Antonio Franchi
email: afranchi@laas.fr

Antonio Petitti
email: petitti@ba.issia.cnr.it

Alessandro Rizzo
email: alessandro.rizzo@nyu.edu

Decentralized Parameter Estimation and Observation for Cooperative Mobile Manipulation of an Unknown Load using Noisy Measurements

In this paper, a distributed approach for the estimation of kinematic and inertial parameters of an unknown rigid body is presented. The body is manipulated by a pool of ground mobile manipulators. Each robot retrieves a noisy measurement of its velocity and the contact forces applied to the body. Kinematics and dynamics arguments are used to distributively estimate the relative positions of the contact points. Subsequently, distributed estimation filters and nonlinear observers are used to estimate the body mass, the relative position between its geometric center and its center of mass, and its moment of inertia. The manipulation strategy is functional to the estimation process, and is suitably designed to satisfy nonlinear observability conditions that are necessary for the success of the estimation. Numerical results corroborate our theoretical findings.

I. INTRODUCTION

Cooperative manipulation by teams of mobile robots has been one of the hot research topics in the last decades, with applications in the fields of search and rescue, disaster recovering, cooperative transportation, and service robotics. Many aspects of cooperative robotics have been recently studied in great detail, such as optimal control [START_REF] Sieber | Formation-based approach for multi-robot cooperative manipulation based on optimal control design[END_REF], path planning [START_REF] Yamashita | Motion planning of multiple mobile robots for cooperative manipulation and transportation[END_REF], leader-follower control schemes [START_REF] Yufka | Formation-based cooperative transportation by a group of non-holonomic mobile robots[END_REF]. However, most of the prior work models the payload with a point mass, or with a rigid body with known dynamical parameters [START_REF] Lee | Bilateral teleoperation of multiple cooperative robots over delayed communication network: theory[END_REF], [START_REF] Satici | Nonholonomic cooperative manipulation of polygonal objects in the plane[END_REF].

The real-time knowledge of inertial parameters of unknown loads makes collective manipulation tasks more effective and is beneficial in terms of reduction of the control effort. Thus, the benefits provided by on-line estimation techniques are at least twofold: first, more effective control techniques for manipulation, like force control and pose estimation [START_REF] Yong | Inertia parameter estimation of planar object in pushing operation[END_REF], [START_REF] Kubus | On-line estimation of inertial parameters using a recursive total least-squares approach[END_REF], can be applied to achieve better performance with a reduced control effort. Second, timevarying manipulation tasks can be effectively implemented. For example, in transport application it is not rare that the payload is increased by an external cause, or that part of the load is lost during the transportation. Hence, an effective, real-time estimate of the inertial parameters would allow to implement adaptive control techniques, as well as event-driven control algorithms. Finally, the benefits of the Fig. 1: A group of ground mobile manipulators performing a manipulation task. Each robot exerts a force on the object using a planar manipulator. Robots measure only the end-effector velocity and communicate using peer-to-peer ad-hoc connections. All-toall communication is not possible. The objective is the distributed observation of the position of the geometric center of all the contact points G w.r.t. the center of mass C and the distributed estimation of the mass, the rotational inertia, and the relative positions of the contact points (C 1 , . . . ,C n ) w.r.t. C. estimation are even improved if they are achieved through a totally distributed approach, which would add flexibility, reduced computational and communication overhead, and fault tolerance [START_REF] Lynch | Distributed Algorithms[END_REF]. Not much work has been done in the past concerning distributed estimation of inertial parameters. Moreover, the main limitations of the existing research reside in the centralization of the approaches, and in the use of acceleration and absolute positioning measurements [6] [7].

This work seeks to overcome the limitations of the existing approaches, by defining, to the best of our knowledge, the first totally distributed estimation scheme for the inertial parameters of an unknown load manipulated by a pool of Ground Mobile Manipulators (GMMs). The proposed approach relies on the application of contact forces to points which neither accelerations nor relative (and, consequently, absolute) positions are measured, and makes use of only velocity measurements, possibly corrupted by noise, which may deteriorate the estimation performance [START_REF] Ljung | System Identification: Theory for the User[END_REF].

The proposed approach is grounded on our preliminary results presented in [START_REF] Franchi | Distributed estimation of the inertial parameters of an unknown load via multi-robot manipulation[END_REF], where noiseless measurements have been considered.

It leverages geometrical and dynamical analysis, and the theory of nonlinear observers to estimate the relative positions of the contact points, which are used to derive the inertial parameters of the unknown payloads. Our algorithm allows the full use of the proposed methodology in generic cooperative manipulation tasks where the force has to be chosen in a closed-loop control fashion relying on the current center-of-mass position estimate.

The paper is structured as follows. In Sec. II, we formalize the distributed estimation problem. In Sec. III, we introduce the distributed estimation procedure and describe the main phases of the algorithm. Then, we first focus on the estimation of the relative positions of the contact points in Sec. IV, and describe in detail the procedure for the estimation of the inertial parameters in Sec. V. The results of the numerical simulations and the accuracy bounds are reported in Sec. VI, and Sec. VII provides the conclusions.

II. PROBLEM STATEMENT

We consider a connected network composed of n mobile robots able to move in a plane, see Fig. 1. The robotic network is represented by an undirected graph G = {I , E }, where I = {1, . . . , n} is the node set, corresponding to robots, and E ⊂ I × I is edge set, corresponding to communication links. Notably, if (i, j) ∈ E then robot i can exchange data with j, and vice versa. Furthermore, we indicate with N i = { j ∈ I : (i, j) ∈ E } the set of neighbors of robot i. The team objective is to manipulate, in a cooperative fashion, an unknown load B. The position of the center of mass (CoM) C of the load B, with respect to a common reference frame

W = {O -x y}, is p C ∈ R 2 .
Using a manipulator, each robot i can exert a force f i on the load B in the contact point

C i ∈ B, whose position in W is p C i ∈ R 2 .
Indicating with m ∈ R >0 and J ∈ R >0 , respectively, the mass and the moment of inertia of B, the dynamics of B, subject to forces f 1 , . . . , f n , reads

pC = 1 m n ∑ i=1 f i (1) ω = 1 J n ∑ i=1 (p C i -p C ) ⊥ T f i , (2)
where ω ∈ R is the rotational rate of B. The linear operator (•) ⊥ , applied to a vector v ∈ R 2 , rotates it of π/2, as

v ⊥ = Qv = 0 -1 1 0 =Q v x v y = -v y v x . (3)
We assume that each robot i performes noisy measurements ṗC i ∈ R 2 of the velocity ṗC i of the contact point C i , i.e.,

ṗC i = ṗC i + ν i , (4)
where ν i ∼ N(0, Σ i ) is a white Gaussian noise with zero mean and covariance matrix Σ i ∈ R 2×2 . Finally, we assume that control inputs and communications are not affected by noise. Problem 1 (Distributed Estimation of Inertial Parameters). Given a network of n robots moving on a plane and manipulating a load B. Design a distributed strategy such that each robot i, for all i ∈ I , is able to estimate 1) the mass m of B, 2) the moment of inertia J of B, and 3) the relative positions of the contact point with respect to the load's center of mass, that is,

p C i -p C ∈ R 2 .
We remark that this quantity varies in time.

Each robot i can only 1) locally measure the velocity ṗC i of the contact point C i ; 2) locally control the applied force f i acting on C i ; 3) communicate only with its one-hop neighbors, belonging to the set N i .

Henceforth, variables with the superimposed symbol • refer to noisy measurements, while variables with the superimposed symbol • refer to estimates.

III. ESTIMATION ALGORITHM OVERVIEW

We indicate with p G = 1 n ∑ n i=1 p C i the geometric center of all the contact points, and we use the following compact notation for vector differences:

z i j = p C i -p C j , z i = p C i -p G , and z C = p G -p C . Thus, p C i -p C = z i + z C .
The following fact holds:

Fact 1. Assuming that z 1 and z 2 are the relative positions between two points of B expressed in W , and considering two time instants t and t , the rigid body constraint can be used to compute z 2 (t ) from z 1 (t ), z 2 (t ), and z 1 (t ):

z 2 (t ) = Γ(z 1 (t ), z 2 (t ), z 1 (t )) = (5) = z 2 (t ) T z 1 (t ) z 1 (t ) + z 2 (t ) T z ⊥ 1 (t ) z ⊥ 1 (t ) z 1 (t )
.

