LPV Model-Based Fault Diagnosis UsingRelative Fault Sensitivity Signature

Approach in a PEM Fuel Cell. ?

S. De Lira ∗ V. Puig ∗ J. Quevedo ∗

∗Automatic Control Department, Universitat Politecnica de Catalunya(UPC), Rambla de Sant Nebridi, 10, 08222 Terrassa (Spain);

Tel:+(34) 93 401 1682; Fax: +(34) 93 739 8628e-mail: salvador.de.lira@upc.edu

Abstract: In this paper, the problem of fault diagnosis in a PEM Fuel Cell (PEM FC) systemusing a model-based approach is addressed. A Linear Parameter Varying (LPV) model is usedto catch the non linear dynamics of the PEM FC. A new fault diagnosis method is proposedbased on structured residuals generation and sensitivity analysis evaluation. Robustness in faultdiagnosis is increased by use of a relative fault sensitivity approach. The proposed methodologyis applied to a Polymer Electrolyt Membrane Fuel Cell system. Finally, simulation results usingthe proposed approach presents a better isolability performance than classical Boolean faultsignature approach.

Keywords: Fault Detection, Fault Diagnostic, PEM FC.

1. INTRODUCTION

The energy generation systems based on fuel cells are com-plex since they involve thermal, fluidic and electrochem-ical phenomena. Moreover, they need a set of auxiliaryelements (valves, compressor, sensors, regulators, etc.) tomake the fuel cell working at the pre-established optimaloperating point. For these reasons, they are vulnerableto faults that can cause a emergency shut down or apermanent damage of the fuel cell. To guarantee a safeoperation of the fuel cell systems, it is necessary to usesystematic techniques, like the recent methods of FaultTolerant Control (FTC) in Blanke et al. (2003), whichallow increasing the fault tolerance of this technology. Thefirst task to achieve active tolerant control is based onthe inclusion of a fault diagnosis system operating in real-time. The diagnosis system should not only allow the faultdetection and isolation but also the fault magnitude esti-mation. In this paper, a LPV model based fault diagnosisis proposed as a way to diagnose faults in fuel cell systems.The model-based fault diagnosis is based on comparing on-line the real behaviour of the monitored system obtainedby means of sensors with a predicted behaviour obtainedusing a LPV dynamic model with an observer scheme.In case of a significant discrepancy (residual) is detectedbetween the model and the measurements obtained by thesensors, the existence of a fault is assumed. If a set ofmeasurements is available, it is possible to generate a setof residuals (indicators) that present a different sensitivity? This work was supported in part by the Research Commission ofthe Generalitat of Catalunya (Grup SAC ref. 2005SGR00537) andby Spanish Ministry of Education (CICYT projects ref. DPI-2005-05415, ref. DPI2007-62966 and ref. DPI2008-01996) and ConsejoNacional de Ciencia y Tecnologa (CoNACYT) and cooperation withDepartment of Universities, Research and Society of Information.

to the set of possible faults. The contributions of this paperare: first, the use of a LPV observer for fault detection andsecond, the use of the relative residual fault sensitivityanalysis that allows to isolate faults that otherwise wouldnot be separable. The structure of this paper is the follow-ing: in Section 2, the foundations of the proposed faultdiagnosis methodology are recalled. In Section 3, LPVmodel based fault detection methodology is described. InSection 4, the proposed fault diagnosis is presented. InSection 5, the PEM fuel cell system used to illustrate theproposed fault diagnosis methodology is presented withthe fault scenarios that can appear. Finally, in Section6, the application results of the proposed methodology ofdiagnosis are presented.

2. FOUNDATION OF THE FAULT DIAGNOSISMETHODOLOGY

2.1 Introduction

The task of fault diagnosis consists of determining thetype of fault with as much details as possible (fault lo-cation, time and size). The proposed methodology of faultdiagnosis which is used in this paper is mainly based onclassic FDI theory of model-based diagnosis described inGertler (1998), Staroswiecki and Comtet-Varga (2001) andIsermann (2005). Model-based diagnosis can be dividedin two subtasks: fault detection and fault isolation. Theprinciple of model-based fault detection is checking theconsistency of measured and predicted behaviors. Theconsistency check is based on computing residuals rk. Theresiduals are obtained from the discrepancy of measuredinput (uk) and outputs (yk) at operating point (ϑk) usingthe set of sensors installed in the process with an analyticalrelationship which is obtained by system modelling:

rk = ψ (yk,uk, ϑk) (1)

where ψ is the residual generator function that dependson the type of detection strategy used (parity equationGertler (1998) or observer (Chen and Patton (1999)). Ateach time instance, k, the residual is compared with athreshold value (zero in ideal case or almost zero in realcase).

