Safety robotic lawnmower with precise andlow-cost L1-only RTK-GPS positioningJean-Marie CODOL1,2,3, Michèle PONCELET1, André MONIN2,3, Michel DEVY2,3

Abstract— In this paper, we will introduce an autonomousrobotic lawnmower, equipped by a safety and low-cost RTK-DGPS centimetric positioning system available also in semi-urbanenvironment. The GPS-RTK sensors are a pair of L1-only GPSreceivers (L1-only GPS receivers are cheaper than dual-frequencyones because of the existence of patents on the usage of thesecond frequency). This work is an extension of a collaborationbetween NAV ON TIME and BELROBOTICS, consisting onevaluate GPS replacement for the current mower area limit (aburied wire). The objective of the latest work is to ensure theGPS mission realization, keeping the same safety as the buriedwire one. In this context, this paper will present a completestatistical approach to L1-only RTK-positioning system in urbanenvironment. The result of this approach have been embeddedinto the mower machine, by using a Linux operating systemequipped with an ARM-9 processor running at 400MHz, andan UHF radio-communication to the reference station, this onehaving the role of realize path planning, geographical databasemanaging, remote and IHM communication.

I. INTRODUCTION

Navigation system is a critical work in autonomous roboticsystems. Robotic critical applications need guarantees in termsof precision, integrity, safety and availability. To reach thisgoal, we propose here to take into account these aspectsin a statistical approach for the design of a low-cost RTKnavigation system. This work was supported by NAV ONTIME and the LAAS-CNRS. In a first part we will presentthe original machine and the available solutions for GNSSnavigation. Then the positioning design who guarantees theprevious concepts, in particular the integrity one. Before toconclude presenting a 24 hour experiment.

II. MOBILE ROBOT DESIGN

A. BIGMOW machine

BIGMOW lawnmower robot was designed by BEL-ROBOTICS. The guenuine robot evolves on area limited bya buried wire: the area limit is detected by a wire sensorembedded into the mower. This sensor allows the machineto perform a turn around when the area limit is reached,and automatic return to charging operation (by following thewire). This robot is widely used by professional gardeners.Additionally, this robot is safe, so it can evolve in humanenvironment, the safety is guarantee by ultrasound and contactsensors, placed in the front of the machine. The hardware andprimary software architecture are presented in figure 2. Ourexperiments were done on an semi-urban terrain in Toulouse,

1NAV ON TIME, 42 Av. du Général Decroutte, 31100 Toulouse, France2CNRS;LAAS; 7 Av. du colonel Roche, F-31077 Toulouse Cedex 4, France3Université de Toulouse ; UPS, INSA, INP, ISAE ; UT1, UTM, LAAS ;

F-31077 Toulouse, Cedex 4, France

France, presented in photos of figure 1. This terrain is ideal(because of it is a little more difficult to real final application)when we know that these final applications will be to mowgolf courses, or sports terrains.

Fig. 1. The tests were performed on an urban terrain near Toulouse, France.The main difficulties was to navigate near the buildings.

Fig. 2. The machine guidance internal states are presented on the leftside of the figure. Transition between these states depends on the sensorsmeasurements, by an algorithm (the state machine transition process).

III. DGPS FOR MOBILE ROBOTS

Standard GPS positioning precision in urban environmentis incompatible with mobile robot operation, therefore wepropose to use DGPS-RTK technique. DGPS consists on acouple of receiver, one static and the other embedded onthe machine, the DGPS positioning process needs both GPS

measurements to perform measurements differentiation. RTKtechnique consists in solving integer ambiguities on eachcarrier phase measurement tracking loop. In this context, oneaccess to centimetric positioning. This positioning is relative,Figure 3 presents the differential pseudorange measurement∆ρit model with respect to geometrical constraints such as

∆ρit = pt.uit + ∆bt + εiρ,t

∆ϕit = pt.uit + λai + ∆bt + εiϕ,t

where ∆ρ and ∆ϕ stands for the differential pseudorange andcarrier phase measurements (between mobile and reference),p stands for the position, u the unit vector supporting the lineof sight, ∆b the differential receiver clock bias, a the integercarrier phase tracking loop ambiguity, λ is the carrier phasewavelength, t and i the time and satellite indexes.

Fig. 3. Differential GPS positioning eliminates the atmospheric delays.By differencing the pseudorange measurements between the mobile and thereference receivers, we estimate the relative antenna positioning in an accuracyway. Here p is the relative positioning and u is the unit vector from thebaseline to the satellite direction. The differential pseudorange measurementcontains term p.u added to the clock bias, but not atmospheric delays.