The proposed algorithm consists of four steps that lead the estimates performed by each robot to converge to the real value of the inertial parameters. Each of the four steps, described in the following, converges in a given time interval. We indicate with t 0 the starting time of the algorithm and with t k , k = 1, . . . , 4, the end time of each step. We remark that the steps are sequentially executed, i.e., no information obtained at any step has to be fed back to previous steps at any time.

Step 1: an estimation z i j of z i j becomes known after t 1 . Each robot i applies an arbitrary force f i (t) to the body and uses ṗC i and ṗC j , with j ∈ N i , to estimate z i j . This is achieved through a least squares estimation that converges at time t 1 and is detailed in Sec. IV.

Step 2: an estimation Ĵ of J becomes known after t 2 . For t ≥ t 1 , four concurrent substeps are executed to produce an estimate Ĵ of the moment of inertia J.

Sub-step 2.1 each robot i computes ẑi j (t) and sign(ω), using ṗC i , ṗC j (with j ∈ N i ), and z i j (see Sec. IV).

Sub-step 2.2 each robot i computes ẑi (t), using ẑi j (t) and the algorithm in [START_REF] Aragues | Distributed centroid estimation from noisy relative measurements[END_REF].

Sub-step 2.3 each robot i applies a force f i (t) = k z ẑ⊥ i (t). While the body moves, each robot i locally estimates the rotational rate of B as

ωi (t) = sign(ω) zi j z i j , ( 6
)
where j is any neighbor in N i . Then, all robots update their local estimates ωi using a dynamic consensus algorithm [START_REF] Zhu | Discrete-time dynamic average consensus[END_REF] to attain a common estimate ω. Sub-step 2.4 each robot performs an estimate of J, denoted with Ĵi , as detailed in Sec. V-A. Then, an average consensus algorithm [START_REF] Olfati-Saber | Consensus and cooperation in networked multi-agent systems[END_REF] is used to reach an agreement on a common estimate Ĵ.

Step 3: an estimation p C i -p C of p C i -p C becomes known after t 3 .

Each robot applies an arbitrary nonzero force f i (t) and produces an estimate ω(t) of the rotational rate ω(t). Then, each robot computes ẑC , relying on the estimate Ĵ previously performed, and using the nonlinear observer detailed in Sec. V-B. The applied forces must verify the weak condition 1 n ∑ n i=1 f i (t) = 0, as stated in Proposition V.1. After the convergence time of the observer, indicated with t 3 , the unknown vector p C i -p C is estimated using the formula

(p C i (t) -p C (t)) = ẑi (t) + ẑC (t) = (7) = ẑi (t) + Γ(ẑ C (t 3 ), ẑi j (t 3 ), ẑi j (t)),
where Γ is defined in (5) and j ∈ N i .

Step 4: an estimation m of m becomes available after t 4 . Each robot i estimates pC (t), by applying an arbitrary nonzero force f i (t) and estimates pC (t) as

pC (t) = ṗC i (t) -ω(t) (p C i (t) -p C (t)) ⊥ . ( 8
)
We observe that all the quantities in the right hand side of ( 8) are computed during the previous steps and are locally available after t ≥ t 3 . Based on pC , each robot computes an estimate mi , as detailed in Sec. V-C. An average consensus algorithm is then used to converge to a common estimate of the mass m, which, for t ≥ t 4 , will be known by all the robots.

IV. ESTIMATION OF THE RELATIVE POSITIONS OF THE CONTACT POINTS

Contact points C i , i ∈ I , belong to the rigid body B; Thus, the following relation holds for all (i, j) ∈ E :

z T i j z i j = const. ( 9
)
Differentiating both sides of (9), we obtain żT i j z i j = 0, [START_REF] Ljung | System Identification: Theory for the User[END_REF] which implies that żi j is perpendicular to z i j . Therefore, we have

z i j z i j = sign(ω) ż⊥ i j ż⊥ i j , i.e., z i j = sign(ω) z i j y i j , (11)
where we let

y i j = ż⊥ i j ż⊥ i j
. Thus, robot i computes

ẑi j = z i j y i j , (12)
where

y i j = ( ṗC i -ṗC j ) ⊥ ṗC i -ṗC j
and z i j can be computed using the strategy detailed in the following. It is clear that z i j cannot be estimated if ω ≡ 0, ∀t, since this implies żi j ≡ 0. Thus, considering any time interval in which ω = 0 we differentiate with respect to time both sides of (11) obtaining żi j = sign(ω) z i j ẏi j .

(

) 13
Since ẏi j is not directly known, we apply a first-order lowpass filter to both sides of (13), denoting with ż f i j and ẏ f i j the filtered versions of żi j and ẏi j , respectively (refer to the Appendix of [START_REF] Franchi | Distributed estimation of the inertial parameters of an unknown load via multi-robot manipulation[END_REF] for a detailed explanation). Taking the squared norm of both sides after filtering, we obtain

ż f i j 2 = z i j 2 k 2 f y i j -y f i j 2 , (14)
where k f is the gain of the low pass filter. Finally, z i j 2 can be obtained by solving the linear least squares problem

    ż f i j (t 1 ) 2 . . . ż f i j (t q ) 2     = z i j 2     k 2 f y i j (t 1 ) -y f i j (t 1 ) 2 . . . k 2 f y i j (t q ) -y f i j (t q ) 2     , (15)
where t 1 . . .t q are the q > 0 acquisition times of the noisy measurements.

Furthermore, an estimate of sign(ω) at time t is given by

sign(ω) = sign ż f i j (t) T y i j (t) -y f i j (t) . (16)

V. ESTIMATION OF INERTIAL PARAMETERS

In this section, we describe three algorithms for estimating, in the presented order: (i) the moment of inertia J, (ii) the time-varying vector z C , i.e., the position of the center of mass C relative to the geometric center p G , and (iii) the mass m.

A. Estimation of the Moment of Inertia J

Noting that p C i -p C = z i + z C , we can rewrite (2) as ω = 1 J n ∑ i=1 z ⊥ i T f i + 1 J z ⊥ C T n ∑ i=1 f i , (17)
where z i can be retrieved locally by each robot during Step 2. Thus, the only unknown quantities in (17) are J and z C .

If each robot i applies a force f i = k z z ⊥ i at each time t, being k z any constant, then the second sum in (17) vanishes. Consider, in fact

n ∑ i=1 f i = k z n ∑ i=1 z ⊥ i = k z n ∑ i=1 (p C i -p G ) ⊥ = k z Q n ∑ i=1 (p C i -p G ) = k z Q n ∑ i=1 p C i - n ∑ i=1 p G = k z Q (np G -np G ) = 0.
Thus, (17) simplifies as

ω = k z J n ∑ i=1 z ⊥ i T z ⊥ i = k z J n ∑ i=1 z i 2 . ( 18
)
We observe that quantity k z∑ n i=1 z i 2 in (18) is constant over time. Therefore, this yields a constant angular acceleration, which allows the distributed identification of J by means of the following distributed algorithm:

1) Before applying any force, each robots distributively computes the constant value w = k z∑ n i=1 ẑi 2 . This can be done in a distributed way by means of a standard average consensus algorithm; 2) Each robot applies a constant force f i = k z ẑ⊥ i . This can be done only based on local information;

3) Thanks to the local estimate ω of ω, each robot computes a local estimate Ĵi of J using the approach presented in the Appendix of [START_REF] Franchi | Distributed estimation of the inertial parameters of an unknown load via multi-robot manipulation[END_REF]; 4) When the local estimates converge, the robots run a further consensus phase, attaining an agreement on a common estimate Ĵ. This operation averages out the uncertainty in the estimates Ĵi caused by the noise in ω and ẑi . We note that no perfect time synchronization on the start time of the application of forces f i is needed, since each robot will eventually apply the force f i = k z ẑ⊥ i . We observe that design or technical constraints, such as the necessity of keeping the angular or linear velocity of the body bounded, may hold. In this case, the forces required in this phase of the estimation could be applied only for a limited time interval. In this case, the movement can be easily stopped when needed using a pure damping force based on a local velocity feedback. However, should the time be not enough for estimation purposes, the process can be repeated several times after each stop, to ensure the acquisition of the measurements necessary to identify J.