Robust residual evaluation allows obtaining a set of faultsignatures, φ(ϑ) =

[φ1(ϑ), φ2(ϑ), ..., φnφ(ϑ)

]where each

indicator of fault is obtained as follows:

φi(ϑ) ={

0 if |ri| ≤ τi1 if |ri| > τi

(2)

where τi is the threshold associated to the residual ri(k).Fault isolation consists of identifying the fault that affectsthe system. It is carried out by using the fault signatures, φ(generated by the detection module) and its relation withall the considered faults, f(k) = {f1(k), f1(k), ..., fn(k)}The method most often applied is a relation defined on theCartesian product of the set of faults FSM ⊂ φ× f , whereFSM is the theoretical fault signature matrix (Gertler,1998). An element FSMij of this matrix will be one,if a fault fj(k) is affected by the residual ri(k). In thiscase, the value of the fault indicator φi(k) must be equalto one when the fault appears in the monitored system.Otherwise, the element FSMij will be zero.

However in practice, the existence of parametric uncer-tainty forces the use of robust methods, that can be activeif they act at the residual generation stage or passive ifthey act in the decision-making process.

3. LPV FAULT DETECTION

3.1 Lineal Parameter Varying Model

There exists different ways to obtain LPV models (Murray-Smith and Johansen (1997) and Barahyi and Patton(2003)). Some methods use non-linear equations of thesystem to derive a LPV model such as state transforma-tion, substitution of functions and methods using the wellknown Jacobian linearization. Another kind of methodsuses multi-model identification that consists basically intwo different steps. Fist a set of LTI model is identifiedat different equilibrium points by classical methods (on-line or off-line). As second part of this methodology amulti-model is obtained by using an interpolation law thatcommutes the local LTI model according to the operatingpoint. A LPV system in discrete time state space in a faultfree case is represented by;

xk+1 = A(ϑk)xk + B(ϑk)uk + wk (3)

y = C(ϑk)xk + D(ϑk)uk + vk

where xk ∈ Rnx , uk ∈ Rnu and yk ∈ Rny are,respectively, the state, input, and output vectors. Theprocess and measurement noises are wk ∈ Rnx and vk ∈Rnv . The type of LPV systems considered in this paperassumes an affine dependence within the parameter vectorΘ space

Θ ={ϑk ∈ RΘ

∣∣ϑk ≤ ϑk ≤ ϑk}

Lineal Parameter Varying Observer

A Linear Parameter Varying (LPV) observer with Luen-berger structure for the state estimation of the systemdescribed in (3) is given by

xk+1 = A(ϑk)xk + B(ϑk)uk + (4)

L(ϑk)(yk − yk) + wk

yk = C(ϑk)xk + D(ϑk)uk + vk

where L is the observer gain to be designed to guaranteestability for ϑk ∈ Θ. This gain is computed at operatingpoint ϑk using LMI formulation for Pole-Placement withina wide class of pole clustering regions that is foundedin an extended Lyapunov Theorem (see Chilali (1996)).The motivation for seeking pole clustering in specificregions inside the unitary circle is to obtain a fast observerdynamics for all considered operating points.

4. FAULT ISOLATION

4.1 Fault Sensitivity Analysis

The isolation approach presented in Section 2 uses a set ofbinary detection (Boolean) tests to compose the observedfault signature. However, the use of binary codificationof the residual produces a lack of information that canlead to wrong diagnosis when applied to dynamic systems.This derives in some faults that are not isolabable becausethey present the same theoretical binary fault signature(Puig et al., 2006). To avoid this problem is possibleto use other additional information associated with therelationship between the residuals and faults, such as sign,sensitivity, and order or activation time, to improve theisolation results (Puig et al., 2006).