For a short baseline (less than 10km), the pseudorange mea-surements give us access to metric positioning precision, andtens of meters integrity (the same precision is reached usingEGNOS SBAS). The usage of carrier phase dual-frequencyreceiver in a DGPS way permit to reach centimeter accu-racy and integrity[1][2][3] . Thus mono-frequency receiverscan be used to perform the same precision performancesas dual-frequency one, despite an initialization time (someminutes)[4]. During this initialization period, one have accessto positioning with real typed ambiguity estimate (by evaluat-ing integer ambiguities as real typed values, table I resume theGPS and DGPS precision and integrity capabilities. FinallyPrecise Point Positioning technique (PPP)[5], allows integerambiguity resolution by using precise satellites monitoring,but this method need a worldwide expensive infrastructure.

TABLE IEXPECTED POSITIONING PRECISION AND INTEGRITY

Method Precision (m.) Prot. level (m.) delay (y/n)urban open urban open

GPS 50 5 100 10 nDGPS 20 2 50 5 n

RTK L1/L2 0.02 0.02 0.05 0.05 nRTK L1 0.02 0.02 0.05 0.05 y

PPP 0.02 0.02 0.05 0.05 y

Here protection level stands for a probability of being out-side the given area being 1e−5/hour. The solution presentedhere use low-cost mono-frequency DGPS RTK, in urbanenvironment.The improvement relies here in RTK integritymonitoring.

IV. INTEGRATE THE NAVIGATION SYSTEM INTO THEEXISTING PLATFORM

To integrate the DGPS RTK navigation helper into the BIG-MOW machine, we plugged on board an ARM-9 card runningat 400MHz with an embedded Linux operating system. Thisnavigation element contains also one mono-frequency GPSreceiver, an interface to machine guidance system, and alsoa radio communication (to communicate with the referencestation). Figure 4 presents the hardware and communicationarchitecture. This architecture have been patented by NAV ONTIME.

Fig. 4. Our navigation system architecture consist on performing the globalnavigation processes on the reference station. Measurement grabbing andtransmission is done on the robot. This allow also a short time autonomyin the case of short connection lost time.

We have chosen to perform the navigation process (in-cluding path planning, positioning and monitoring) on thereference station for two reasons: first this allows to mon-itor multiple machines, then because the navigation processneeds a lot of resources (processing power for carrier phaseambiguity resolution, for path planning, and memory for thegeographical database ...). These elements does not need to beembedded on each machines. The reference station performpath planning, positioning, monitoring ... and send back tothe embedded system, periodically, the navigation information.The navigation information contains the real-time guidanceorders. Thus, on BIGMOW machine, the guidance orders arecompliant with existing ’follow the wire’ orders.

V. RTK-GPS AND INTEGRITY

By using integer carrier phase ambiguity resolution, weperform centimetric RTK positioning. The advantage of usingmono-frequency receiver instead of a multi-frequency one isthe price (we consider a factor 100 between them). Thanksto this advantage, mono-RTK (mono-frequency RTK) is achallenge in robot navigation. Here we perform a completestatistical approach of this method, allowing robustness capa-bility of the navigation system. We will see, in a first part,how to construct an integer carrier phase ambiguity searchspace, and then how to perform the elimination test on eachof these hypothesis. The contribution in this paper is the usage

of explicit simple statistical tests to perform the RTK processin presence of multipath.

A. Floating ambiguity for RTK

Construct integer carrier phase ambiguity search spaceconstruction is divided in two ones : first estimating theambiguities as real typed values( in a Gaussian least squarecontext), then the integer hypotheses set construction. Thesearch space is the set of integer values in an interval. Wewill study this method. Let us consider the state vector Xcontaining robot pose R and real types ambiguities A, asGaussian random variables and let P the X correspondingto variance-covariance matrixes.

X = [R,A]T

X ∼ (X, P )

So we can define here our linear system

Xt = FXt−1 + wt

yt = HXt + vt

with F the dynamic system matrix, H the observation ma-trix, y the measurement vector, w and v Gaussian noisesrespecting E

[wwT

]= Q and E

[vvT

]= R. In [6], authors

propose to estimate ambiguities by a least square minimisationprocedure on pseudorange and carrier phase measurementsp(At|ϕ0:t, ρ0:t). In urban environment, due to multipath effecton pseudorange, it is more robust to use only carrier phasemeasurements. Given real typed ambiguities estimates At, oneaccess to integer values by choosing, for each ambiguity termai, an interval I where

∫Ip(ai)da = Pi. We construct, in this

interval I , the list of integer hypothesis {ai}. Knowing ai ∈ Z,one have

∑i p(ai ∈ {ai}) =

∫Ip(ai)da = Pi. So the integer

ambiguity search space is a N -combination of integers. Theprobability of containing the true ambiguities in our searchspace is P = Π(Pi). Note that considering Ni hypothesis onambiguity term i, the search space contains N = Πi<NNihypothesis.

In figure 5, we can see 2D case of the integer extraction.If the real typed estimated ambiguities are correlated, we canperform a smart ambiguity search (eliminating the ambiguitywhen the Mahalanobis distance exceed a rejection thresholds),we can see a 2D example in figure 5. If the test fails, we donot expand the sub-tree for this hypothesis.