B. Observer for the Relative Position z C of the CoM

Assume that during the manipulation task each robot applies an arbitrary force f i (t). It is straightforward to verify that f i (t) can be expressed as

f i (t) = 1 n n ∑ i=1 f i (t) + ∆f i (t) = f mean (t) + ∆f i (t). (19)
Then, (17

) becomes ω = 1 J n ∑ i=1 z ⊥ i T f mean (t) + n J z ⊥ C T f mean (t)+ 1 J n ∑ i=1 z ⊥ i T ∆f i + 1 J z ⊥ C T n ∑ i=1 ∆f i = (20) n J z ⊥ C T f mean (t) + 1 J n ∑ i=1 z ⊥ i T ∆f i ,
given that ∑ n i=1 z ⊥ i T = 0 and ∑ n i=1 ∆f i = 0. Thus, (20) can be written as

ω = z ⊥ C T f + η, ( 21
)
where we let f = n J f mean and η = 1 J ∑ n i=1 z ⊥ i T ∆f i . By means of standard dynamic consensus algorithms, it is possible to reach an agreement on f. To this purpose, each robot i needs to exchange only the local quantity f i (t) with its neighbors. This implies that robot i can locally compute ∆f i = f i -f. By exchanging the local quantity z ⊥ i T ∆f i with its neighbors and applying again the dynamic consensus algorithm, also η can be locally computed in a distributed way. Therefore, in the following we can safely assume that both f and η are locally known to each robot.

Since z C is a vector with constant norm rigidly attached to the object, we have

ż⊥ C = -z C ω. ( 22
)
Combining ( 21) and ( 22), we obtain the following autonomous nonlinear system

         ẋ1 = -x 2 x 3 ẋ2 = x 1 x 3 ẋ3 = x 1 fy -x 2 fx + η y = x 3 , (23)
where we let z x C = x 1 , z y C = x 2 , ω = x 3 , and f = ( fx fy ) T . The system output is assumed to be y = x 3 = ω, since the rotational rate is locally estimated by each robot using [START_REF] Yong | Inertia parameter estimation of planar object in pushing operation[END_REF]. Therefore, estimating z C is equivalent to observe the state of the nonlinear system (23) with output y = x 3 = ω, and where fy , fx , and η are known inputs. Before designing a suitable nonlinear observer, the observability of system (23) is studied. Proposition V.1. If x 3 ≡ 0 and fx (t) fy (t)

T ≡ 0 T , then system ( 23) is locally observable in the sense of [START_REF] Hermann | Nonlinear controllability and observability[END_REF].

Proof. The observability matrix [START_REF] Hermann | Nonlinear controllability and observability[END_REF] is

O =   0 0 1 fy -fx 0 -fx x 3 -fy x 3 -fx x 1 -fy x 2   , ( 24
)
whose determinant is det 23) is locally observable in the sense of [START_REF] Hermann | Nonlinear controllability and observability[END_REF] iff O is invertible, from which the thesis follows.

(O) = -x 3 ( f 2 x + f 2 y ). System (
Thus, vector z C is observable from local velocity measurements if and only if the rotational rate of the object and the average vector of the applied forces are not identically zero. The nonlinear observer is designed as follows. Theorem V.1. Consider the following dynamical system ẋ1 = -x2 x 3 + fy (x 3 -x3 )

ẋ2 = x1 x 3 -fx (x 3 -x3 ) ẋ3 = x1 fy -x2 fx + k e (x 3 -x3 ) + η, (25)
where k e > 0. If x 3 ≡ 0 and fx (t) fy (t) T ≡ 0, then system (25) is an asymptotic observer for system (23), i.e., defining x = ( x1 x2 x3 ) T and x = (x 1 x 2 x 3 ) T , x → x asymptotically.

Proof. Define the error vector as e = (e 1 e 2 e 3 ) T = ((

x 1 -x1 ) (x 2 -x2 ) (x 3 -x3 )) T ; the error dynamics is given by ė =   0 -x 3 -fy x 3 0 fx fy -fx -k e   e. (26)
Define the following candidate Lyapunov function:

V (e) = 1 2 e 2 1 + e 2 2 + e 2 3 , (27)
whose time derivative along the system trajectories is V (e) =e 1 (-e 2 x 3 -fy e 3 )+

which is negative semidefinite. Considering the set V = e s.t. V (e) = 0 = {e s.t. e 3 = 0}, and generic vector ē = ( ē1 ē2 0) T ∈ V , it is easy to verify by means of (26) that the first and second time derivatives of e 3 along a trajectory containing ē are given by de 3 dt ē = fy ē1 -fx ē2

d 2 e 3 dt 2 ē = de 1 dt ē = -x 3 ( fy ē2 + fx ē1 ). (29)
Therefore, if x 3 is not vanishing, then the largest invariant set M ⊂ V consists of the only equilibrium point (0 0 0) T . Thus, the thesis holds due to the invariance Krasovskii-LaSalle principle [START_REF] Slotine | Applied nonlinear control[END_REF].

We remark that observer (25) can be implemented in a distributed fashion by resorting only to local information.

The estimation error of the proposed observer vanishes asymptotically in the ideal case of absence of noise. Actually, each robot sets the force fa = n Ĵ f mean as input for the local observer, which is affected by noise, due to the presence of Ĵ. Furthermore, the observer relies on the noisy estimate ω, computed using [START_REF] Yong | Inertia parameter estimation of planar object in pushing operation[END_REF]. Due to its asymptotic stability, we expect that in presence of noise the estimation error will remain bounded around the actual value of the parameter. The definition of a formal proof of the estimation error boundedness will be given as future work. However, in Sec. VI, we will numerically characterize the bound of the estimation error with respect to noise terms.

C. Estimation of the Mass

Assume that each robot applies an arbitrary force f i (t) and that f mean (t), defined as in (19), is not zero. Thus, (1) becomes

pC = n m f mean . (30)
We remind that each robot can distributively compute f mean . Furthermore, each robot is able to estimate the velocity of the center of mass as

pC (t) = ṗC i (t) + ω(t) (ẑ i (t) + ẑC (t)) ⊥ . (31)
Therefore, similarly to Ĵi , each robot can locally compute an estimate mi using the approach in the Appendix of [START_REF] Franchi | Distributed estimation of the inertial parameters of an unknown load via multi-robot manipulation[END_REF]. Finally, the robots agree on a global estimation m using an average consensus algorithm in order to average out the noise of each local mass estimator.

VI. SIMULATIONS AND ACCURACY BOUNDS

We validate the estimation algorithm by running numerical simulations. We assume n = 4 robots manipulating a Cshaped planar rigid body with mass m = 5 kg and moment of inertia J = 8.6891 kg m 2 . Communications among robots occur through the links E = {(1, 2), (2, 3), (3, 4)}. We assume that each robot is able to measure the velocity of the contact point, and that the measurement is affected by a Gaussian noise with zero mean and covariance matrix Σ i = σ 2 I, with σ = 0.2 m/s, and where I ∈ R 2×2 is the identity matrix. The algorithm starts with the estimation of the relative distance between neighboring contact points: each robot sets an arbitrary force and executes Step 1. We observe that the estimation must stop when the measured noisy signals zi j have a level such that the signal-to-noise ratio is too low to perform an estimate. In this case, the estimation stops when zi j ≤ 1 m/s (the measured z12 is illustrated in Fig. 2, as an example). Figure 3 illustrates the errors in the estimation of the distances using the strategy presented in Sec. IV. Handling noisy measurements involves a certain inaccuracy in the estimation process, whose standard deviation is quantified in the following. Suppose to perform a least squares estimation using τ observations (υ t , ψ t ), t = 1, . . . , τ, of the model ψ = θ υ. The estimate θ = (ϒ