In this work, a new method for fault diagnosis thattries to better exploit the information provided by thefault residual is proposed for diagnosis system designing.According to Gertler (1998), the sensitivity of the residualto a fault is given by

Sf =∂r

∂f(5)

which is a transfer function that describes the effect onthe residual (r) of a given fault (f ). Sensitivity providesquantitative information about the effect of the fault onthe residual and qualitative information in their sense ofvariation (sign). The use of this information at the stageof diagnosis allows separating faults that although showthe same theoretical binary fault signature, they presentdifferent sensitivity values. In order to perform diagnosis,the algorithm will use a theoretical fault sensitivity matrixFSMsensit. Each value of this matrix, denoted as Srifj ,contains the sensitivity of the residual ri to the faultfj . Although sensitivity depends on time in case of adynamic system, here the steady-state value after a faultoccurrence is considered as it is also suggested in Gertler(1998). However several simulation results show a dynamicdependency on operating points for Srifj matrix elements.In order to perform real time diagnosis, the observedsensitivity Sorifj should be computed using the current

value of the residual ri(k) at operating point ϑk when afault f(k) is detected.

ri(k) = Sori (ϑk) f(k) (6)

4.2 Relative fault sensitivity approach

From (6), it is possible to observe that using FSMsensit, inreal time requires the knowledge of the fault magnitude oran estimation of it at a specific operating point. To solvethis problem, this paper attempts to design the diagnosisusing a new concept called relativity sensitivity rather thanabsolute sensitivity given in (5). The observed relativefault sensitivity is defined as:

Srel,orirl=Sorifj (ϑk)

Sorlfj (ϑk)=ri(ϑk)rj(ϑk)

(7)

which corresponds to the ratio of one residual ri(k) withrespect to another specific one (rl). Then, the relative sen-sitivity will be insensitive to the unknow magnitude of thefault. A new FSM , called FSMsensitrel (see Escobet et al.(2009)), which corresponds to theoretical fault signaturematrix based on relative sensitivity is then introduced. Theelements of this matrix Srel,trirlfj

, is given by

Srel,trirl,fj=Strifj (ϑk)

Strlfj (ϑk)=∂ri(k)/∂fj(k)(ϑk)∂rl(k)/∂fj(k)(ϑk)

(8)

In this case, for a set of n faults, a relative fault sensitivitymatrix FSMsensitrel should be used as shown in Table 1.

f1 f2 · · · fn

r2/rl Srel,tr2rl,f1

Srel,tr2rl,f2

· · · Srel,tr2rl,fn

r3/rl Srel,tr3rl,f1

Srel,tr3rl,f2

· · · Srel,tr3rl,fn

· · · · · · · · · · · · · · ·rm/rl Srel,t

rmrl,f1Srel,t

rmrl,f2· · · Srel,t

rmrl,fn

Table 1. Theoretical fault signature matrixusing relative sensitivity respect to rl at ϑk

The diagnostic algorithm used to assess real-time observedrelative sensitivities using (7), is based on a ratio of residu-als, will provide a vector in relative sensitivities space. Thevector generated will be compared with vectors of theoret-ical fault places stored into the relative sensitivity matrixFSMsensitrel . The theoretical fault signature vector witha minimum distance with respect to the fault observedvector is postulated as the possible fault:

min ={dsf1(k), . . . , dsfn

}(9)

where the distance is calculated using the Euclidean dis-tance between vectors

dsfn (k) = sqrt

(Srel,or2r1,f1

(ϑk)− Srel,tr2r1,f1(ϑk)

)2

+ ...

+(Srel,ormr1,fn

(ϑk)− Srel,trmr1,fn(ϑk)

)2

(10)

5. CASE STUDY

In order to test the fault diagnosis methodology proposedin this paper, a PEM Fuel Cell is used as real processapplication case study.

5.1 PEM Fuel Cell System

Fuel cells are electrochemical devices that not only convertthe chemical energy of a gaseous fuel directly into elec-tricity and are widely regarded as a potential alternativestationary and mobile power source but also are environ-mentally friendly (EESI, 2000),(Yacobucci and Curtright,2004). Polymer Electrolyte Membrane Fuel Cells (PEMFC) are at developement stage for automotive applicationsbecause of its capability in high power density, solid elec-trolyte, long cell and stack life. The overall reaction of thefuel cell is described by

2H2 +O2 ⇒ 2H2O (11)

In this paper, a PEM FC model developed in Pukrushpanet al. (2002) is used as the case study for fault diagnosis.The overall FC system could be partitioned in two sub-systems: fuel cell stack and auxiliary components. Stack,anode, cathode and membrane hydration belong to fuelcell stack subsystem, while compressor, supply and returnmanifold, cooling and humidifier are the auxiliary compo-nents. Figure 1 presents a conceptual diagram of the FCsystem.

