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JOURNAL OF IEEE ROBOTICS AND AUTOMATION MAGAZINE, VOL. 6, NO. 1, JANUARY 2011 1

Micro-Drone for Wind Vector Estimation and GasDistribution Mapping

Patrick P. Neumann, Sahar Asadi, Achim J. Lilienthal, Matthias Bartholmai, and Jochen H. Schiller

Abstract—This paper presents the development and validationof an autonomous gas-sensitive micro-drone, which is capable ofestimating the wind vector in real time using only the on-boardcontrol unit of the micro-drone and performing gas distributionmapping. Two different sampling approaches are suggested inorder to address this problem. On one hand, a predefinedtrajectory is used to explore the target area with the micro-drone in a real-world gas distribution mapping experiment. As analternative sampling approach we introduce an adaptive strategy,which suggests next sampling points based on an ArtificialPotential Field (APF). Initial results in real-world experimentsdemonstrate the capability of the proposed adaptive samplingstrategy for gas distribution mapping and its use for gas sourcelocalization.

Index Terms—anemometric sensor, autonomous Micro UAV,chemical sensing, gas distribution modeling, gas source localiza-tion, gas sensors, mobile sensing system, quadrocopter, sensorplanning, artificial potential field.

I. INTRODUCTION

At present, the release of hazardous and greenhouse gases isan acute threat and mainly responsible for extensive problems,both global (ozone hole and global warming) and local (pol-lution, poisoning hazards caused by accidents). Gases may bereleased in many different ways for various reasons: as exhaustgases from traffic or industry, as flue gases from fires, or asa consequence of incidents with chemicals. A fundamentalrequirement for emission control of, e.g., geodynamicallyactive regions, waste disposals, landfills, Carbon Capture &Storage areas (CCS), industrial sites, and contaminated areasis the availability of measurements of relevant gas concentra-tions in the area of interest with high spatial and temporalresolution. In order to obtain a truthful representation of thegas distribution, it is essential to collect spatially distributedconcentration and wind measurements. For economical anddeployment-related reasons, a stationary sensor network isin many cases not a viable solution. Accordingly, a quicklydeployable, mobile measurement device is needed.

Micro Unmanned Aerial Vehicles (MUAVs), especiallyquadrocopters, are suitable for gas distribution mapping asthey can be controlled precisely and equipped with a varietyof sensors. Furthermore, quadrocopers have the ability to

Manuscript received July 01, 2011. This work was supported by BMWiwithin the MNPQ programme (file number 28/07) and the EC (contractnumber FP7-224318-DIADEM).

Patrick P. Neumann and Matthias Bartholmai work for the BAM FederalInstitute for Materials Research and Testing, D - 12205 Berlin, Germany (cor-responding author to provide phone: +493081043629; fax: +493081041917;e-mail: [email protected]). Sahar Asadi and Achim J. Lilienthal aremembers of the AASS research center, Mobile Robotics and Olfaction Lab,Orebro University, SE - 70182 Orebro, Sweden. Jochen H. Schiller works forthe Institute of Computer Science, FU University, D - 14195 Berlin, Germany.

hover over a certain position, which allows more informativegas concentration measurements with slowly responding andrecovering chemical sensors in comparison to, e.g., a plane.Blimps, on the other hand, have a worse size-to-payload ratioand are more affected by the wind.

In this paper we first describe a gas-sensitive micro-droneand present an approach to estimate the wind vector (windspeed and direction) without a dedicated anemometer. Next,we exemplify how to address environmental monitoring taskswith the micro-drone and compare two sampling approaches tomodel gas distribution: sampling along a predefined sweepingtrajectory and a recently developed adaptive approach wherethe next sampling location is selected based on the continu-ously updated gas distribution model. Finally, we present real-world experiments and observe that the predictive variancemodel often provides a more accurate estimation of the gassource location than the modeled concentration mean.

In the remainder of this paper, we first describe the re-lated work (Sec. II) and propose a gas-sensitive micro-drone(Sec. III). Then, we introduce and validate a wind vectorestimation approach that uses the existing on-board sensors ofthe micro-drone only (Sec. IV). In Sec. V we summarize thegas distribution mapping algorithm used in this paper. Finally,we present and evaluate two different sampling strategiesto model the gas distribution with the micro-drone usingpredefined trajectories and adaptive sampling (Sec. VI and VII,respectively), draw conclusions and identify directions forfuture work (Sec. VIII).

II. RELATED WORK

Statistical Gas Distribution Modeling - Probably themost straightforward statistical gas distribution modeling ap-proaches use a grid of stationary sensors and discretize themodel at the same resolution. In [1], each grid point is assignedwith the average measurement, and in [2], instead, with themaximum value over the sampling period.

An alternative to a network of stationary sensors is to usea single mobile sensor that consecutively collects samples atpredefined locations. Under the assumption of a stationary gasdistribution, consecutive sampling is theoretically equivalentto simultaneous distributed measurements. Pyk et al. [3] in-terpolate the sensor measurements at locations other than themeasurement using bi-cubic or triangle-based cubic filtering,depending on whether the measurement locations formed anequidistant grid or not. A disadvantage of this method isthat no spatial averaging is carried out and that fluctuationstherefore appear directly in the map. Hayes et al. [4] use agroup of mobile sensors to create a histogram representation of


the distribution. The histogram bins collect the number of odorhits (these are measurements above some threshold) receivedby all sensors in the corresponding area while they performeda random walk behavior. This method requires even coverageof the environment and discards potentially useful informationby using only binary information.

The Kernel extrapolation Distribution Mapping (KernelDM) algorithm introduced by Lilienthal and Duckett dis-cretizes the available space into grid cells and computes anestimate of the distribution mean for each cell by using asymmetric Gaussian kernel [5]. The Gaussian kernel weighsthe importance of each sample to estimate gas distributionat each grid cell based on its distance from the respectivemeasurement point. Kernel DM does not rely on even coverageof the environment. Lilienthal et al. [6] extended this approachin the Kernel DM+V algorithm, which estimates the localvariance in addition to the mean of the gas distribution model.