T ϒ) -1 ϒ T Ψ, where ϒ = [υ T 1 . . . υ T τ ] T and ψ = [ψ T 1 . . . ψ T τ ] T . The standard deviation σ θ of the estimates θ is σ θ = σ ψ τ τ ∑ τ t=1 υ 2 t -(∑ τ t=1 υ t ) 2 , (32)
where σ ψ is the standard deviation of the observations ψ. Thus, the uncertainty of the estimation of the constant parameters z i j , m, and J has the form of (32) [START_REF] Van De Geer | Least squares estimators[END_REF]. Subsequently, Step 2 is executed toward the local estimation of the moment of inertia Ĵi . The estimation process starts as soon as robot i has locally collected a sufficient number of samples, and yields the local estimates Ĵ1 = 8.7053 ± 0.0035 kg m 2 , Ĵ2 = 8.7208 ± 0.0035 kg m 2 , Ĵ3 = 8.7320 ± 0.0032 kg m 2 , and Ĵ4 = 8.7151 ± 0.0035 kg m 2 . Each robot checks the convergence of the least squares estimation evaluating the variance of the estimator [START_REF] Van De Geer | Least squares estimators[END_REF]. Then, the local estimates Ĵi are exchanged over the network and an average consensus is run to agree on the same estimate, that is, Ĵ = 8.7183 ± 0.0004 kg m 2 . The result of such estimation is reported in Fig. 4. The estimate of the moment of inertia Ĵ and the observation of ω(t), known thanks to the previous step, are used for the

[s] ω [rad/s] z x C [m] z y C [m] ω [rad/s] ẑx C [m] ẑy C [m] ω obs [rad/s]
Fig. 5: Observation of the vector z C and of the angular rate ω: dashed lines refer to observed values, while continuous lines refer to real values. For the angular rate, the measure ω (continuos light blue line) in input to the observer is also plotted. observation of z C . During this step, each robot applies the same constant force f i = f, for all i = 1, . . . , 4. In Fig. 5, the observations ẑC and ω obs are illustrated.

We now characterize numerically the uncertainty of the nonlinear observer in estimating z C , by running 1000 independent trials for different values of the variance of the noise on the angular rate, σ 2 ω obs . For each trial, a sinusoidal signal with random amplitude, frequency, and phase is used for the components of the force applied by each robot. The simulation yields a an almost constant trend and independent from the value of σ ω obs . Therefore, its mean value can be considered as a good approximation of the standard deviation, i.e., σ z x C = 0.075 m and σ z y C = 0.033 m. Once the observer converges, the estimation of pC and m can be executed. The estimation of the mass, illustrated in Fig. 6, is carried out using the estimation of the angular rate computed by the observer, ω obs . First, each robot estimates locally, respectively, m1 = 4.8367±0.0451 kg, m2 = 4.8491±0.0455 kg, m3 = 4.8824 ± 0.0453 kg, and m4 = 4.8384 ± 0.0447 kg and then, after the average consensus, the network agrees on the value m = 4.8517 ± 0.0113 kg.

VII. CONCLUSION

In this paper, we have addressed the problem of the distributed estimation of the inertial parameters of an unknown load manipulated by a network of robots. We assume that each robot is able to control the force exerted on the load and to measure only the velocity of the point where the force is exerted. Only local communication between neighboring robots is allowed. In partic-ular, we have focused on the influence of the measurement noise on the estimate by defining suitable strate- gies. The algorithm has been validated through several numerical simulations.

e 2 (x 3 e 1 + 3 = -k e e 2 3

 2133 fx e 3 ) + e 3 ( fy e 1 -fx e 2k e e 3 ) =e 1 e 2 x 3e 1 fy e 3 + e 2 x 3 e 1 + e 2 fx e 3 + e 3 fy e 1e 3 fx e 2k e e 2 ,

Fig. 2 :zFig. 3 :

 23 Fig.2:The measured velocity difference z12 . The trends of z23 and z34 are very similar and not reported here due to space constraints.

Fig. 4 :

 4 Fig. 4: Estimation of the moment of inertia J of B. (a) Least squares estimation of J: the estimate converges as soon as the number of samples is sufficient. (b) After the convergence of the estimator, the network runs an average consensus to reach an agreement on Ĵ.

Fig. 6 :

 6 Fig. 6: Estimation of the mass m of B. (a) Least squares estimation of m: the estimate converges as soon as the number of samples is sufficient. (b) After the convergence of the estimator, the network runs an average consensus in order to reach an agreement on m.

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Preprint version, final version at http://ieeexplore.ieee.org/ 4 2015 IEEE ICRA

Preprint version, final version at http://ieeexplore.ieee.org/ 5

Preprint version, final version at http://ieeexplore.ieee.org/ 6 2015 IEEE ICRA

Work partially supported by the Short Term Mobility Program of CNR Italy.


Patrice Bellot
email: patrice.bellot@univ-amu.fr

Véronique Moriceau
email: moriceau@limsi.fr

Josiane Mothe
email: josiane.mothe@irit.fr

Eric Sanjuan
email: eric.sanjuan@univ-avignon.fr

Xavier Tannier
email: xtannier@limsi.fr

Overview of INEX Tweet Contextualization 2014 track

Keywords: Short text contextualization, Tweet understanding, Automatic summarization, Question answering, Focus information retrieval, XML, Natural language processing, Wikipedia, Text readability, Text informativeness

140 characters long messages are rarely self-content. The Tweet Contextualization aims at providing automatically information -a summary that explains the tweet. This requires combining multiple types of processing from information retrieval to multi-document summarization including entity linking. Running since 2010, the task in 2014 was a slight variant of previous ones considering more complex queries from RepLab 2013. Given a tweet and a related entity, systems had to provide some context about the subject of the tweet from the perspective of the entity, in order to help the reader to understand it.

Motivation

The task in 2014 is a slight variant of previous ones and it is complementary to CLEF RepLab. Previously, given a tweet, systems had to help the user to understand it by reading a short textual summary. This summary had to be readable on a mobile device without having to scroll too much. In addition, the user should not have to query any system and the system should use a resource freely available. More specifically, the guideline specified the summary should be 500 words long and built from sentences extracted from a dump of Wikipedia.

In 2014 a small variant of the task has been explored, considering more complex queries from RepLab 2013, but using the same corpus. The new use case of the task was the following: given a tweet and a related entity, the system must provide some context about the subject of the tweet from the perspective of the entity, in order to help the reader answering questions of the form "why this tweet concerns the entity? should it be an alert?".

In the remaining we give details about the 2014 track in English language set up and results.

We refer the reader to the CLEF Working Notes for the pilot task in Spanish.

Data collection

The official document collection for 2014 was the same as in 2013. Between 2011 and 2013 the corpus did change every year but not the user case. In 2014, the same corpus was reused but the user case evolved. Since 2014 TC topics are a selection of tweets from RepLab 2013, it was necessary to use prior WikiPedia dumps. Some participants also used the 2012 corpus raising up the question of the impact of updating the WikiPedia over these tasks.

Let us recall that the document collection has been built based on yearly dumps of the English WikiPedia since November 2011. We released a set of tools to convert a WikiPedia dump into a plain XML corpus for an easy extraction of plain text answers. The same perl programs released for all participants have been used to remove all notes and bibliographic references that are difficult to handle and keep only non empty Wikipedia pages (pages having at least one section).

The resulting automatically generated documents from WikiPedia dump, consist of a title (title), an abstract (a) and sections (s). Each section has a subtitle (h). Abstract and sections are made of paragraphs (p) and each paragraph can contain entities (t) that refer to other Wikipedia pages.

As tweets, 240 topics have been collected from RepLab 2013 corpus. These tweets have been selected in order to make sure that:

-They contained "informative content" (in particular, no purely personal messages); -The document collections from Wikipedia had related content, so that a contextualization was possible.

In order to avoid that fully manual, or not robust enough systems could achieve the task, all tweets were to be treated by participants, but only a random sample of them was to be considered for evaluation.

These tweets were provided in XML and tabulated format with the following information:

the category (4 distinct), -an entity name from the wikipedia (64 distinct) -a manual topic label (235 distinct).

The entity name was to be used as an entry point into WikiPedia or DBpedia. The context of the generated summaries was expected to be fully related to this entity. On the contrary, the usefulness of topic labels for this automatic task was and remains an open question at this moment because of their variety.

Like in 2013, the entire evaluation process was carried out by organizers.