Fig. 1. PEM FC process diagram

A model-based dynamic analysis gives an insight of thesubsystem interaction and control design limitation be-cause of different control objectives (see Pukrushpan andStefanopoulou (2004)).

5.2 PEM FC Dynamic Model

For simulation purposes the model proposed in Pukrush-pan et al. (2002) will be used. This model has the followingcharacteristics:

• The law of mass conservation is used for mass balanceestimation.

• Physic laws and some empirical equations are used.• The properties are based on electrochemical, thermo-

dynamic and zero-dimensional fluid mechanics prin-ciples.

The resulting model dynamic equation set is described by

mO2 = WO2,i −WO2,o −WO2,r

mH2 = WH2,i −WH2,o −WH2,r

mN2 = WN2,i −WN2,o

ωcp = 1Jcpωcp

(Pcm − Pcp)Psm = γRa

Vsm(WcpTcp −Wsm,oTsm)

msm = Wcp −Wsm,o

mw,an = Wvan,i −Wvan,o −Wvmbr

Pom = RairTrmVrm

(Wca,o −Wrm,o)

(12)

where the subindex i,o, represent inlet and outlet flowrespectibly and subindex an, rm, mbr, sm, cp meansanode, return manifold, membrane, supply manifold andcompressor, respectively.

5.3 PEM FC Linear Parameter Varing Model

For fault detection previous model will be approximatedby a LPV model that it is scheduled with operating pointusing the stack current as scheduling variable along theoperating range.

The LPV model has been obtained through an off-lineidentification process performed along different operatingpoints in the operating range (OPR) of interest, where g =(ph − pl)/∆OPR, since high (ph) and low (pl) limits wereselected with an increment (∆OPR), where OPR ∈ Rg.In state space (SS) form, the structure of PEM FC linearmodel is described by

A(ϑk) =

a11 0 a13 0 a15 0 0 a18

0 a22 0 0 a25 0 a27 0a31 0 a33 0 a35 0 0 a38

0 0 0 a44 a45 0 0 0a51 0 a53 a54 a55 a56 0 0a61 0 a63 a64 a65 0 0 00 a72 0 0 a75 0 a77 0a81 0 a83 0 0 0 0 a88

; B(ϑk) =

0 b12

0 b22

0 0b41 b42

0 00 00 b72

0 0

C(ϑk) =

0 0 0 c14 0 0 0 0c21 0 c23 c24 0 0 0 00 0 0 0 c35 0 0 0c41 c42 c43 0 0 0 0 0

; D(ϑk) =

0 00 d22

0 00 d42

(13)

where x = [mO2 mH2 mN2 ωcp Psm msm mw,an Prm]T ,u = [vcm Ist]T and y = [ωcp rO2 Psm vst], states andoutputs are given in compatible unit magnitudes. Theresulting linear matrix system structure was denoted as(13), where each ij-th element is computed as a polynomialcorrelation of the scheduling variable from a non-linearregression.

5.4 Faulty PEM FC scenarios implementation

In order to test the proposed methodology in the PEMFC system, a set of common possible fault was selectedand implemented in simulation as a Fault Generator Block(FGB)(Figure 2). Through this block it is possible to selectand simulate them. Each selected fault acts over a specificpart of the overall system. But on other hand, interactionoccurs because of process dynamics and multiplicativeeffects of the faults. The Table 2 describes the set of faultswhich were considered.

6. RESULTS

The implementation of the fault diagnosis system (FDS)following the approach proposed in Section 3 has been

ID Fault Description

f1 There is an increase of friction in the compressor motor.

f2 Suddenly change in the system pressure because thesystem is not capable to avoid an atmospheric pressurechange.

f3 A suddenly obstruction at air inlet pipe is presented.The result is a decrease in the inlet diameter.

f4 Air leak in the air supply manifold.

f5 A degradation in the humidifier performancesis presented at stack upstream.

f6 Degradation in the cells at stack is presented because ofcontact-sensitivity reactions against a reaction killer.

f7 The 30 % of the cells suddenly are broken down.

f8 The fluid resistance increases due to water blocking,the channels or flooding in the diffusion layer.

f9 Hydrogen leak in the hydrogen supply manifold.