In this paper, we use a micro-drone equipped with agas sensor and capable of measuring the local wind vector.To estimate the gas distribution model, we use the KernelDM+V/W algorithm [7], which is an extension of KernelDM+V that also considers wind information to compute thegas distribution model. The algorithm is described in moredetail in Section V.

Sensor Planning - Having a limited number of sensors,time, and power to monitor spatial phenomena, it is criticalto plan sampling locations that provide most informativesamples to build an accurate model of the environment. Severalpublications on spatial monitoring address this problem. Theselection of sampling points is typically based on differentcriteria such as the expected accuracy of estimated measure-ments and resource constraints, e.g., mobility, time, power, andwireless communication.

To monitor spatial phenomena with a sensor network,Krause et al. [8] apply Gaussian Process (GPs) and useMutual Information (MI) between explored and unexploredareas to optimize sensor placements. Based on temperatureand precipitation data sets, Krause et al. show that maximizingthe MI between explored and unexplored areas performs better(in terms of prediction accuracy) than entropy or geometricalcriteria.

To explore the area with one mobile sensor, where priorinformation about distribution and environment is not avail-able, one straightforward solution is to sample in predefinedlocations. We have applied this sampling method for gasdistribution mapping in an experiment in the geochemicallyactive Tuscany Region. The results are presented in Sec. VI.

To consider resource constraints, an alternative to predefinedsampling strategies is to adaptively select sampling locationsusing information about sampling locations and measurementvalues. Most of the previous work on informative path plan-ning has either dealt with nonadaptive approximation algo-rithms [9], that plan and commit to the paths before anyobservations are made, or with adaptive (often myopic, i.e.,limited look-ahead) heuristics, that update and replan as newinformation is collected [10]. Partially Observable MarkovDecision Processes (POMDPs) have been used to performadaptive path planning in complex environments [11]. Singh

et al. [12] extend a non-myopic approach to perform adaptiveinformative path planning by addressing a tradeoff betweenexploration and exploitation.

In this paper, we introduce an adaptive sampling methodwith path planning for a gas-sensitive micro-drone whichaccomplishes a tradeoff between exploration and exploitationby using an Artificial Potential Field (APF) approach. Theproposed APF approach combines three criteria to select thenext sampling locations: maximizing the coverage area byusing information about previous sampling locations, targetingareas with high predictive mean and high predictive variancein current statistical gas distribution model.

Artificial Potential Fields in Mobile Robotics - APFmethods are used in a number of robotic applications includinglocal navigation and obstacle avoidance. APF approaches havealso been used for the spatial formation of a set of sensors,spatial monitoring, and coverage problems.

In [13], an APF approach is used to deploy a decentralizedmobile sensor network in an unknown environment. Eachsensor is repelled from obstacles and other sensors and aviscous force is applied on the sensor to reach an equilibriumstate. The spatial configuration of sensors is affected bychanges in the environment (e.g., movement of obstacles) thatcan shift the equilibrium state.

To direct sampling locations, we use an APF which com-bines the repulsive and attractive forces on a single mobilesensor; the attractive term directs sensor towards areas withhigh values of predictive mean and variance and repulsiveterm applies a repulsion force to previous sampling locations.Samples are collected consecutively and APF changes at eachiteration based on the measurement values and locations,therefore, there is no unique equilibrium state to which themobile sensor tends to achieve in contrast to the methodintroduced in [13]. For simplicity, we assume that there isno obstacle in the environment.

Environmental Monitoring using Gas-sensitive UAVsPrevious work on environmental monitoring using gas-sensitive Unmanned Air Vehicles (UAVs) addressed the prob-lems of measuring the spatial distribution of chemical plumesand searching for the emission source.

Kovacina et al. [14] developed a rule-based, decentralizedcontrol algorithm that relies on constrained randomized be-havior. The algorithm respects UAV restrictions on sensors,computation, and flight envelope and was validated in a simplesimulation environment with an UAV swarm searching for andmapping a chemical cloud within a region.

The use of a blimp based gas-sensitive UAV for deminingtasks including chemical mapping strategies based on a be-havioral and a neuronal model of the moth is investigated byBermudez i Badia et al. [15]. The chemical mapping strategieswere tested in simulations and real world experiments.

Bamberger et al. [16] developed a Stigmergic Potential Field(SPF) based approach to coordinate movement, transient acts,and task allocation among cooperating UAVs. Experimentswere performed with a single UAV, which was deployedto a simulated plume (using simulated sensors). The UAVconducted an autonomous search of the designated area andcharacterized the spatial extent of the plume successfully.


An expert system for contaminant mapping based on agenetic algorithm with physical reasoning using the windvector, online concentration measurements, and estimates ofthe source location to perform path planning for UAVs ispresented by Kuroki et al. [17]. The method was tested insimulations using the Gaussian plume / puff model.

In the project AirShield (Airborne Remote Sensing forHazard Inspection by Network Enabled Lightweight Drones)an autonomous swarm of MUAVs was developed to supportemergency units and improve the information basis about dis-asters. Within this project, two steering strategies of a swarmof MUAVs to efficiently cover a region of interest in orderto achieve a spatial 3D coverage for aerial plume detectionwere compared: the Self-repelling Random Walk (SRW) andthe Cooperative-repelling Random Walk (CRW) [18]. Thesesteering strategies were evaluated in simulations with respectto the 3D coverage.

Our developed APF approach is also a self-repelling strat-egy. However, a 2D version of the SRW presented in [18]is not considered within this work as it does not incorporatesensor data.

