An Inertial/RFID Based LocalizationMethod for Autonomous Lawnmowers ?

Alessio Levratti ∗ Matteo Bonaiuti ∗∗ Cristian Secchi ∗

Cesare Fantuzzi ∗

∗ Alessio Levratti, Cristian Secchi and Cesare Fantuzzi are withDepartment of Engineering Sciences and Methods (DISMI), Universityof Modena and Reggio Emilia, via G. Amendola 2, Morselli building,Reggio Emilia I-42122 Italy. E-mail: {alessio.levratti, cristian.secchi,

cesare.fantuzzi}@unimore.it∗∗ Matteo Bonaiuti is with Centro Interdipartimentale per la RicercaApplicata e i Servizi nel settore della Meccanica Avanzata e della

Motoristica (INTERMECH), University of Modena and Reggio Emilia.E-mail: matteo.bonaiuti@unimore.it

Abstract:Robotic lawnmowers currently available in the market cover their assigned area using a randomreflection navigation strategy. While this strategy has been widely accepted for autonomousvacuum cleaning systems, it poses quality problems in outdoor applications since a randomiccrossing of the garden can lead to an uneven mowing. In this paper we propose a localizationalgorithm based on a modified Constrained Kalman Filter that allows to implement an efficientnavigation strategy and to increase the quality of service of the mower. This method properlymerges data coming from an Inertial Measurement Unit (IMU) and from an RFID (Radio-Frequency IDentification) antenna with information given by the Hall sensors of the wheelsof the robot. The proposed algorithm has been verified first by simulation, and then withexperiments by building a prototype lawnmower robot.

Keywords: Mobile robots; Inertial Measurement Unit; Kalman filters; RFID; Sensor fusion;Path planning; Coverage.

1. INTRODUCTION

Autonomous lawnmowers are a clear example of the bene-fits that robotics can take to our daily life. Unfortunately,in order to keep a competitive price, robotic mowers pro-ducers have to keep the robot as simple as possible and thisposes severe constraints on the behaviour of these systems.Most of the autonomous lawnmowers on the market usea random reflection navigation algorithm (Brooks, 1986;Inaki, 2010) to ensure the full coverage of an area. Thisalgorithm makes the robot going straight until it encoun-ters an obstacle or the border of the map, then it makesthe robot turn to a random angle, and then makes it gostraight again. This navigation algorithm is very cheapto implement since almost no sensors are required and ithas proven to be very successful in the vacuum cleanersmarket. Nevertheless, while randomic navigation strategiesensure a very high probability for the full coverage of anarea, they do not ensure a uniform coverage. When mowinga garden using this navigation strategy, after some time ithappens that some areas are almost arid while in someother areas the grass grows higher than expected, leadingto a poor aesthetic result.In order to obtain a uniform mowing, it is necessary tobe able to implement a more sophisticated navigation

? This work was funded by Regione Emilia Romagna in the scopeof the research project DiRo (Distretto della Robotica Mobile)

strategy and consequently, capability of the lawnmowerto localize itself within the garden (whose map is known)is required.The problem of localizing a mobile robot in an outdoorenvironment has long history in the literature. In (Chaeet al., 2010) a Kalman filtering approach to localize arobot operating in an outside environment using DGPS(Differential Global Positioning System) and INS (InertialNavigation System) is proposed. This method is quiteexpensive and becomes inaccurate when the satellite sig-nal is weak, such as when the robot is under trees ornear walls. Moreover (Newstadt et al., 2008) proposesa similar method based on the sensor fusion of DGPS,encoder data and a magnetic compass. This method couldbe inaccurate due to magnetic interference produced bymotors and other electronic devices mounted on the robotitself. In (Zhao et al., 2008) a laser scanner is exploited forlocalizing a robot in dynamic outdoor environment. Themain drawback of these, and of most of the mainstreamlocalization strategies, is that, in order to obtain goodperformance, they exploit sensors that are too expensiveto be used in a commercial lawnmower. Moreover, whenusing laser scanners for gardening applications, some arti-ficial landmarks would need to be installed in the gardenand this intervention may be unacceptable for aestheticreasons.Localization can also be achieved using cheaper sensors.