Tweet contextualization [START_REF] Sanjuan | Overview of the inex 2010 question answering track (qa@inex)[END_REF] is evaluated on both informativeness and readability. Informativeness aims at measuring how well the summary explains the tweet or how well the summary helps a user to understand the tweet content. On the other hand, readability aims at measuring how clear and easy to understand the summary is.

Informativeness Informativeness measure is based on lexical overlap between a set of relevant passages (RPs) and participant summaries based on LogSim divergence introduced in [START_REF] Sanjuan | Overview of the inex 2010 question answering track (qa@inex)[END_REF]. Given an integer λ > 30, and two texts T, S the LogSim divergence can be restated as:

LS(Ω S |Ω T ) = ω∈Ω T P (ω|Ω T ). min(Φ T (ω), Φ S (ω)) max(Φ T (ω), Φ S (ω) (1)
where for any text Z, Ω Z is the set of n-grams in Z and for any n-gram ω ∈ Ω Z :

Φ Z (ω) = log(1 + λP (ω|Ω Z )) (2)
The λ parameter used in LS formula represents the summary allowed maximal length in words (500 in our case).

Once the pool of RPs (t-rels) is constituted, the process is automatic and can be applied to unofficial runs. The release of these pools is one of the main contributions of Tweet Contextualization tracks at INEX [START_REF] Sanjuan | Overview of the inex 2011 question answering track (qa@inex)[END_REF][START_REF] Sanjuan | Overview of the inex 2012 tweet contextualization track[END_REF].

In previous editions t-rels were based on a pooling of participant submitted passages. Organizers then selected among them those that were relevant. In 2013, to build a more robust reference, two manual runs by participants were added using different on line research engines to find relevant WikiPedia and copying the relevant passages into the reference.

This year, even though there were only five participants, the variety of submitted passages was too high compared to the number of runs. One reason was that this year topics included more facets and converting them into queries for a Research Engine was less straightforward. As a consequence, it was not possible to rely on a pooling from participant runs because it would have been too sparse and incomplete. It was finally decided to rely on a thorough manual run by organizers based on the reference system that was made available to all participants at http://qa.termwatch.es A manual query in Indri language was set up for every topic over five. These queries have been refined until they provide only a set of relevant passages using the reference system on the 2013 corpus. From this RPs we extracted two trels, one merging all passages for each tweets, another by only considering Noun Phrases (NPs) in the passages to reduce the risk of introducing document identifiers in the passages.

The average length of queries to build the reference is 8 tokens with a minimum of 2 and a maximum of 14. Therefore efficient queries are much shorter than tweets. The average number of relevant tokens in the t-rels based on passages is 620, and on the t-rels based on NPs is only 300.

Readability By contrast, readability is evaluated manually and cannot be reproduced on unofficial runs. In this evaluation the assessor indicates where he misses the point of the answers because of highly incoherent grammatical structures, unsolved anaphora, or redundant passages. Since 2012, three metrics have been used: Relaxed metric, counting passages where the T box has not been checked; Syntax, counting passages where the S box was not checked either, and the Structure (or Strict) metric counting passages where no box was checked at all.

As in previous editions, participant runs have been ranked according to average, normalized number of words in valid passages.

Results

In 2014, 4 combined teams from six countries (Canada, France, Germany, India, Russia, Tunesia) submitted 12 runs to the Tweet Contextualization track in the framework of CLEF INEX lab 20145 . The total number of submitted passages was 54, 932 with an average length of 32 tokens. The total number of tokens was 1, 764, 373 with an average of 7, 352 per tweet.

We also generated two reference runs based one the organizer's system made available to participants using 2013 and 2012 corpus respectively.

To read the scores, the lower they are the better since these are divergences. Informativeness results based on passage t-rels are presented in Table 1, and those on NPs t-rels in Table 3. Statistical significance of differences between scores in Table 1 are indicated in Table 2. Readability results are presented in Table 4.

Both informativeness rankings in Table 1 and in Table 3 are highly correlated, however discrepancies between the two rankings show that differences between top ranked runs rely on tokens outside NPs, mainly verbs since functional words are removed in the evaluation.

Table 4 reveals that readability of reference runs is low, meanwhile they are made of longer passages than average to ensure local syntax correctness.

Since reference runs are using the same system and index as the manual run used to build the t-rels, they tend to minimize the informativeness divergence with the reference. However, average divergence remains high pointing out that selecting the right passages in the restricted context of an entity, was more difficult than previous more generic tasks. Considering readability, the fact that

Two other teams from Mexico and Spain participated to the pilot task in Spanish submitting three runs not considered in this overview.

ref2013 -2.00 2.00 2.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 ref2012 2.00 ---1.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 361 2.00 ---1.00 2.00 2.00 2.00 3.00 3.00 3.00 3.00 3.00 3.00 360 2.00 -------3.00 3.00 3.00 3.00 3.00 3.00 359 3.00 1.00 1.00 -----2.00 2.00 2.00 3.00 3.00 3.00 368 3.00 3.00 2.00 ----2.00 3.00 3.00 3.00 3.00 3.00 3.00 369 3.00 3.00 2.00 -----3.00 3.00 3.00 3.00 3.00 3.00 370 3.00 3.00 2.00 --2.00 --3.00 3.00 3.00 3.00 3.00 3.00 356 3.00 3.00 3.00 3.00 2.00 3.00 3.00 3.00 ---3.00 3.00 3.00 357 3.00 3.00 3.00 3.00 2.00 3.00 3.00 3.00 ---3.00 3.00 3.00 364 3.00 3.00 3.00 3.00 2.00 3.00 3.00 3.00 ---3.00 3.00 3.00 358 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 ---363 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 ---362 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 ---Table 2. Statistical significance for official results in table 1 (t-test, two sided, 1 = 90%, 2 = 95%, 3 = 99%, α = 5%).

reference runs are low ranked confirms that finding the right compromise between readability and informativeness remains the main difficulty of this task.

This year, the best participating system for informativeness used association rules. Since contextualization was restricted to some facet described by an entity, it could be that association rules helped to focus on this aspect. The best participating system for readability used an advanced summarization systems that introduced minor changes in passages to improve readability. Changing the content of the passages was not allowed, however this tend to show that to deal with readability some rewriting is required. Moreover, since this year evaluation did not include a pool of passages from participants, systems that provided modified passages have been disadvantaged in informativeness evaluation.


Tommaso Caselli
email: t.caselli@trentorise.eu

Laure Vieu
email: vieu@irit.fr

Carlo Strapparava

Guido Vetere
email: gvetere@it.ibm.com

Enriching the "Senso Comune" Platform with Automatically Acquired Data

Keywords: Word Sense Alignment, Verb Frame Acquisition, Lexico-semantic Resource

This paper reports on research activities on automatic methods for the enrichment of the Senso Comune platform. At this stage of development, we will report on two tasks, namely word sense alignment with MultiWordNet and automatic acquisition of Verb Shallow Frames from sense annotated data in the MultiSemCor corpus. The results obtained are satisfying. We achieved a final F-measure of 0.64 for noun sense alignment and a F-measure of 0.47 for verb sense alignment, and an accuracy of 68% on the acquisition of Verb Shallow Frames.

Introduction

This paper describes current research activities on automatic methods for the enrichment of the Senso Comune 1 platform to achieve a robust and interoperable lexicosemantic resource for Italian. At this stage of development, we will report on two tasks, namely word sense alignment and automatic extraction of verb shallow frames, as a way for achieving conceptual interoperability [START_REF] Witt | Multilingual language resources and interoperability[END_REF]) [START_REF] Fang | Creating an interoperable language resource for interoperable linguistic studies[END_REF] among different language resources. The remainder of this paper is organized as follows: Section 2. will shortly presents the Senso Comune Initiative and its model. Section 3. is focused on two case studies for Word Sense Alignment (WSA, henceforth) as a preliminary and necessary step to make Senso Comune conceptually interoperable with other lexico-semantic resources. We focused on verb and noun alignment between the Senso Comune Lexicon and the Italian section of Mul-tiWordNet [START_REF] Pianta | Multi-WordNet: developing an aligned multilingual database[END_REF]. In Section 4. we will report on the automatic acquisition of Verb Shallow Frames (VSFs, henceforth) as a strategy to achieve interoperability on other levels of linguistic analysis. VSFs have been extracted from the Italian section of the MultiSemCor corpus [START_REF] Bentivogli | Exploiting parallel texts in the creation of multilingual semantically anno-tated resources: the MultiSemCor Corpus[END_REF] and compared with automatically acquired VSFs from a large corpus of Italian (the La Repubblica Corpus, [START_REF] Baroni | Introducing the "la Repubblica" corpus: A large, annotated, TEI(XML)-compliant corpus of newspaper italian[END_REF]). The data thus collected, which associate specific VSFs to verb senses (namely synsets) will provide a basis for the development of a VerbNet-like lexicon for Italian. Finally, section 5. will draw on conclusions and future work.