This method is not the one used in our positioning pro-cess. Instead, we construct triple difference carrier phasemeasurement[7][8]. These measurement are ambiguities free.So the ambiguity search space is constructed by a differentprocess.

B. Triple difference for RTK

Recently, some improved triple difference positioningfilters[8][9]. These filters reach real-time performances, allow-ing embedded positioning process directly into robots. Tripledifference filter does not deal with real typed ambiguity terms.Thus construct the integer search space is done by a variablechange

Fig. 5. The search space for a couple of ambiguities is, on each ambiguity 1Dspace, the integers values into an interval where the probability is controlled.If the real types estimates values of ambiguities are correlated, so a naivesearch is not the optimal one.

∆ϕit = pt.uit + ai + ∆bt + εiϕ,t

ai = ∆ϕit − pt.uit −∆bt − εiϕ,tWe can deduce for each satellite double difference carrier

phase measurement (difference between measurement i anda pivot p), a Gaussian estimate of the ambiguity term ai.We construct the same search space as presented in previoustitle, about floating ambiguity. By this way, the probability ofnot containing the right ambiguity set in the search space iscontrolled statistically.

C. Integer ambiguity resolution : Gaussian noise case

The integer ambiguity resolution latency is a known prob-lem, called the Time To Fix (TTF). Clearly, TTF is the timeneeded to eliminate all the wrong hypothesis in the searchspace (including removing of all the hypotheses if the trueone is not in our search space). We chose to applied asimple hypothesis test (primary test) at each period T . Thenull hypothesis (H0 is the right ambiguity set) is tested. Weconsider the primary tests independent, and so we construct aN-binomial test.If the tested hypothesis contains the true ambiguities set,the residual norm statistical distribution is a centralized Khi-2 distribution. Given a PFA (Probability of False Alarmor ’first kind’), one can determine a threshold for primarytest. We perform this test multiple times and we eliminatethe hypothesis of the search space if this primary test failsmore than F times on N tests. So, if the primary tests areindependent, the probability of eliminating Ho follows beingin the search space is p(elim(H0)) and probability of keep awrong hypothesis Hi, p(keep(Hi)) are

p(elim(H0)) =∑

F<k<N

CkNPFAk(1− PFA)N−k

p(keep(Hi)) = 1−∑

F<k<N

CkNPNDki (1− PNDi)

N−k

where PND is the probability of non-detection (or error ofsecond kind). PNDi depends on PFA and the distributionof Hi residual norm (see figure 6(a)).

(a) Our khi-2 test consist on partitioning the residualnorm space in two parts, one of them having aprobability PFA. The test return ’true’ if the residualis out of this PFA interval.

(b) In presence of multipath effect, the previous workcan be reused, by modifying the threshold separatingthe partitions. We set it to ’PFA in worst case’, allowinga controlled integrity test.

Fig. 6. Summary of Khi-2 test. Here Khi-2(n) represent a n degreecentered khi-2 distribution, and Khi-2(d,n) represent a n degree, d center,non-centralized khi-2 distribution

D. Integer ambiguity resolution with Multipath

In the case of multipath, each carrier phase measurementsresidual norm distribution became a non-centralized khi-2 dis-tribution, and the noises are time-correlated. The first problemis eliminated by taking a different threshold on the primarytest (we fix PFA and deals with the worst-case distribution tokeep an upper bound of the test power). The second problemis solved by modifying primary tests period, taking accounttime to prevent correlation in multipath effect (some secondsis sufficient in dynamic case). The figure 6(b) show the newprimary test modelization.

To conclude, the key of our work is to define the PFAvalue and to use the worst case model for carrier phase noisespectrum. So the probability to not solve the true integerambiguity (the risk) is controlled.

VI. RESULTS

The validation of the new robotic lawn-mower navigationsystem was done on some lands in France. A successfuldemonstration was done in October 2010, near the stadiumof Toulouse, including a ’slalom path’ around plots.

The terrain presented in figure 1 is entirely mowed by thenew robot since many months. In figure 7 we can see a 24hour squared trajectory (the not aligned lines are trajectory toreturn to charging operation).

Although the ground truth is not available, the ’return tocharging’ operation need the robot to reach an electrical plugin a range of ± 5cm. This operation is realized with successduring many weeks, at a frequency of one return to chargingof two hours every two hours.

Fig. 7. The mowed terrain coverage during 24 hours, including the automaticreturn to station procedure.

VII. CONCLUSION

To conclude, we presented here a robotic lawn-mowersystem guided by a low-cost RTK-GPS navigation system.The positioning system have been seen as a stochasticalprocess, this way permitting to control the integrity. Finally themain result was presented : a 24 hours autonomous mowing,including the ’return to charging’ processes. This navigationsystem should be reused in many kind of robot, including areasecurity or mobile transport systems.

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