Real-world experiments with MUAVs in outdoor environ-ments are rarely available in the literature, especially in thearea of gas source localization and gas distribution mapping.Almost all of the related work is validated in simulatedexperiments only. However, a gas dispersal simulation doesnot capture all relevant real world effects and it is thereforeunclear how the obtained results extend to realistic environ-ments. A key contribution of this paper is that several real-world experiments were performed in uncontrolled outdoorenvironments.

Wind Vector Estimation using MUAVs - Kroonenberg etal. present in [19] the adaption of a pitot tube for winged smallsize UAVs. A pitot tube is the state-of-the-art flight speeddetermination method for aircrafts. But for a quadrocopter,a pitot tube is hardly applicable because of the inconsistentflight direction and low flight speeds (≤ 12ms−1). Further-more additional hardware would be needed to compensate themicro-drone’s inclination angle and turn the pitot tube nearlyin flight direction. This extra weight would reduce the availablepayload and the flight time of the micro-drone drastically.

There are other methods which consider wind information inthe control of MUAVs. In [20], a mathematical model is usedto estimate the aerodynamic and speed stability of a micro-drone using real-time measurements.

Instead, we present an approach to estimate the wind vectorbased on the on-board sensors of the micro-drone, whichmakes additional anemometric sensors superfluous.

III. GAS-SENSITIVE MICRO-DRONE

The Federal Institute for Materials Research and Testing(BAM), in cooperation with Airrobot GmbH, has developeda mobile and flexible aerial-based measurement system aspart of an R&D project funded by the Federal Ministry ofEconomics and Technology (BMWi) [21]. One result of theproject is a gas-sensitive sensor module (approx. 200g) for theAirrobot AR100-B micro-drone (Fig. 1).

(a)

(b)

Fig. 1. (a) The Airrobot AR100-B micro-drone and (b) the gas-sensitivepayload.

A. Robotic Platform

The Airrobot AR100-B micro-drone (in this article mostlyreferred to as micro-drone) has a diameter of 1m and isdriven by four brushless electric motors. The micro-drone canprecisely navigate to a certain region of interest for remotesensing without endangering persons in critical areas. Themaximum payload mass amounts to 200g with a total flightmass of about 1.3kg. The maximum flight time is about 20- 30min. The micro-drone can withstand a maximum windspeed of 8ms−1. The flight control relies on an on-boardInertial Measurement Unit (IMU), which also provides thebasis for the wind vector estimation presented in Sec. IV. Itconsists of a three axis accelerometer and a three axis rotationrate sensor. Magnetic field sensor (compass) and GPS improvethe accuracy of the IMU, and are used to compensate for thesensor drift. A barometric pressure sensor is used to control thealtitude of the micro-drone. Communication with the groundstation is established by a wireless radio link. Data packets caninclude control instructions or data coming from the micro-drone’s on-board sensors. The operating distance of the remotecontrol and communication link is 1km. The micro-drone canbe operated manually or in GPS mode, e.g., by autonomouswaypoint following.

B. Integration of Gas Sensors

A commercially available gas detector (Drager X-am 5600),which is originally designed as a handheld device for personalsafety, is the base unit of the gas-sensitive payload. It featureslow mass and compact design. The modular concept allowsapplication and ad hoc exchange of the four gas sensors, whichenables users to customize the device for specific scenarios.The Drager gas detector can measure many combustible gases


and vapors with a catalytic sensor as well as different (toxic)gases with electrochemical and infrared sensors.

An additional electronic board with the dimension of an AAbattery controls the communication between the gas detectorand the micro-drone via an integrated microcontroller andappropriate device interfaces (IrDA, RS232, and I2C). A tem-perature and humidity sensor (SHT15, Sensirion AG, Swiss)was also integrated as both factors may affect the measurementdata (however, no compensation for varying temperature orhumidity was applied in the experiments presented in thiswork). The casing of the gas detector is protected against waterand dust and therefore capable of working outdoors.

C. Gas Transport to the Sensors

Gas transport to the sensors is a critical process due to theinduced disturbance by the rotors of the micro-drone, whichbasically dilutes and disperses the surrounded gas-air mixture.This could be problematic for scenarios where punctual gassources are present or the gas sensors work at the lowerlimit of detection. We showed in [21], that measurements ofgas concentrations in a large volume is feasible for the gas-sensitive micro-drone.

To improve the measurement capabilities for small plumes,three different design approaches that lead to less diluted gas-air mixture at the gas sensors were implemented and analyzedwith respect to their functional performance: the passive, semi-active, and active gas transport approach. When applying thepassive gas transport approach, no artificial airflow is used tobring the gas to the sensors. When applying the semi-active gastransport approach, the gas-air mixture is conveyed through acarbon fiber tube using the suction effect of one rotor. Thetube of the active gas transport approach protrudes from theradius of the micro-drone by nearly 0.3m. Here, an axial fanwas mounted inside the tube to draw in the gas-air mixture.

Sensor response and decay can be sped up to some degreeby an artificially generated airflow to achieve faster andmore accurate gas concentration measurements with shorterresidence time of the micro-drone as shown in [22].Experimental Setup - Reproducible environmental conditionsare needed in order to compare the different gas transportapproaches. We used a gas source with a constant release rateand stable airflow conditions. An experimental setup to createsuch a controlled environment was build up at BAM. A CO2

gas bottle was used as the emission source. A fan generatedthe stable airflow conditions and dispersed the gas additionally.A defined measuring position was chosen for all experimentsapprox. 1m downwind from the fan in the height of the gasflow. A second Drager X-am 5600 gas detector was used asreference system to provide reference measurements. In theseexperiments we used a CO2 infrared sensor [22].

One experiment for each gas transport approach was per-formed. At the beginning of each trial, the gas concentrationwas adjusted so that the reference sensor measured a sta-ble value of 0.5% by volume. Afterwards, the micro-droneequipped with the gas-sensitive payload and one of the threegas transport mechanisms was flown to the measuring pointto perform CO2 measurements in flight for approx. 100s.