Recently new RFID based (Finkenzeller and Waddington,2003) localization methods have been proposed. Due tothe highly non-Gaussian noise which characterize thesesensors, usually PF (Particle Filter) based methods areused to estimate the position of a mobile robot (Joho et al.,2009; Hahnel et al., 2004; Schneegans et al., 2007) obtain-ing accurate position estimation. These results, however,can only be obtained by using a high number of par-ticles and by significantly increasing the computationalburden of the algorithm. For service robot applications,like autonomous lawnmowers, the available computationalpower is limited for cost reasons. Thus, it is not possibleto implement computationally demanding algorithms asparticle filters. In (Choi et al., 2010, 2011) a triangulationbased method, where many tags are densely present on thefloor is proposed. In gardening applications, this approachis unfeasible because it would imply to dig a lot of RFIDin the garden.In (Boccadoro et al., 2010) an efficient ConstrainedKalman Filter (CKF) is proposed for localizing a mobilerobot. However it is required that at least one RFID isalways detected by the robot.This research is made in cooperation with a companyleading in the production of gardening tools. The goalof this paper is to design a new approach for the local-ization and the navigation of robotic mowers. We aim atobtaining a uniform mowing of the garden while respectingthe cost budget for extra sensors. The proposed approachuses a low cost three degrees of freedom IMU (InertialMeasurement Unit) and an RFID (Radio-Frequency IDen-tification) antenna with an RFID reader to estimate theposition of the robot through RFID tags placed only on theborder of the working area (the garden). The localizationis obtained extending the CKF proposed in (Boccadoroet al., 2010) for merging the RFID readings with theodometric data coming from the Hall sensors of the wheelsand with the orientation information given by the IMU.In order to mow the whole garden without leaving un-treated areas and to avoid passing too many times on thesame area, we exploit the estimated position for developinga planner based on a double blaustrophedon path (twospirals, one perpendicular to the other), as suggested in(Das et al., 2011) and in (Shiu and Lin, 2008).

2. RFID SENSOR CHARACTERIZATION

It has been shown in Aliberti et al. (2008) that thereading region of an RFID in a dry indoor environmentcan be approximated with an ellipse. In the consideredframework, RFID tags will be placed on the border ofa garden, fixed to the perimetral cable that delimitsthe garden when an automatic lawnmower is used. Inthis condition, it can happen that the RFID is coveredby grass, mud or dust. In this section, an experimentalcharacterization of the reading region of the RFID underrealistic conditions is presented.For this experiment we used the RFID reader CAEN RFIDOEM A528. The antennas we tested are:

• CAEN WANTENNAX004 (linearly polarized)• CAEN WANTENNAX009 (linearly polarized)• CAEN WANTENNAX005 (circularly polarized)• Prototype antenna WANTENNAXVARIOUS (circu-larly polarized)

We tested both linearly and circularly polarized antennasin order to determine the one providing the best detectionarea and radiation pattern. Ideally the detection shouldnot be influenced by the orientation of the tag.During the characterization experiments we tested differ-ent tags, to identify the one providing the widest readingregion, according to our application, and with the smallestdimensions, in order to insert it inside a peg that will beburied in the ground:

• UPM RAFLATAC Wet Inlay RAFSEC short-dipole:a rectangular-shaped tag, bigger than the other testedtags, but with very good performance;

• LAB ID Inlay UH3D40: a square-shaped omnidirec-tional tag;

• LAB ID Inlay UH331: a rectangular-shaped tag;• LAB ID Inlay UHI4015: the tested tag with smallestdimension;

The experiment was made in order to identify the com-bination of devices with the most stable and well-shapedreading region but also to minimize the power consump-tion and the cost.First a support for the RFID reader and antenna wascreated with a 3D printer (see Fig. 1). Then we fixedit at the border of a graph paper sheet. The choice ofcreating the support in chalk was taken according to thefact that a metal support could alter the electro-magneticfield generated by the antenna thus altering its readingregion and the result of the experiments.The first set of experiments was made with the RFID tagsput on the graph paper. Then we measured the readingefficiency η defined as:

η =Tags

Acqs(1)

where Tags is the number of read tags per unit time andAcqs is the number of query done by the reader.Then we repeated the experiment by putting the RFID tagon the mud and repeated all the measurements. Finally wedipped the RFID tag in the mud and then repeated all themeasurements, to be sure that the RFID system is reliableeven in hard conditions, such as tags covered with mud,dust or grass.The experiments have shown that the most suitable combi-nation of RFID antenna, reader and tags has been found tobe WANTENNAX005 + A528 + UPM RAFLATAC WetInlay RAFSEC short-dipole. We chose a circularly polar-ized antenna to avoid the dependence of the measurementon the orientation of the RFID label. Even with the labelcovered with mud and grass, the reading region resultsstable and with only a little smaller dimensions.The chosen reader could provide to the antenna up to500mW power, but in order to reduce the power consump-tion of the robot and the localization error due to the largedimensions of the reading region, which could increasethe uncertainty in the measurement, we provided only200mW during the validation experiments. The resultingreading region can be seen in Fig. 2. The red rectangle incoordinates (0, 0) represents the position of the antenna.The yellow shaded area represents the region from whicha tag can be detected with 100% efficiency. Here η iscomputed with Eq.1.

Fig. 1. The support used for the characterization of theRFID devices.

Distance from the axis of the antenna [cm]

Dista

ncefrom

theante

nna

[cm

] Identification efficiency map

000

2020

20−20−40

40

40

40

60

6080

80

η[%

]

100

Fig. 2. The reading region obtained with A528RFID reader, WANTENNAX005 antenna and UPMRaflatac wet inlay RAFSEC labels.

3. THE MOWING STRATEGY

We considered the problem of localizing a mobile robotoperating in an outdoor environment of known dimensionwith n RFID tags (each with a unique code) placed on itsborder at known positions.We exploit the fact that RFID tags can be programmedto have a unique identification code and a limited areafrom where they can be read. When a code is read bythe robot, it can be uniquely associated to an RFID and,consequently, to its neighbouring region. Furthermore,the robot is endowed with an IMU from which it getsorientation information.In the following, the mowing strategy will be illustratedfor a differential drive robot, as our prototype. Everythingcan be easily extended to robots with different kinematicstructures.

3.1 The off-line set-up

First of all we discretize the working area (the garden tobe mowed) of the robot using an occupancy grid map,initializing the cells “to be mowed” with low cost values.The dimensions of the cells are chosen to be a little smallerthan the dimension of the blade mounted under the robot,in order to ensure a small overlap when covering the field.Exploiting the fact that the positions and the reading areasof the RFIDs are known, we build a data structure thatwill be used in the localization algorithm. Let Ar be thereading area of the r − th RFID and let A = ∪n

r=1Ar. LetC be the configuration space of the robot. The set A∩C is

discretized with a granularity much smaller than the oneused for generating the occupancy grid. We indicate withΛ the set of all the generated cells and with λi = (xi, yi, ϑi)the i− th cell. Each cell represents a pose from which therobot can read at least one RFID.We introduce an n−dimensional binary vector ρ for indi-cating which tags are read and which are not. If the j− thtag is detected, then ρ(j) = 1 and otherwise ρ(j) = 0.For each λi ∈ Λ, we build ρi, namely the binary vectorrepresenting the RFIDs that are detected by the robotwhen it stands at the pose λi. The poses λi and the vectorsρi are stored in a hash-table structure.

3.2 The localization algorithm

The proposed method is differentiated according towhether RFID tags are read or not by the robot. In thefirst case the algorithm, based on a three step KalmanFilter, makes a prediction according to the model of therobot (differential drive), it corrects the prediction withthe RFID measurement and then corrects the estimatedposition with the last three steps of the Extended KalmanFilter doing the measurement update step with the IMUdata. If no RFID is read from the actual position of therobot, then the algorithm makes the data fusion with asimple Extended Kalman Filter (Welch and Bishop, 2006)merging the odometric data with the information providedby the IMU.