The Senso Comune Initiative: a short introduction

Senso Comune (SC) aims at building an open knowledge base for the Italian language, designed as a crowd-sourced initiative that stands on the solid ground of an ontological formalization and well established lexical resources. The SC platform is specified in three modules comprising a top level module, which contains basic ontological concepts and relations, inspired by DOLCE (Descriptive Ontology for Linguistic and Cognitive Engineering) (Masolo et al., 1 http://www.sensocomune.it/ 2002), a lexical module, which models general linguistic and lexicographic structures, and a frame module providing concepts and axioms for modeling the predicative structure of verbs, nouns and adjectives. On the top level module, DOLCE basic ontological distinctions are kept. For instance, DOLCE's Endurant and Perdurant match Senso Comunes Continuant and Occurrent, respectively. The main difference with respect to DOLCE top level is represented by the merging of DOLCEs Abstract (e.g. mathematical entities, dimensional regions, ideas) and Non-Physical Endurant (e.g. social objects) categories into the Senso Comune category Non-Physical Entity.

The adoption of a legacy dictionary as a foundation for the resource has led to modeling SC on a distinction between lexicographic structures and linguistic facts. Similarly to models like LMF [START_REF] Buitelaar | Towards linguistically grounded ontologies[END_REF] and Lemon [START_REF] Chiarcos | Towards open data for linguistics: Linguistic linked data[END_REF], the purpose is to provide a structure to accommodate linguistic resources where lexical units are associated with their acceptations. In SC, the distinction between the lexicographic meanings and relationships (such as synonymy, hyponymy, antinomy, among others) from the formal account of their phenomenal counterparts (e.g. concepts, equivalence, inclusion, disjointness) brings a number of benefits. As an immediate consequence, this separation prevents that lexicographic entries will be directly mapped to logic propositions, while preserving the possibility of relating entries from a lexicon to any suitable ontology. For instance, SC separates the notion of lemma from that of lexeme. A lemma in SC captures the section of a dictionary where an etymologically consistent bundle of senses (called Meaning Record) of a given lexeme is described by means of a lexicographic apparatus (e.g. definition, grammatical constraints, usage examples). A Meaning Record is part of a Lemma whose instances and attributes form the body of the SC lexicon. Each instance of a Meaning Record, where a specific sense of a Lemma is described, can be mapped to the Meaning class. Such a mapping between instances of Meaning Record and the Meaning class can be done by exploiting different mechanisms in OWL2 syntax (e.g. punning, annotations, among others). An important aspect is that different Meaning Record instances can be mapped to the same Meaning class, thus facilitat-ing the mappings of meaning record instances from different language resources (e.g. such as for the alignment between the MultiWordNet synsets and the SC lexicon entries). Similarly, lexical relations do not have any ontological import and correspondences between lexical relations and ontological relations must be introduced on the basis of dedicated heuristics2 . The lexicon entries have been obtained from a reverse engineering procedure from the De Mauro GRADIT dictionary [START_REF] De Mauro | Grande dizionario italiano dell'uso[END_REF] and consists of 2,071 fundamental Italian lexemes3 for a total of 11,939 meanings. Verbs account for 3,827 senses, corresponding to 643 lemmas, with an average polysemy of 5.9 senses per lemma, while nouns have 4,586 senses, corresponding to 1,111 lemmas with an average polysemy of 4.12 senses per lemma. All nominal entries have been manually classified according to the ontological classes described in the SC ontological module. A classification of the verb entries will start in the near future. Currently in SC, word senses are not hierarchically structured and no semantic relation is extensively encoded (so far, synonyms relations for noun senses amount to 49 entries, covering less the 5% of the fundamental noun senses). This means that with respect to other lexico-semantic resources, such as WordNet, senses of polysemous entries have a flat representation, where each (fundamental) meaning is report one following the other.

Conceptual Interoperability with Word Sense Alignment

Following [START_REF] Matuschek | Dijkstra-wsa: A graph-based approach to word sense alignment[END_REF], WSA can be formally defined as a list of pairs of senses from two lexicalsemantic resources. A pair of aligned senses denotes the same meaning. To clarify, consider this example for two sense descriptions of the word "day", taken from translated SC Lexicon and MultiWordNet (MWN), respectively:

• amount of hours of work done in one day [SC Lexicon]

• the recurring hours established by contract or usage for work [MWN] The two sense descriptions are equivalent and refer to the same meaning, thus they must be aligned. MWN is a computational multilingual lexicon perfectly aligned to Princeton WN 1.6. As in WN, concepts are organized in synonym sets (synsets), hierarchically connected by means of hypernym relations, and includes other semantic relations such as parthood and troponymy among others4 . The main motivations for the selection of MWN for the WSA can be summarized as follows: i.) WN/MWN is one of the most used lexico-semantic resource for different NLP tasks; ii.) WN/MWN has already been used as a pivot lexicon both for the alignment and for the merging of other lexica or language resources (for instance, (Niemann and Gurevych, 2011); [START_REF] Navigli | BabelNet: The automatic construction, evaluation and application of a wide-coverage multilingual semantic network[END_REF] for the alignment of WN and Wikipedia; [START_REF] Navigli | Meaningful clustering of senses helps boost word sense disambiguation performance[END_REF] for the alignment of WN and the Oxford English Dictionary; [START_REF] Shi | Putting pieces together: Combining framenet, verbnet and wordnet for robust semantic parsing[END_REF] ) no distinction between core senses and subsenses for polysemous entries; ii.) no presence of hypernyms or taxonomic structures in the entries; and iii.) no domain labels (e.g. Biology, Architecture, Sport . . . ) associated with senses. Moreover, the low number of MWN glosses in Italian prevents a straightforward application of state-of-the-art methods for sense alignment. MWN sense descriptions must be built up from other sources. The main issue we are facing is related to data sparseness, that is how to tackle sense alignment when we have few descriptions in Italian (MWN side) and few meta-data and no structuration over senses (SC side).

We focused our alignment tasks on verb and noun senses in order to understand the feasibility of this task by means of automatic approaches. Provided the limits both of the MWN Italian section and of the SC Lexicon, we decided to apply two methods, namely Lexical Overlap and Sense Similarity.

Lexical Overlap

In the Lexical Overlap method, for each word w and for each sense s in the given resources R ∈ {MWN, SC} we constructed a sense descriptions d R (s) as a bag of words in Italian. Provided the different characteristics of the two resources, two different types of bag of words have been built.

As for the SC Lexicon, the bag of words is represented by the lexical items in the textual definition of s w , automatically lemmatized and part-of-speech analyzed with the TextPro tool suite [START_REF] Pianta | TextPro Tool Suite[END_REF] with standard stopword removal. On the other hand, for each synset, S, and for each part of speech in analysis, the sense description of each MWN synset was built by optionally exploiting:

• the set of synset words in a synset excluding w;

• the set of direct hypernyms of s in the taxonomy hierarchy in MWN;

• the set of synset words in MWN standing in the relation of nearest synonyms with s;

• the set of synset words in MWN composing the manually disambiguated glosses of s from the "Princeton Annotated Gloss Corpus"5 . To extract the corresponding Italian synset(s), we have ported MWN to WN 3.0;

• the set of synset words in MWN composing the gloss of s in Italian (when available);

• for verbs, the set of synset words in MWN standing in the relations of entailment/is entailed, causes/is caused with s;

• for nouns, the set of synset words in MWN standing in the relations of part of /has part, has member/is member with s.