Table 2. Description of the fault scenariosimplemented in FGB.

Fig. 2. Fault Generator Block (FGB) and Fault DiagnosisSystem (FDS) implementation diagram

done using MATLAB/SIMULINK environment. The PEMFC Model already developed and described in Pukrushpanet al. (2002) was used as case study. A FGB and FDSsubsystems blocks were added to the PEM FC simulatordeveloped by Pukrushpan et al. (2002). The aim of thoseblocks is to diagnose the faults described in Table 2.

6.1 Fault Detection Process (FDP)

Structured residuals. Using the measured inputs andoutputs presented in Section 5.3 and using the structuralanalysis methodology (Blanke et al., 2003), the followingset of residuals can be obtained:

r1 = ωcp − ωcp;r2 = rO2 − rO2;r3 = Psm − Psm;r4 = vst − vst;

(14)

Those residuals are implemented using an observer inorder to reduce model uncertainty and measurement noise.

LPV Observer Design. The optimal observer gain L(ϑk)is computed using LMI formulation for Pole-Placementwith a region defined by an affix (−q, 0) and a radius rsuch that (−q + r) < 0, where in this case r = 0.1 andq = 0 (see (Chilali and Gahinet, 1996)).

An observability analysis along the operating point rangeof interest shows observability problems because of thehigh condition number for slow eigenvalues, degrading the

observer performance (Pukrushpan and Stefanopoulou,2004). A large observer gain is required, producing a largeovershoot in residual evaluation being not suitable forfault diagnosis system implementation, because a largeobserver gain can produce degradation of residual gener-ation. In order to avoid a large observer gain, a reducedobserver is designed: a closed-loop observer for fast eigen-value output estimation should be used while an open-loop observer is used for slow eigenvalues output esti-mation. To implement the reduced output observer, thesystem matrices are transformed to the canonical modalform: A(ϑk,2) = PA(ϑk)P−1, B(ϑk,2) = PB(ϑk) andC(ϑk,2) = C(ϑk)P−1, where P is the transformationmatrix. Then the structure of A(ϑk,2) has the eigenvaluesof A(ϑk) on its diagonal, and then a partition can be per-formed as two submatrices. The reduced output observergain uses the first sixth columns and rows of ϑk,2. Thisassumption involves the sixth first eigenvalues of A(ϑk)(λ1

to λ6) to estimate L(ϑk,2). The global observer gain iscomputed by

L(ϑk) = P−1

[L(ϑk,2)

0

](15)

Using this gain with reduced order output approach im-proves the state estimation. Figure 3 describes the estima-tion quality of outputs, when a set of step current changesis applied.

Fig. 3. Faultless Process vs. Estimated signals andresidual performance during a set of operatingpoint(Ist) changes:(Ist, Ts)⇒

{(191, 0) (189, 20) (194, 50) (192, 80) (191, 110)

}6.2 Fault Isolation Process (FIP)

Using the set of residuals (14) and the faults described inTable 2, a theoretical binary fault signature matrix (FSM)presented in Table 3 is obtained. Looking at this tableconsidering only the binary signature faults f1, f2 andf5 are not isolable because they present the same binarysignature. However, the rest of faults can be isolated onefrom another using just binary information. One of themain contributions of the proposed approach in this paperis the capability for isolation of faults that with only usingbinary information would not be possible.

Based on FDP information, the FIP tries to determinethe fault cause. In this case, in order to perform a success-ful fault diagnosis, the FIP block must contain knowledgeabout the fault that has appeared in the system.

f1 f2 f3 f4 f5 f6 f7 f8

r1 (−)1 (−)1 (+)1 0 (−)1 0 0 0

r2 (−)1 (−)1 (−)1 (−)1 (−)1 (−)1 (+)1 (−)1

r3 0 0 (−)1 0 0 (−)1 0 0

r4 0 0 (−)1 (−)1 0 (+)1 (−)1 0

Table 3. PEM FC Fault Binary Signature forthe proposed set of faults.