Algorithm 1. Localization Algorithm

1 : µk = f(

µk−1,uk

)

2 : Σk = Φk−1 ·Σk−1 ·ΦTk−1 +Ψk ·Rk ·ΨT

k

3 : ρ = setRho()4 : ρ = ExpSmooth(ρ)5 : ρ = getRho(µk,Λ)6 : if (ρ 6= 0) & (ρ 6= ρ) then7 : ∀λi ∈ Λ s.t. ρi = ρ:

7a : Prob(λi) ∼ (µk, Σk)|λi

7b : pi = ε · Prob(λi)

8 : µk =∑

λi s.t.ρi=ρ

λi · pi

9 : Σk =∑

λi s.t.ρi=ρ

[λi − µk] · [λi − µk]T· pi

10 : else11 : µk = µk

12 : Σk = Σk

13 : endif14 : Kk = Σk · ΓT

k · (Γk · Σk · ΓTk + σ2

IMU )−1

15 : µk = µk +Kk · [ϑIMU,k − g (µk)]

16 : Σk = (I −Kk · Γk) · Σk

The algorithm is recursive and the k−th step is discussed.Lines 1 and 2 are the firsts two steps of the classical

Extended Kalman Filter: µk = (x, y, ϑ)T

k is the statevector of the system which represents the position and

the orientation of the robot at step k, uk = (δR, δL)T

k

is the input vector with δR and δL the advancements ofthe right and left wheel respectively. The vector uk ischaracterized by a noise due to the drift of the wheelsand is modelled with a gaussian white noise with zeromean and covariance Rk (Martinelli and Siegwart, 2003).

The function f(

µk−1,uk

)

is the time propagation modeldefined as:

f(

µk−1,uk

)

=

xk = xk−1 +δR + δL

2· cos

(

ϑk−1 +δR − δL

2d

)

yk = yk−1 +δR + δL

2· sin

(

ϑk−1 +δR − δL

2d

)

ϑk = ϑk−1 +δR − δL

d(2)

The term

(

δR − δL2d

)

is due to the discretization of the

numerical integration via a second-order Runge-Kuttamethod (Oriolo et al., 2002).Here d is the dimension of the axle of the robot. Giventhe time propagation function, let Φk−1 and Ψk be re-spectively its Jacobians computed in µk−1 and the inputvector uk. Σk−1 is the covariance matrix computed at theprevious step of the algorithm, while Rk is the covarianceassociated to the input.At each step, the antenna searches for neighbouringRFIDs. A scan of the ρ vector is then performed (line3). An element is set to 0 if the corresponding RFID hasnot been read and to 1 otherwise. In order to avoid falsepositive readings, we filter the ρ vector using exponentialsmoothing (line 4) as suggested in Boccadoro et al. (2010).Thus, we store the value of the ρ string for nw steps in thepast and we choose a parameter α ∈ (0, 1) for properlytuning the smoother and we obtain:

ρk =

[

nw−1∑

l=0

αl

]−1

·

nw−1∑

l=0

αl · ρ(k−l) (3)

where ρk represents the value of the string ρ at timek. Furthermore, after the prediction step, it is possibleto estimate the RFIDs that should be detected at theconfiguration µk by using the data structure Λ. We willindicate the corresponding value of the estimated readingas ρ (line 5).If some RFIDs are read and if the filtered string of theread RFIDs ρ and the expected string of RFIDs ρ aredifferent, it means that µk is inconsistent with the readtags and that it can be updated using the detected RFIDsand the corresponding reading regions.If the conditions at line 6 of the Algorithm 1 are satisfied,all the poses λi from which the tags corresponding to ρcan be read are fetched from the data structure Λ (line 7).Each λi represents a possible pose where the robot couldbe, given the reading of the RFIDs. Thus, we associate aprobability of being in each λi by evaluating the multivari-ate normal distribution with mean µk and covariance Σk

in λi (line 7a). In line 7b, a weight is associated to eachλi introducing normalizing factor ε. Finally in lines 8 and9 we compute the mean and the covariance matrix of thepredicted position updated using the RFIDs.If the conditions at line 6 are not satisfied it means thateither no RFIDs are detected or that the prediction madeusing odometry is consistent with the detected tags. Inboth cases the information coming from RFIDs is notuseful for improving the estimate of the pose. Thus, theprediction obtained using odometry is used (lines 11 and12).Once the prediction phase is over, the correction step of

