetraveled) approaches infinity, but one attribute of interest isto try and acquire a good estimate as early as possible. Priorapproaches to such coverage and sampling problems canbe grouped as deterministic complete coverage (such as theboustrophedonic coverage, or “lawnmower” algorithm [4]or stochastic methods).

In this paper, we compare the GP-frontier based explorerto two other exploration techniques: global maximum vari-ance search, and lawnmower coverage. Global-maximumvariance search involves predicting the variance at everylocation in the region and then search over the entire gridworld. These two operations are computationally expensivecompared to a small set of predictions needed for ourapproach. As a reminder, our approach needs predictionsonly at the locations that lie on the planning window bound-ary (Figure 2(b)). Also, Global-maximum variance searchgenerates longer trajectories (Figure 7(b)) thus making itpower inefficient compared to our approach. The traditionalapproach to covering a partially observable, obstacle-free re-gion is to employ a boustrophedonic or lawnmower coverage.Such complete surveys (Figure 7(c)) are infeasible, as we arelimited by battery life on the robots.

We compare these exploration techniques by computingthe Root Mean Squared Error (RMSE) of the generatedrepresentation relative to the ground truth data (Figure 5(b)):

RMSE(d) =

√∑c∈E′(f

t(c)− f(c))2

|E ′|, (4)

where RMSE is the root mean squared error after traveling agiven distance d. c ∈ E ′ is the set of cells from the discretizedworld, f t(c) is the predicted value at c with the GP at timet, and f(c) is the ground truth value at c. The plots inFigure 8 show that, as the travel distance increases, moreof the world is explored by all the techniques and they allconverge to a good representation of the world. Nevertheless,the GP-frontier explorer generates a good representation ofthe spatial field with less traveled distance, by choosing right

Fig. 8. Comparison of RMSE over travel distance. Plots from differentexploration techniques validated on simulated data. Note that the plot startsat 100m.

Fig. 9. Comparison of RMSE over travel distance. Plots from differentexploration techniques validated on real Chlorophyll concentration data fromAmazon flood plains.

locations to visit and map, thus providing better results thanother techniques compared in this paper.

Figure 9 presents the RMSE comparison when operatingin a larger field and working in the environment createdusing real chlorophyll concentration dataset. Even here, theGP-frontier based explorer performs well in the beginningand later performs on par with maxima-variance searchtechnique. The larger field and fast changing weight function(Eq. (2)) affect the performance of our technique. We arecurrently working on optimizing this weight function.

2) Evaluating the sampler: A smart sampler can chooselocations with a spectrum of measurements to representthe diversity in the spatial field, or it can sample fromlocations that give high rewards. For our application, we

Fig. 10. Simulated distribution of chlorophyll density overlaid with thecandidate locations (red dots) selected for sampling water. (a) Look-backSelective Sampling approach, (b) Submodular Secretary Algorithm.

Fig. 11. (a) Rogers Reservoir, Durango, CO, where field experiments were conducted. (b) The explorer trajectory (yellow) and the chosen samplingcandidates (red circles). (c) The spatial mapping of chlorophyll density (µg/l) generated using explorer measurements. Red-dots are the chosen candidatelocations for water samples.

(a) (b)Fig. 12. Results form experiments with synthetic and real data. The barplots indicate the sampling score between the two sampling methods. Theerror bars show the standard deviation over five real-time trial.

want the samples from hotspot regions that are high inchlorophyll density. However, we also do not want all thesamples to be from the same spot. Hence, to evaluatesuch a system we propose a sample scoring metric whichevaluates the sampling techniques according to their abilityto choose non-neighboring samples from hotspot regions.The maximum value (Mvalue) that can be achieved by anysampling technique is computed by summing the first klargest values among the data measurements (f(x)) providedby the explorer. The scoring function (Eq. (5)) is the ratio ofvalue achieved by the sampling algorithm to the maximumachievable value:

Score =

∑l∈L∗ f(l)

Mvalue. (5)

We compare our look-back selective sampling with thesubmodular secretary algorithm [11] and Figure 10 shows thesample locations chosen (red dots) by both the algorithms.We compare the score from our sampling technique withthat from submodular secretary algorithm. The results inFigure 12 illustrate that look-back selective sampling is moresuitable for our application. This is because the submodularsecretary algorithm divides the whole segment into windowsand does not consider the candidates between the windows.However, in our application of sampling from a boundedregion, we are not constrained by not being able to go backspatially to take a sample.

Figure 13 illustrates the performance of whole system,explorer and the sampler working together to achieve goodsample quality. We conducted a series of experiments withthree explorer-sampler pairs. The results show that the mul-tirobot system with proposed components performs well by

Fig. 13. Sampling scores achieved by the complete system, using differentcombinations of explorers and the look-back selective sampler.

achieving samples with high sampling scores.

B. Field experiments

Our goal in this paper is to sample water from a closedwater body for ex-situ analysis. We are interested in gettingsamples that are rich in chlorophyll. Rogers Reservoir, lo-cated in Durango, Colorado (Figure 11(a)), is a drinking-water reservoir and monitoring this water body is veryessential for the city. For our field experiments, we used twoClearpath Heron vehicles (see Figure 1), one equipped withwater quality sensor—the explorer—and another equippedwith water sampling apparatus—the sampler. The explorerwas equipped with a water quality sensor that collects mea-surements at 1Hz. Repeated trials were performed, lastingfrom 30min to 1 h. Figures 11(b) and (c) show the trajectoryfollowed by the explorer and a representation of chlorophylldistribution in the region of survey. The candidate locationschosen by the sampler are shown with red circles. Thefield experiments also confirmed that the proposed look-back sampling technique achieves higher sampling scores(Figure 14).

The methods worked as expected on the real robots. Nev-ertheless, it is worth to mention some of the additional issuesthat need to be taken care of during field experiments: GPSerrors and antenna-case leaks; the fact that a dense coverageshould be run every time before the actual experiment toensure that we have the most recent data as ground truthto evaluate our method; if candidate locations are too close,reaching them could be a challenge because of the noisy

Fig. 14. Results from field experiments. Comparison of sampling scoresbetween the two sampling methods.

control. Especially in the marine domain, weather can affectthe schedule and also the properties of the environment.

V. CONCLUSIONS

In this paper, we proposed a heterogeneous multirobot sys-tem for physical sampling of a water body providing methodsfor two related subproblems: one exploration algorithm tobuild the phenomenon map, which concurrently drives thesampling algorithm to actually collect physical samples.The core of the approach is to combine efficient real-time estimation of a variable upon which our phenomenonof interest is conditionally dependent with the subsequentcollection of data. Due to vagaries of field conditions, animportant consideration was that our approach should alsobe an anytime algorithm so that useful results are obtainedeven if weather or other factors lead to early termination. Ourapproach allows us to efficiently collect a set of informativesamples lowering the uncertainty over it and sample frommore significant hotspots, as compared to other methods.This is validated by simulation and the feasibility and prac-ticality was demonstrated via field experiments.

With respect to future and ongoing work, we are scalingup the approach for application over larger regions in morechallenging outdoor environments. This entails the use offaster and more capable marine vehicles. Explicitly modelingand accounting for communication interruption in the deci-sion making process is also an important next step to ensurereliability and robustness over large regions of space andtime [28], [29]. The consideration of time-varying modelswill also be an interesting step towards more large-scaledeployment in marine environments.

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