Stadistic f1 f2 f3 f4 f5 f6 f7 f8

r2/r1

std 0.01 0.01 0.00 5.19 0.45 0.04 0.04 0.04mean 0.02 0.03 -0.06 -0.23 -0.04 0.48 0.48 0.48min 0.01 0.02 -0.07 -9.53 -0.77 0.40 0.40 0.40max 0.03 0.04 -0.06 9.52 0.48 0.51 0.51 0.51

r3/r1

std 0.00 0.00 0.00 0.28 0.08 0.01 0.01 0.01mean 0.00 0.00 -0.02 0.00 0.07 0.15 0.15 0.15min -0.07 -0.03 -1.15 -12.72 -14.22 -16.55 -16.04 -16.50max 0.00 0.00 -0.02 0.50 0.15 0.17 0.17 0.17

r4/r1

std 0.07 0.07 0.02 69.68 620.73 40.16 40.29 40.45mean 0.00 0.04 -1.12 -1.58 28.92 -92.11 -92.36 -92.44min 0.00 0.00 -0.02 -0.54 -0.11 0.15 0.15 0.15max 0.15 0.19 -1.10 128.88 702.93 -57.28 -57.40 -57.56

Table 4. Statistics Analysis of Theoretical faultsignature matrix using relative sensitivity re-

spect to r1 for operating point vector;[185, 205]A.

In order to improve isolability, the relative fault sensi-tivity signature method proposed in Section 4 is used.This method takes into accout residual fault sensitivitieswithout requiring to know the fault magnitude. Morevoer,this approach also reduces the sensitivity dependency withthe operating point (see Table 4) because of the use ofrelative sensitivies as a ratio of residuals.

Due to lack of space, this section only shows the resultscorresponding to f2, which is one of the most usual faultpresented in fuel cell system during normal operationconditions (see Escobet et al. (2009)). In order to testthe LPV model-based fault diagnosis approach, a set ofdifferent operating point conditions were selected in therange of [185, 205] Amp. This selection tries to obtain theoptimal performance specifications for the fuel cell, thatis, λO2 ≈ 2 and Pnet ≈ 40kW ).

The theoretical fault ratios in the selected operating pointsand its statistics analysis are presented in Table 4. InFigure 5, the theoretical relative fault sensitivity is rep-resented in the space of residual ratios. The ellipticalregion around each theoretical fault ratio corresponds toan isolation threshold volume that has been calculatedby statistical analysis (Velleman and Hoaglin, 1981). Thisthreshold introduces robustness in the isolation processtaking into account measurement noise and model uncer-tainty.

The residual evolution when fault f2 appears at sample95 is shown in Figure 5. Note that the system suffersa step change in operating point (stack current changefrom 191 to 194 A) at sample 40, producing an impulse inthe residual not signficantly enough to cross the residualthreshold. However, when the fault appears at 90, theresidual r3 crosses above upper threshold value and r4

crosses under lower threshold value, while r1 and r2 doesnot cross their threshold. Then, according the observerfault signature and the binary fault signature presented inTable 3, the candidate faults are f1, f2 and f5.

On the other hand, the evolution of the observed relativefault sensitivity in the space of theoretical relative faultsensitivity signature is shown in Figure 5. From this figure,

Fig. 4. Residual evolution.

it can be noticed that the evolution of the observed relativesensitivity pass around several fault places after the faultis detected and the isolation process is initiated. Finally,when residuals reach steady state, the observed relativesensitivity enters in the region of uncertainty around faultf2. According to the isolation criterion (9), this is the finalcandidate fault.

Fig. 5. Evolution of observed relative sensitivity ratio inspace of residuals ratios in case of fault f2.

7. CONCLUSION

In this paper, a new LPV model-based fault diagnosismethodology based on the relative fault sensitivity hasbeen presented and tested. An advantage of this newmethodology is twofold: first, the variation of the dynamicswith the operating point is considered by using an LPV ob-server when generating residuals. Second, a fault isolationalgorithm based on the relative fault sensititivy conceptis proposed. This method allows isolating faults that arenot isolable considering only a binary (or a sign) faultsignature matrix. To prove this methodology, a PEM fuelcell case study well-known in the literature has been used.The case study was modified to include a set of possiblefault scenarios that try to reflect the most common faults.All the considered faults have been tested with the newdiagnosis methodology, which has diagnosed correctly allof them.

ACKNOWLEDGEMENTS

The authors would like to tank to the Instituto deRobotica i Informatica Industrial (IRI/UPC-CSIC) for its

knowhow sharing, specially to J. Riera, M. Serra and D.Feroldi.

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