the Extended Kalman Filter takes place. Line 14 computesthe Kalman gain, in line 15 the estimated yaw angle of therobot is corrected by merging the prediction with the datacoming from the IMU. Finally, in line 16, the covariancematrix Σk, is updated, in order to keep track of the esti-mation uncertainty. Here g (µk) is the measurement modelfunction computed with the just obtained estimation of theorientation, Γk is its Jacobian computed in µk−1, ϑIMU,k

is the yaw angle measured by the IMU at the time step kand σ2

IMU is its variance.Thus the robot can correct (if it is necessary) its estimatedposition every time it reaches the border of the workingarea, while the correction provided by the fusion withthe IMU keeps on correcting the orientation while therobots works in the middle of the garden. The drift of thegyroscopes is compensated by stopping the robot duringits task for few seconds, and then by considering the anglerates registered with the still robot as offsets. This simplestrategy has been proven successful in several field tests.Using the estimated pose of the robot, a path planningstrategy has been designed for obtaining a smart anduniform coverage of the whole lawn. In order to take intoaccount possible localization imprecisions that may lead tosome uncovered areas, a path consisting of two orthogonalspirals is generated for a square garden. This path isredundant and it increases the duration of the mowingtask but, at the same time, decreases the possibility ofleaving uncovered areas. This algorithm generates the pathto follow by selecting those cells of the occupancy grid inwhich the robot has spent less time, which have a lowercost, and then by increasing the cost of those cells in whichthe robot has already passed through. With respect to therandom navigation case, by using this method the cuttingredundancy is greatly decreased, as well as the energyconsumption and resulting in a better-looking final shapeof the lawn. This planning strategy can also be extended toirregularly shaped fields using vertical cell decompositionor other standard techniques (Lavalle, 2006).

4. SIMULATIONS

In this section is illustrated the effectiveness of the pro-posed localization algorithm through computer simulation.The used computer is a laptop with an Intel Core i3 350Mprocessor with a clock speed of 2.27 GHz and 4GB ofRAM. We used MATLAB R2010b(64bit) for the simu-lation. The simulated robot moves in a working area of(10×10)m with forty tags scattered along its edge (one tageach meter). We set nw = 5 and α = 0.99 as parametersof the exponential smoothing. We used a discretization ofthe reading region (as described in Section 3.1) with cellsof dimension (50× 50)mm and π/18 rad.The paths generated can be seen in Fig. 3. The red solidline represents the estimated path, while the blue dottedline represents the simulated ground truth. The yellow starrepresents the starting position, the red star and the bluestar represents respectively the final estimated positionand the ground truth. The purple stars are the RFIDlabels. The dark green thick line indicates the border ofthe map.

In Fig. 3(a) the paths generated with the proposed methodcan be evinced. The robot comes out of the working areaof only a few cm and the final positions, the ground truth

X [m]

Y[m

]

0

0

0

10

10

10

5

5

1

9

(a)

X [m]

Y[m

]

0

0

10

10

5

5

−2

12

(b)

Fig. 3. The simulated paths for the proposed method, Fig.3(a), and with the “only odometry” localization, Fig.3(b).

one and the estimated one, are almost overlapping (theestimated position is only 185 mm away from the groundtruth and the square mean error between the estimatedpath according to the ground truth is only 164 mm).As a comparison, we simulated the robot which is local-izing itself using a dead-reckoning algorithm, i.e. comput-ing its time propagation model using only data given byodometry (i.e. the Hall sensors mounted on the wheels). Ascan be evinced from the pictures (Fig. 3(b)), in the dead-reckoning case the robot leaves the working area of severalcentimetres, and its final position, according to the groundtruth, is far from the estimated one (about 2119 mm) andthe mean square error is 1328 mm.