The alignment of senses is based on the notion of lexical overlap. We used Text::Similarity v.0.09 module6 , and in particular the method Text::Similarity::Overlaps, to obtain the overlap value between two bags of words of s w . Text similarity is based on counting the number of overlapping tokens between the two strings, normalized by the length of the strings. To overcome the so called "lexical gap" problem [START_REF] Meyer | What psycholinguists know about chemistry: Aligning Wiktionary and Word-Net for increased domain coverage[END_REF], i.e. a reduced number of overlapping words, we have extended the noun sense descriptions of MWN with the Italian Wikipedia glosses extracted from BabelNet [START_REF] Navigli | BabelNet: The automatic construction, evaluation and application of a wide-coverage multilingual semantic network[END_REF]. As for our task, we have retained only those BabelNet entries which have a corresponding synset word in MWN.

Sense Similarity

In the second approach, Sense Similarity, the basis for sense alignment is the Personalized Page Rank (PPR) algorithm [START_REF] Eneko | Personalizing PageRank for Word Sense Disambiguation[END_REF] relying on a lexical-semantic knowledge base model as a graph G = (V, E) as available in the UKB tool suite7 . The PPR algorithm ranks the vertices in a graph obtained from a lexical knowledge base according to their importance within the set and assigns stronger initial probabilities to certain kinds of vertices in the graph. The result of the PPR algorithm is a vector. To build the SC Lexicon vectors, we have used two approaches: i.) apply the PPR algorithm on the Italian data using as lexical knowledge base the MWN lexicon; and ii.) apply the PPR algorithm on automatic translations8 of the SC glosses using as lexical knowledge base WN 3.0. In both cases, the PPR vectors of the SC Lexicon are semantic representations overall the entire MWN or WN synsets of the textual definition of s. As for the MWN synsets, instead of building the PPR vector by means of the lexical items, we have passed to the UKB tool suite the MWN synset id, thus assuming that the MWN synset is already disambiguated. The vector representations of the MWN synsets have been obtained both from the MWN and from the conversion of MWN to WN 3.0. Finally, given two PPR vectors, namely ppr mwn and ppr sc for the MWN synset w sy n and for the SC Lexicon sense w sc , we calculated their cosine similarity. On the basis of the similarity score, the sense pair is considered as aligned or not.

Results and Evaluation

Each alignment method has been evaluated on its own with respect to Precision, Recall and F-measure over two manually created Gold Standards, one for verbs, which is composed by 44 lemma for a total of 350 aligned sense couples, and one for nouns, which is composed by 46 lemmas for nouns for a total of 166 aligned sense couples. We selected random match (rand) as a baseline. The random match works as follows: for the same word w in the SC Lexicon and in MWN, it assigns a random SC Lexicon meaning to each synset with w as synset word, returning a one-to-one alignment. The identification of the correct aligned pairs has been obtained by applying two types of thresholds with respect to all proposed alignments (the "all pairs" row in the tables): i.) a simple cut-off at specified values (0.1; 0.2); ii.) the selection of the maximum score (either lesk measure or cosine; row "max score" in the tables) between each synset S and the proposed aligned senses of the SC Lexicon. As for the maximum score threshold, we have retained as good alignments also instances of a tie, thus allowing the possibility of having one MWN synset aligned to more than one SC Lexicon sense.

Lexical Overlap Results

Different combinations of the sense representation of a synset have been created. We developed two basic representations: SYN, which is composed by the set of synset words excluding the target word w to be aligned, all of its direct hypernyms, the set of synset words in MWN standing in the relation of nearest synonyms and the synset words obtained from the "Princeton Annotated Gloss Corpus"; and SREL, which contains all the items of SYN plus the synset words included in the selected set of semantic relations. The results are reported in Both basic synset configurations, SYN and SREL, outperform the baseline rand for both parts of speech in analysis. The alignment of nouns performs better than that for verbs in both sense representations and with all filtering methods. A manual exploration of the data for verbs and nouns has highlighted that, on the one hand, we suffer from data sparseness on the SC Lexicon side as no extension of the sense description of the glosses is possible, and, on the other hand, that senses are described in ways that are semantically equivalent but with different lexical items. This explains the low Recall figures for both parts-of-speech.

The difference in performance of the SREL configuration with respect to the SYN configuration for both parts-ofspeech is not statistically significant (p > 0.05), suggesting that the impact of additional semantic relations (as encoded in MWN) is limited. Both for verbs and nouns we decided to select the SYN basic configuration as the best sense representation because it has a simpler bag-of-words and better Precision.

To improve the results, we have extended the SYN representation for nouns with the lexical items in the corresponding glosses of BabelNet (+BABEL). The results are illustrated in Table 3. The extension of the basic sense representations with additional data is positive, namely for Recall at a low or null cost for Precision for all filtering methods. It is interesting to notice that for nouns both the two basic sense descriptions, SYN and SREL, and the SYN+BABEL configuration have comparable F1 values between the no threshold and the maximum score data. Nevertheless, the filtering based on the maximum score improves the quality of the proposed alignment by removing false positives (P=0.69 for SYN, SREL, and SYN+BABEL) without impacting on the number of good instances retrieved (R=0.42 for SYN and SREL, R=0.44 for SYN+BABEL).

Sense Similarity Results

The results for the Sense Similarity obtained from the Personalized Page Rank algorithm on the basis of the method described in Section 3.2. are illustrated in Table 4 for the vectors obtained from MWN and in Table 5 for those obtained from WN 3.0 (using automatic translation of the SC glosses). Similarly to the Lexical Match, the Sense Similarity outperforms the baseline rand both when using MWN as lexical knowledge base and when using WN 3.0. Overall, the differences in performance with the Lexical Match results are not immediate. The differences are strictly related to the different nature of the sense descriptions, i.e. a semantic representation based on a lexical knowledge graph, which can catch semantically related items out of the scope for the Lexical Match approach. We want to point out that the performances of this approach are strictly dependent on two interrelated aspects: i.) the coverage of the dictionary entries used by the lexical knowledge base, and ii.) the set of relations which are represented in the lexical knowledge base.

Concerning the use of MWN as lexical knowledge base, the overall results are lower than those obtained for Lexical Overlap, and the use of automatic translations and WN 3.0. Comparable results with Lexical Overlap are obtained only for Recall with no filtering (all pairs row in Table 4) both for nouns and verbs. As a manual error analysis has shown, these results are stricly related to the structure of MWN as lexical knowlege base, i.e. poor coverage in terms of relations and entries in the dictionary. For instance, we identified that most of the vectors for SC verbs have not been created due to the lack of entries in the lexical knowlege base dictionary. This aspect also support our previous observations on the results of Lexical Match.

On the contrary, the use of WN 3.0 provides interesting figures. Although not all MWN synsets have a corresponding entry in WN 3.0, the size of the English dictionary and the relations among the entries in the WN 3.0 graph provide more aligned pairs with respect to MWN, as shown by the figures for Recall in Table 5. In particular, by observing the Recall values for no threshold filtering (row all pairs Merging Lexical Match and Similarity with WN 3.0

The methods used for aligning senses in the two lexicosemantic resources differ in nature both with respect to the creation of the sense descriptions (simple bag of words vs. semantic representation) and to the ways with which the alignment pairs are extracted and computed. As a strategy to improve the results, we conducted a further alignment experiment by merging together the results obtained from the best sense descriptions and best filtering methods for Lexical Match and Sense Similarity, namely similarity with WN 3.0. We considered Precision and F1 scores to identify the best results. This led us to select the i.) the SYN sense description filtered with maximum score for verbs (P=0.59, F1=0.29); ii.) the SYN+BABEL sense description filtered with maximum score for nouns; iii.) the similarity with WN 3.0 with the cut-off threshold at 0.2 both for verbs and nouns. The results of the merging are illustrated in Table 6. The merging has a positive impact on the alignments of both parts-of-speech, signaling that different methods are focused on capturing different portions of the data. Global F1 scores are improved both for nouns and verbs. Nevertheless, the figures for Precision are still not totally satisfactory. In both cases the performance gains originate from the higher precision of the similarity approach with WN 3.0 with automatically translated glosses which minimizes the limits of the Italian section of MWN and of the SC Lexicon.