Fig. 2. Comparison of the gas transport approaches: Measured CO2

concentration at stable environmental conditions with micro-drone in flight.

Fig. 3. Micro-drone flying below a visualized plume in a wind tunnel at aflow speed of 2ms−1.

Results - The results of the experiments are shown in Fig. 2.Clear differences can be seen between the different gas trans-port approaches. In contrast to measurements in a large volumeof the same gas concentration, none of the approaches iscapable to measure the reference gas concentration of 0.5%by volume. The highest measured concentrations (peaks) layaround 0.32 (passive), 0.30 (semi-active), and 0.39 (active)% by volume, which is 64, 60, and 78% of the referencemeasurements. The averaged measurement results, after thesensor responded were 0.18±0.02 (passive), 0.26±0.01 (semi-active), and 0.33 ± 0.02 (active) % by volume, which is 36,52, and 66% of the reference measurements.

The reason for the generally lower measurements comparedto the reference sensor is the rotor movement of the micro-drone. The active gas transport method can avoid this dilutioneffect best with the long carbon fiber tube. The disadvantagesof this method are, however, the additional weight (approx.76g), the position of the tube inlet, which strongly dictatesthe measurement results as well as the enlarged drone sizethat is exposed to wind. A tradeoff between the applicabilityand sensitivity is given by the semi-active payload (approx.26g). Using the semi-active gas transport it turns out that flyingrather below the plume is advantageous. In Fig. 3 it can beseen that the plume in front of the micro-drone is still intact,while the rotors redirect the plume completely downwards.

The semi-active gas transport approach was used in thereal-world experiments as it offers high applicability andreasonable sensitivity.


Fig. 4. The wind triangle defined by the flight vector ~v, the ground vector~w, and the wind vector ~u.

IV. ESTIMATION OF THE WIND VECTOR

The local wind vector is important for many existing gasdispersion models [23] to characterize the dispersion prop-erties of the plume, as well as for gas source localization,plume tracking [24] and for gas distribution modeling (Sec. V).Wind measurements are furthermore important since highwind speeds and strong wind gusts in the target area mayalso limit the use of the micro-drone presented in Sec. III-A,which can only resist wind speeds of up to 8ms−1.

The response of many gas sensors is caused by directinteraction with the chemical compound and thus representsonly a small area around the sensor surface. Additionally, asingle gas sensor does not provide directional information. Inorder to mitigate these limitations, directional information inform of the wind vector is useful. Consequentially, the on-board measurement of the wind vector in real-time is crucial.

In the following section a new approach introduced in Neu-mann et al. [21] is described and validated, which estimatesthe wind vector based on the existing measurement data of themicro-drone’s on-board sensors (IMU). This approach makesadditional anemometric sensors superfluous and is, to the bestof the authors’ knowledge, unique.

A. Theory

The wind vector estimation presented in this section is basedon the wind triangle (Fig. 4). The wind triangle is commonlyused in navigation and describes the relationship between theflight vector ~v, the ground vector ~w, and the wind vector ~u.Here, we can consider the 2D case since the knowledge ofthe gravity vector is available. Two of the three vectors orfour of the six parameters of the wind triangle (flight speed|~v|, ground speed |~w|, wind speed |~u|, drift angle α, and theangles β and γ) are needed in order to derive the remainingparameters. However, only the ground vector is directly givenby the GPS receiver of the micro-drone.

We estimate the flight vector ~v based on the roll and pitchangle of the micro-drone as well as on the orientation ofthe system with respect to the magnetic north pole using acompass. The micro-drone’s IMU provides the correspondingangles φ (roll) and θ (pitch). Fig. 5 shows the local coordinatesystem of the micro-drone.

~eroll =

0cosφsinφ

, ~epitch =

cos θ0

− sin θ

(1)

Fig. 5. Micro-drone with local coordinate system. The viewing directionof the micro-drone is considered as the inverse normal vector −~nY Z =(−1, 0, 0).

The inclination angle of the micro-drone ψ is calculatedfrom the cross product of the rotated unit vectors from Eq. 1and the normal vector ~nXY = (0, 0, 1) from the XY -planeparallel to the ground (Fig. 5) using Eq. 2. Finally, the angle ψcan be used to calculate the flight speed. The relation betweenψ and the flight speed |~v| was determined experimentally (seeSec. IV-B).

ψ = cos−1

(~nXY · (~epitch × ~eroll)|~nXY | · |~epitch × ~eroll|

)(2)

To calculate the flight direction vdir, we first need tocompute the angle λ between the viewing direction of themicro-drone, considered as inverse normal vector −~nY Z =(−1, 0, 0), and the projection of the vector ~epitch × ~eroll ontothe XY -plane using Eq. 3. To decide whether the vector~epitch×~eroll is located on the left or right of the micro-dronewith respect to the viewing direction, Eq. 4 can be solved. Thisdistinction is required as the result of Eq. 3 will be withinthe interval [0, 180]. The flight direction vdir is calculatedby using the angle λ and the compass angle of the viewingdirection of the micro-drone δcompass.