5. EXPERIMENTAL RESULTS

In order to validate the proposed algorithm, a prototypelawnmower robot has been built (Fig. 4). The robot hasthree motors: two brushless DC motors for the wheels anda direct drive brushless DC motor for the blade. Eachmotor has its own driver. These motors are provided withHall sensors, which have been used to compute the speedof each wheel. The used IMU (a Silicon Sensing Pin-PointGyro Evaluation Board) has three gyroscopes, one for eachaxis, and is fixed on the top of the axle of the robot.The high-level control of the robot is performed by theReal-Time controller NI cRIO, programmed with Lab-

VIEW 2010 (SP1). This controller is provided with ananalog input module (NI9201), an analog output module(NI9263), a digital input module (NI9422) and a RS232interface module (NI9870).Under the robot, a three edged blade is used to accomplishthe cutting task. The blade diameter is 25cm. The RFIDantenna and the CompactRIO controller are located onthe front side of the robot. The 25V battery is located onthe back of the robot.

Fig. 4. The built prototype.

The experiments took place in a square arena with 2m sideand with eight RFID tags put slightly outside (40 cm) ofthe border of the field. The experiments took place on asynthetic grass carpet.The RFID antenna reading region, was approximated ac-cording to the results obtained in Section 2 with an ellipseof semi-axis 250 mm and 350 mm respectively.The map was discretized in an occupancy grid of 10 × 10cells (squares of 200 mm side). The dimension of thecell was decided taking into account the dimension of theblade of the lawnmower. Thus the robot, during its spiralshaped movement, partially covers cells in which it hasalready been, reducing the probability of leaving uncoveredareas. We set nw = 5 and α = 0.99 as parameters of theexponential smoothing.The robot starts its task from the middle of the first celland moves along the first spiral. Once it finishes the firstspiral, it gets back to the starting point and then startsmoving following the second spiral. Once the robot finishesthe second spiral it gets back to the starting point.In Fig. 5 the experimental results are shown. The thickdark line marks the perimeter of the lawn. White cellsrepresent areas where the robot hasn’t passed through,dark green cells represent areas where the robot has passedthrough while doing the first spiral and light green cellsrepresent those cells where the robot has passed throughduring the second spiral. Purple stars represents the po-sition of the RFID labels. The yellow star and the blackarrow represents respectively the initial position and ori-entation of the robot.In Fig. 5(a) the behaviour of the dead-reckoning local-ization can be seen. The robot moves accordingly to thepath-planner through the two spirals, but it goes almostone meter away from the border of the working area. Thisis unacceptable, because regulations (Regulation, 2010)require that the robot is allowed to leave the assigned areaof a maximum distance equal its length. Furthermore thecoverage of the area isn’t satisfactory at all.We also did an experiment using as localization algorithman Extended Kalman Filter which merges only the odo-metric information with the IMU data: results are shownin Fig. 5(b). In this case, the efficiency of the robot is

greater than the one obtained in the dead-reckoning case.The working area is almost covered, but the robot keepson going outside of the working area (about 40cm, almostthe length of the robot).Finally we repeated the experiment with the robot local-izing itself with the proposed strategy. The robot coversthe 100% of the working area, and it leaves the assignedmap of just few centimetres only when it’s turning.

(a) (b)

(c)

Fig. 5. The coverage of the robot in the case of “onlyodometry” localization, Fig. 5(a), in the case of sensorfusion with an IMU, Fig. 5(b), and for the proposedlocalization algorithm, Fig. 5(c).

6. CONCLUSIONS AND FUTURE WORK

In this paper a novel localization algorithm, based on amodified Constrained Kalman Filter, has been proposed.Simulations and experiments have been proposed to val-idate the results of the paper. With this new approachto navigation, autonomous lawnmowers can increase theirlife (the lawn is mowed in less time, so the battery lifelasts longer and mechanical parts are less subject to wear)and their efficiency (better final shape of the garden andless energy consumption) while respecting the cost budgetimposed by the market.To further test the efficiency of the proposed method, ex-periments in a wider working area and in areas of irregularshape will take place.Future work aims at improving the prototype of therobot. Furthermore, the current carrying perimetral wiresurrounding the garden will be explicitly considered andexploited for gaining further insights on the position of therobot and better results in the navigation.

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