λ = cos−1

(~nXZ · (~epitch × ~eroll)XY

|~nXZ | · |(~epitch × ~eroll)XY |

)(3)

~nXZ · (~epitch × ~eroll)XY =

< 0 , if ~epitch × ~eroll is left> 0 , if ~epitch × ~eroll is right= 0 , otherwise

(4)The flight direction vdir is calculated using the angle λ and

the compass angle of the viewing direction of the micro-droneδcompass.

vdir =

(360 − λ+ δcompass) mod 360, if Eq. 4 < 0

(λ+ δcompass) mod 360, otherwise(5)

Finally, the wind vector ~u is calculated with the estimatedflight vector ~v and the measured ground vector ~w using thewind triangle (Fig. 4) and the law of cosines. The drift angleα is the result from the difference of wdir and vdir.


|~u| =√|~v|2 + |~w|2 − 2|~v| · |~w| · cosα (6)

β = cos−1

(|~v|2 − |~w|2 − |~u|2

−2|~w| · |~u|

)(7)

udir = (wdir + 180 ± β) mod 360 (8)

Eq. 6, 7, and 8 are used to get the wind speed |~u| anddirection udir for 0 < α < 180. The cases α = 0

and 180, respectively, have to be considered separately.The sense of rotation of β in Eq. 8 depends on the flightdirection vdir, i.e., if the flight direction is within the interval[wdir+180, wdir] mod 360, then rotation is clockwise (+β)otherwise anticlockwise (−β).

B. Experimental Study

Setup - The experiments took place in a Gottingen-type windtunnel [25] (TU Dresden, Germany). The tunnel has a flowdiameter of about 3m and an almost 4.5m long test section,which provided sufficient space for the experiments. The speedof the airflow in the wind tunnel can be set precisely with arelative error less than < 1%. The reference was measuredusing pressure sensors in the prechamber and in the free jetof the wind tunnel. Finally, the Bernoulli law [25] was usedto calculate the flow speed v in the wind tunnel.

Different series of measurements were performed in thewind tunnel in different radial orientations of the micro-droneand with different payload configurations. The wind tunnelwas adjusted to speeds from 1.0 up to 8.0ms−1 with anincrement step of 0.5ms−1. For each step, data were collectedfrom the micro-drone’s IMU for about 60s.Results - Fig. 6(a) shows the results from the wind tunnelexperiments. A relationship between the inclination angle ψand the flight speed |~v| based on different series of measure-ments has been achieved. A quadratic function was derivedby interpolation using the method of least squares (Fig. 6(b)),which can be used to directly calculate the flight speed |~v|from the inclination angle.

Further results show that different radial orientations andpayload configurations of the micro-drone (Fig. 6(a)) do notintroduce substantial differences and can thus be summarizedin a single interpolation function. In all cases the RMSE is≤ ±0.74 resulting in an average RMSE of 0.56 ± 0.23.The RMSE for calculating the wind speed is 0, 10ms−1.

C. Validation Experiments

Setup - The validation experiments took place on an open areaat the Orebro University (Sweden). An ultrasonic anemometer(Young 81000, R. M. Young Company, USA) was positionedin a height of approx. 2m. It has an operating range from0 up to 40ms−1 with a resolution of 0.01ms−1 (0.1) andan accuracy of ±1% (±2). Therefore, it provides a highlyprecise reference to the wind vector estimation using themicro-drone.

The experiment started while the micro-drone was manuallypositioned in a distance of 2 - 5m to the anemometer in

(a)

(b)

Fig. 6. Inclination angle ψ at different flow speeds v: (a) comparisonof different radial orientations of the micro-drone with standard payloadcontainer (approx. 200g) and without payload and (b) the reference functiondetermined using the available measurement data. The error bars indicate thestandard deviation ±σ.

a height of 2m. The position was chosen based on theactual wind data in a way that the generated airflow of themicro-drone’s rotors should not influence the anemometer.Measurements with the IMU, GPS, and anemometer wererecorded at a frequency of 24Hz, 4Hz and 1Hz, respectively,for about 20min. The position was controlled automaticallyusing only the on-board GPS of the micro-drone.

For the evaluation of these results we have to make theassumption that the wind vector measured at the anemometerand the micro-drone are comparable, i.e., that the wind fielddoes not change drastically over the distance between thereference measurement with the anemometer and the positionof the micro-drone.Results - A qualitatively and quantitatively good match be-tween the wind speed and direction measured with the micro-drone and the wind speed and direction measured with theanemometer was observed, see Fig. 7(a) and 7(b), respectively.Exceptions in form of small variations can be seen, e.g.,between 150 and 200s, and 1100 and 1150s. Reasons for thesevariations can be inaccuracies of the GPS receiver or a problemwith the position holding system of the micro-drone (e.g.,oversteering). Regarding the reference, the calculated RMSEfor the wind speed is ±0.6ms−1 (moving average of 20s),and ±14 (moving average of 20s) for the wind directionusing directional statistics [26]. Here, the uncertainties aremost likely introduced by the assumption of a homogeneouswind field, the imprecise synchronization of measured GPS


(a) (b)

Fig. 7. Validation of the (a) wind speed estimation and (b) the wind direction estimation.

and IMU data and a given packet loss of the data transmissionin the downlink of the micro-drone.

The results presented in this section are promising. In thisform, the wind vector estimation is of great importance andrepresents a major improvement over existing systems (e.g.,pitot tube) for a quadrocopter. No additional pitot tube oranemometric sensor has to be mounted in order to obtain thewind vector and valuable payload capacity is saved for othersensors. Based on the fact that the micro-drone already runs aKalman filter to obtain less noisy data from the IMU and GPSreceiver, averaging the calculated wind data over the last 20sseems to be sufficient in order to obtain a good estimation ofthe wind vector.

V. STATISTICAL GAS DISTRIBUTION MODELING (GDM)

For gas distribution modeling with the gas-sensitive micro-drone we use the Kernel DM+V/W algorithm introducedby Reggente and Lilienthal [7]. The input to this algorithmis a set D = (x1, r1, v1), . . . , (xn, rn, vn) of gas sensormeasurements ri and airflow measurements vi collected atlocations xi. The output is a grid model that computes anestimate of a confidence, as well as the distribution meanand variance for each cell. The confidence estimate dependson the scaling parameter σΩ and indicates whether a largenumber of measurements is available in the close vicinity ofthe respective cell (confidence close to 1) or not (confidenceclose to 0). We use the 2D version of the Kernel DM+V/Walgorithm to avoid the higher computational complexity of the3D Kernel DM+V/W algorithm [27] and because the limitedbattery capacity of the micro-drone does not permit a full 3Dsearch. In the experiments, the micro-drone was kept at anapprox. constant height in a single 2D plane.

The Kernel DM+V/W algorithm models the informationcontent of each measurement with a two-dimensional, mul-tivariate Gaussian kernel N . The shape and orientation of thiskernel depends on the local airflow vector v and on two meta-parameters σ and γ. If no wind is measured (or if no windinformation is available), the Gaussian kernel has a circularshape that extends according to a spatial scale σ. In case ofa non-zero wind measurement the kernel takes the shape ofan elongated ellipse with the semi-major axis rotated in winddirection and stretched according to the strength of the windand the wind scale γ.

Fig. 8. Pre-programmed flight trajectory of the micro-drone.

VI. GDM WITH PREDEFINED TRAJECTORY

Experimental Setup - Real-world gas distribution mappingexperiments were conducted in the geochemically active Tus-cany Region close to Mount Amiata. A sweeping trajectory ofthe micro-drone over an area of 5×20m2 in the riverbed of theAmbra river in Italy was pre-programmed and uploaded to themicro-drone before the experiments. The step size of the mea-surement points was set to 2.5m in x and 4.0m in y direction.The trajectory is shown in Fig. 8. Four runs were performedin which the gas measuring device was equipped with a CO2

sensor. Measurements were recorded at a frequency of 1Hz.The red dots in Fig. 8 show the positions where the micro-drone stopped to take gas concentration measurements for20s, which corresponds roughly to the response times of thesensors used. The position was controlled using the on-boardGPS of the micro-drone. The flight speed of the micro-dronebetween the stops was set to 1ms−1. Because of the lowflight height of about 0.5m, the height of the micro-dronewas corrected manually during the experiments. Take-off andlanding were also performed manually. Each run took about10min to complete. A naturally bubbling CO2 area sourcewith a size of approx. 3.0× 3.0m2 was within the upper one-third of the experimental area with the center located approx.around x = 4.5m and y = 20.0m.Results - Four sets of maps were created using the KernelDM+V/W algorithm with γ heuristically set to 0.2s, a cellsize of 0.25m and a kernel width σ of 1.0m. The windspeed measured by the micro-drone was rather low duringthe experiments (around 0 − 2ms−1). The predictive meanmaps resulting from the four runs are shown in Fig. 9. In thefirst trial (Fig. 9(a)) the position of the maximum in the mapcorresponds approx. to the position of the emission source inthe map. Figs. 9(b), (c) and (d) show results of the subsequent


Fig. 9. Mean map of the gas distribution of the (a) 1st, (b) 2nd trial, (c)3rd and (d) 4th trial. The center of the area source is denoted by a ⊗. Theconcentration value of CO2 is given in % by volume.

trials where the maximum of the predictive mean appearsapprox. in the middle of each map. Since the time betweenthe experiments was only 5min, a likely explanation is thatthe first run has caused an alteration in the gas distributiondue to the effect of the rotors of the micro-drone, which actlike a mixer that destroys the original gas dispersion pattern.This finding is supported by the observation that the maximumconcentration decreased steadily over the four trials. Furtherexperiments were performed in other parts of the TuscanyRegion with similar results.

VII. GDM WITH ADAPTIVE SAMPLING

Using sweeping trajectories to build detailed gas distribu-tion maps over large areas is time consuming. However, thebatteries of the micro-drone (equipped with payload) onlyprovide power for approx. 20min. With the micro-dronetaking samples for 20s at each measurement position, thebattery restricts the drone to a total of ≤ 60 measurementpositions while a minimum of 100 measurement positions isneeded to cover an area of 5 × 20m2 with a resolution 1m,for example.Basic Sensor Planning Approach - To arrive at a truthfulgas distribution model more quickly, we present an adaptivesampling strategy based on the sensor planning approachin [28]. The basic sensor planning algorithm in [28] usesinformation about the target area, previous sampling locations,and the current statistical gas distribution model and combinesseveral objectives in an APF approach. In particular, threeobjectives are used that direct the sensor towards areas of(1) high predictive mean, (2) high predictive variance, whilemaximizing the coverage area (3). The first two objectives im-plement exploitation of the information in the gas distributionmodel. They are realized with an attractive potential generatedby charges placed in each grid cell center. The strength ofthese charges is given by the corresponding predictive meanand variance. Accordingly, two APF contributions APF

(k)M

and APF(k)V are computed for each cell k. The third ob-

jective that corresponds to exploration is implemented by arepulsive potential generated by placing charges at all previousmeasurement locations, resulting in a third APF contributionAPF

(k)C . In the current implementation, we assign the same

repulsive force to all previous measurements. Finally, the APFcontributions are additively combined with importance factorsβM , βV , and βC for each objective.

Ultimately, a total of nsp suggested measurement pointsare identified by selecting in each iteration the location atwhich the total APF takes its maximum and updating the APFby temporarily placing an additional measurement charge atthe selected location. Theoretically it could happen that theattractive forces towards an increased mean and an increasedvariance in the opposite direction cancel themselves out. Inpractice, it is unlikely that the attractive forces are completelybalanced at the position of the sensor. Even if they would be,the sensor would be directed towards one of the directions andin the next step the symmetry would be broken.

In the proposed approach, we do not use any form ofgradient descent to navigate; therefore, the micro-drone doesnot get trapped in a local minima as in common potentialfield approaches to local obstacle avoidance. In addition, thereare repulsive terms in our approach at all previous samplinglocations and these terms help to escape local minima.Locality Constraint Sampling Strategy - The previouslydescribed sensor planning approach distributes its suggestionsover the target area without any spatial order. Moving themobile gas sensor directly to these locations tends to createa seesaw movement, which empties the batteries sooner,resulting in fewer measurements. Therefore, we add a localityconstraint by selecting out of the nsp suggestions from thebasic sensor planning approach, the most often suggestedclose-by measurement location. This is implemented by amatrix S that has the same discretization as the gas distributionmodel. For each grid cell k, S(k) counts how often the cell wassuggested since it was actually visited the last time. The nextmeasurement point is ultimately selected as the one with thehighest ratio S(k)/d(k), where d(k) is the distance between thecurrent position of the sensor and grid cell k. Thus, a locationfar away from the current position will only be selected if itwas suggested frequently. In the current implementation, weincrease not only the counter for a suggested cell but also thecounter of neighboring cells within a radius of 0.5m. A radiusof 0.5m corresponds to the area directly below the micro-drone(the diameter of the micro-drone is 1m).Path Planning Algorithm for the Micro-Drone - The initialmeasurement location is chosen randomly in the target area.Then the following steps are iteratively performed:- collect gas sensor and wind measurements while keeping themicro-drone at a fixed position for a prolonged time;- average the wind measurements over the measurement time;- compute the gas distribution model using Kernel DM+V/W(see Sec. V) – the input to the algorithm are the positions, gassensor readings and averaged wind measurements;- derive an estimate of the source location from the predictivegas distribution map (detailed below),- determine the nsp suggested sampling locations with the APFbased sensor planning component (Sec. VII),- update the matrix S and select a sampling location thatmaximizes the ratio S(k)/d(k);- fly the micro-drone autonomously to the selected samplinglocation and continue with the first step. (Measurements inbetween two sampling locations are not used to decrease theinfluence of a memory effect in the sensor response due to theslow sensor recovery.)


The algorithm terminates either if the battery runs out or theconfidence map α(k) is above a defined threshold for each cell.Experimental Setup - All experiments were carried out inan 8 × 12m2 outdoor area with the micro-drone equippedwith electrochemical CO sensors. Gas concentration and windmeasurements were recorded with a frequency of 1Hz. Themeasurement time was set to 20s. Next, the wind vectorwas averaged over all the measurements collected at themeasurement point. Each gas sensor measurement was thenincluded into the gas distribution model as if it was acquiredtogether with a measurement of the average wind vector, i.e.,the average wind vector was used for all individual gas sensormeasurements acquired at the measurement position.

The parameters of the Kernel DM+V/W algorithm wereheuristically set to c = 0.15m (grid cell size), σ = 0.40m(kernel width), σΩ = N (0, σ = 0.4) ≈ 1.0, and γ = 0.2s, andequal importance factors for the APF contributions. The flightspeed of the micro-drone between the measurement positionswas set to 1ms−1. Because of the low flight height of about1m, the height of the micro-drone was corrected manuallyduring the experiments. Each run took around 14 - 19 minutesto complete depending on the battery consumption of themicro-drone. A barbecue filled with burning coal and fresh,damp wood was used as a pollution source and was placedapprox. in the middle of the experimental area (at approx.(6.3, 3.8)m from the bottom left corner). The micro-drone wasset to autonomous waypoint mode directly after take-off.Results - The results presented in Fig. 10, 11(a), and 11(b)demonstrate the suitability of the proposed algorithm for gasdistribution mapping and its use for gas source localization.A total number of 16 runs were performed within this ex-periment. Fig. 10 shows for all 16 runs the distance betweenthe true gas source location and six different estimates afterthe last measurement. The first three estimates are derived byselecting grid cells in which the predictive mean, predictivevariance, or the product of mean and variance are maximum.The forth estimate is derived by selecting grid cells in whichthe predictive mean is larger than 90% of the maximum. Thecenter of this area is taken as the source location estimate.In the same way the last two estimates are computed usingthe variance (fifth result) or the product of mean and variance(sixth result). The true source location was within the meanestimation area only in four trials and within the varianceestimation area in six trials. This is in line with previousobservations that the concentration variance often provides abetter indication of the gas source location [29] than the mean.

Fig. 11(a) shows the final snapshot of run number 3 after31 measurement points. The top row shows the previouslyvisited sampling locations (left) and the corresponding meandistribution map r(k) (middle) and variance distribution mapv(k) (right) produced by the Kernel DM+V/W algorithm withσ = 0.4, c = 0.15m and γ = 0.2s as meta-parameters. Thebottom row shows the visualization of the APF with βM =βV = βC (right), the area with the next suggested samplingpoints and source location estimate, which are indicated bygreen and red dots, respectively (middle), and the matrix S,where the white cells are the previously selected cells andthe darkest cells correspond to the most often suggested ones.

Fig. 10. Box-plot of the distance between the gas source location estimateand the true source location of the 16 runs after 24 - 35 taken measurements:A peak mean, B peak variance, C peak mean·variance, D mean, E variance,and F mean·variance. The box shows the lower/upper quartile and the linedenotes the median. The mean is denoted by the small . The × stands foroutliers.

Fig. 11(b) shows exemplarily the trajectory produced by thepath planning algorithm in run 3 with starting position (x, y) =(11.0, 7.0)m (compare with Fig. 11(a)).

Initial results from these runs indicate the potential of adap-tive sampling in combination with gas distribution mapping inproviding a good estimate of the gas source location after arelatively small number of samples.

VIII. CONCLUSIONS AND FUTURE WORK

The combination of a micro-drone with chemical sensorsinto a mobile and flexible gas measurement device creates newpossibilities to estimate the risk potential in a variety of scenar-ios without endangering people. Targeted fields of operationare gas measurements in accident scenarios, emission controland monitoring of critical areas. In this article we describe aprototype of a gas-sensitive micro-drone and demonstrate itsperformance in a number of validation experiments.

An important enhancement for gas distribution modeling isthe possibility to estimate wind vectors without a dedicatedanemometer (that would consume valuable payload) usingonly the micro-drone’s on-board sensors. The proposed windestimation approach was evaluated in wind tunnel and fieldtests and used in the gas distribution modeling experiments.

In the first set of experiments, we computed gas distributionmodels with the Kernel DM+V/W algorithm using gas andwind measurements collected along a predefined sweepingtrajectory. These experiments indicate the potential of the ap-proach and highlight that the micro-drone may not be suitablefor repeated monitoring under low-wind conditions since itintroduces substantial disturbance to the gas distribution.

In the second set of experiments, we applied a novel adap-tive sampling strategy. The basic sensor planning approachuses the statistical gas distribution models obtained with theKernel DM+V/W algorithm. Areas of high mean and varianceare deemed good candidates for further inspection. Corre-sponding locations are prioritized through strong contributionsto an APF. These exploitation contributions are balanced byrepulsive contributions at previous sampling locations, whichpromote exploration. We extend this basic sensor planningapproach by introducing a locality constraint, which makes the


(a) (b)

Fig. 11. (a) The adaptive sampling process: From the previously visited sampling locations (top, left), predictive mean r(k) (top, middle) and variance mapsv(k) (top, right) were created using the Kernel DM+V/W algorithm with σ = 0.4m, c = 0.15m and γ = 0.2s as meta-parameters. The information from thepreviously visited sampling locations and these two maps are used to create the APF with βM = βV = βC (right). Then, a set of next suggested samplingpoints are selected. These points and the estimated source location are denoted by green and red dots, respectively (bottom, middle). The next samplinglocation is chosen based on the locality constraint sampling strategy, which is shown by the matrix S (bottom, left), where the white cells are the previouslyselected cells and the darkest cells correspond to the most often suggested ones. All plots were created after the last time step of the path planning algorithm(run 3, measurement 31). (b) Calculated sample trajectory of the path planning algorithm (run 3) with starting position (x, y) = (11.0, 7.0)m.

proposed trajectory more suitable for a mobile gas measure-ment system since it avoids large jumps between subsequentmeasurement locations. Our initial results with this extendedsensor planning algorithm show the potential of an adaptivesampling approach for gas distribution mapping. We alsoobserve that the produced maps (and particularly the varianceprediction) can provide good estimates of the gas sourcelocation. Our initial conclusion when comparing samplingalong a predefined sweeping trajectory with our proposedsensor planning approach is therefore that with adaptive sensorplanning we tend to arrive more quickly at a meaningfulmap which allows to infer a reasonably accurate estimateof the gas source location. If the sampling device is a gas-sensitive micro-drone, as considered in this paper, then astrategy that avoids sampling at low-informative places isadvantageous because of the resource constraints on the micro-drone. In addition, a lower number of measurements also tendto disturb the gas distribution less. This effect is, however, nottaken into account in our current sensor planning algorithmand we will investigate ways how to introduce a criterionthat allows minimizing the degradation of the observed gasdistribution through the micro-drone itself. A lower number ofmeasurements also tends to disturb the gas distribution less.However, this effect is currently not taken into account in oursensor planning algorithm and we will investigate ways how tointroduce a criterion that allows to minimize the degradationof the observed gas distribution through the drone itself.

The current implementation of the adaptive sensor planningalgorithm does not consider the time when the measurementswere made. We will therefore study extensions of the approachproposed in this paper that introduce time-dependency, forexample through a time-dependent statistical model as in [30].

ACKNOWLEDGMENT

The authors thank the participating colleagues from BAMand Orebro University. The authors also would like to expresstheir gratitude to BMWi (MNPQ Program; file number 28/07)

and to the EC (contract number FP7 224318 - DIADEM:Distributed Information Acquisition and Decision-Making forEnvironmental Management) for funding the research.

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Patrick P. Neumann is a scientist at BAM FederalInstitute for Materials Research and Testing in thedivision 8.1 Measurement and Testing Technology;Sensors in Berlin, Germany, since 2008. He has adiploma degree (M.Sc.) in Computer Science fromthe Freie Universitat Berlin. Currently he is gradu-ating in the field of robotics (direction: mobile robotolfaction).

Sahar Asadi is a Ph.D. student at the AASS re-search center, Mobile Robotics and Olfaction Lab,Orebro University (Sweden) since January 2009. Herresearch topic is statistical gas distribution modelingand sensor planning. She got her M.Sc. (2008)and B.Sc. (2006) in Computer Science both fromUniversity of Tehran, Iran in 2006 and 2008. Hercurrent research interests are mobile robot olfactionand distributed artificial intelligence.

Achim J. Lilienthal is associate professor at theAASS Research Center at Orebro University, Swe-den, where he is leading the Mobile Robotics andOlfaction Lab. His main research interests are mobilerobot olfaction, rich 3D perception, robot vision,and safe navigation for autonomous transport robots.Achim Lilienthal obtained his Ph.D. in computerscience from Tubingen University, Germany and hisM.Sc. and B.Sc. in Physics from the Universityof Konstanz, Germany. His Ph.D. thesis addressesgas distribution mapping and gas source localization

with a mobile robot.

Matthias Bartholmai is Head of the Working Group”Sensors and Measurement Systems” at the FederalInstitute for Materials Research and Testing (BAM)in Berlin, Germany. He graduated in energy andprocess engineering at the Technical University ofBerlin and received a PhD in the field of flameprotection of polymers. His actual range of activityis the development, validation and application of in-novative measuring systems and sensor technologies.

Prof. Dr.-Ing. Jochen H. Schiller is head of theworking group Computer Systems & Telematics atthe Institute of Computer Science, Freie UniversitatBerlin, Germany. His research focus is on wire-less, mobile, and embedded devices, communicationprotocols, operating systems for devices with smallfootprint, and quality of service and security aspectsin communication systems. Up to now, Dr. Schillerpublished 5 books and more than 150 internationalpapers.

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