Merged P R F1 Verb -

Conceptual Interoperability with Verb Shallow Frames

In order to enhance conceptual interoperability on other levels of linguistic analysis for Senso Comune, we have automatically extracted verbal shallow frames (VSFs) from a sense annotated corpus in Italian, namely the MultiSemCor Corpus v1.0, a parallel corpus of English and Italian annotated with WN senses. The final goal is, for each sense annotated verb in the Italian section of MultiSemCor, to extract all available corpus-based example and automatically acquire VSFs. This operation will allow us: i.) to provide a starting set of verb structures associated with (M)WN senses and corpus-based examples for the development of layered annotations in the line of VerbNet; ii.) to investigate on the correlation between verb senses and different VSFs; and, finally, iii.) to experiment on the improvement of verb sense alignment. In this paper we will focus on the description and a preliminary evaluation of the first aspect, that is on the acquisition of VSF structures from the Multi-SemCor Corpus9 . We assumed as a VSF structure the syntactic complements of the verb, with no distinction between arguments and adjuncts, and the semantic type of the complement filler(s The original gold standard used for evaluating the WSA task has been extended to include 52 seed lemmas selected according to frequency and patterns in terms of semantic and syntactic features 10 . For each seed verb, we have extracted all its corresponding synsets in MWN and synset words. This has lead us to identify a total of 167 unique verb lemmas and a total of 417 different synsets. We then extracted from MultiSemCor all associated sentences which contained an annotated instance of the 417 synsets for a total of 4,820 instances. The extraction of the VSFs has been obtained as follows:

• MultiSemCor sentences have been parsed with a state-of-the-art dependency parser [START_REF] Attardi | Reverse revision and linear tree combination for dependency parsing[END_REF];

• for each verb lemma, we have automatically extracted all its syntactic complements standing in a dependency relation of argument or complement, together with the lemma of the slot filler;

• nominal lemmas of syntactic complements have been automatically assigned with one of the 26 semantic types composing the WN supersenses (i.e. noun.artifact; noun.object etc. [START_REF] Ciaramita | Supersense tagging of unknown nouns in WordNet[END_REF])) on the line of [START_REF] Lenci | Lexit: A computational resource on italian argument structure[END_REF]. For each nominal filler, we selected the most frequent WN supersense. Sense frequency had been computed on the basis of MultiSemCor. In case a polysemous noun lemma was not present in the MultiSemCor data or its senses have the same frequency, all associated WN supersenses were assigned. As for verbal fillers, we assigned the generic semantic type of "verb.eventuality". Finally, in case a lemma filler of a syntactic complement is not attested in MWN such as a pronoun or a missing synset word, no values is assigned and the VFS is not constructed. Optionally, when the noun filler was annotated with a synset in MultiSemCor, we have associated it to its corresponding WN supersense.

The information thus collected has been stored in a theoryand model neutral format, as illustrated in Example 1, which is compatible with other representation formats for VSF structure such as that in the PAROLE/SIMPLE/CLIPS lexicon [START_REF] Ruimy | A computational semantic lexicon of italian: SIMPLE[END_REF] and with current research activities in Senso Comune on the annotation of SC Lexicon examples of usage for verbs [START_REF] Chiari | An open knowledge base for italian language in a collaborative perspective[END_REF].

As for the extraction of the VSF structures, we have used a modified version of the system described in [START_REF] Caselli | Customizable scf acquisition in italian[END_REF], which reported an overall F-measure on the acquisition of VSFs from corpus data of 0.601 and a Precision of 0.65. The original system has a filtering mechanism based on maximum likelihood estimate (MLE) and percentage on verb frequency (PVF) which is used to exclude incorrect VSFs on the basis of the frequency of the VFS and the verb lemma in the corpusused for the acquisition. In our version, we have excluded this filtering mechanism, as we are working on verb senses and not lemmas. As a matter of fact, each verb sense has a limited number of annotated instances. For example, the verb aprire [to open] in Mul-tiSemCor has been annotated in 42 sentences with 11 different synsets. By excluding the filtering mechanism, we consider as valid all extracted VSFs. Nevertheless, it can be the case that the extracted VSFs is not correct. In order to provide a preliminary evaluation of the quality of the extracted VSFs with this approach, we have adopted the following method: we have extracted with the original version of the system in [START_REF] Caselli | Customizable scf acquisition in italian[END_REF], all VSFs for the 167 lemmas from a parsed version of the La Repubblica Corpus [START_REF] Baroni | Introducing the "la Repubblica" corpus: A large, annotated, TEI(XML)-compliant corpus of newspaper italian[END_REF]. This has provided us with a repository of VSFs associated to verb lemmas. We then computed the accuracy of the extracted VSFs from the Mul-tiSemCor sentences with those contained in the repository from La Repubblica. The accuracy provides us with a percentage measure of the correctly identified VSFs attested in the repository and of the non-attested ones.

From the 4,820 sentences of the MultiSemCor corpus in analysis, we extracted 3,295 VSFs tokens for the couples verb lemma-annotated sense. The 3,295 VSFs tokens correspond to 418 VSFs types. On top of this 3,295 acquired VSF tokens we computed their accuracy with respect to the La Repubblica repository as described above. The results are illustrated in Table 7. On a manual exploration of the non attested VSFs, we observe that most of them are due to parsing errors and VSFs which have been excluded by the filtering mechanism of the system. We are currently investigating on the application of crowdsourcing techniques on the Senso Comune platform to perfoem a post-processing analysis on the non-attested VFSs.

Conclusions and Future Work

This paper focuses on methods for automatically enrich the Senso Comune platform in the perspective of creating a robust and interoperable lexico-semantic resource for Italian. Two tasks have been tackled: i.) aligning senses between MWN and the SC Lexicon, and ii.) automatically acquire VSFs from a sense annotated corpus.

As for the sense alignment task, the lack of Italian glosses in MWN and the absence of any kind of structured information in the SC Lexicon dictionary are two major challenges for the applications of state-of-the-art techniques for sense alignment. Two different approaches have been experimented: Lexical Match and Sense Similarity obtained from Personalized Page Rank. In all cases, when filtering the data we are facing low scores for Recall which point out issues namely related to data sparseness in our lexica.

When comparing the results of the two approaches, we can observe that: i.) the Sense Similarity by means of automatic gloss translations plus WN 3.0 as lexical knowledge base yields the best Precision both with respect to Lexical Match and to Sense Similarity with MWN; ii.) Lexical Match, with a simple sense description configuration (i.e. the SYN configurations for verbs and nouns), is still a powerful approach; the exploitation of additional semantically related items (e.g. SREL for verbs) or additional sense descriptors (e.g. SYN+BABEL for nouns), though good in principle, has a limited contribution to solve the lexical gap problem in our case and highlights differences in the way word senses are encoded in the two lexica; iii.) Sense Similarity with automatic gloss translations and WN 3.0 performs better than Sense Similarity with MWN, pointing out that MWN as a lexical knowledge base has a lower coverage and that seems worst that having not perfect translations; and iv.) Sense Similarity and Lexical Match appears to qualify as complementary methods for achieving reliable sense alignments. Provided the limits of the two lexica, we have obtained satisfying results both for verb (F1=0.47) and noun sense alignment (F1=0.64). Nevertheless, we consider that there is still room for improving the results, namely in terms of Precision.

The acquisition of VSFs is another important task for achieving conceptual interoperability. The method used for the acquisition of the VSFs is reliable (accuracy=68%), though changes in the acquisition system should be tackled to deal with missing VSFs. The limited amount of not attested VSFs (32%) reduce the manual effort in the post-processing phase and will allow to experiment with crowdsourcing methods for the annotation of VSFs. Furthermore, the data will provide a basis for the development of a VerbNet-like resource for Italian. Future work will concentrate on two different aspects. We are currently investigating methods for automatically assign WN Domains to the SC Lexicon entries. Preliminary results are encouraging. The availability of WN Domain can be used to filter the proposed alignments and remove most cases of false positive data, thus increasing the Precision. Furthermore, we aim at importing the ontological classes of SC in MWN for bootstrapping better sense descriptions and investigating additional taxonomical errors in the (M)WN hierarchy with respect to those identified in [START_REF] Alvez | Complete and consistent annotation of wordnet using the top concept ontology[END_REF]. As for the VSFs, on the one hand, we are planning to integrate the automatically acquired data from MultiSemCor with the manual annotation of the SC example of usage for the verbal entries [START_REF] Chiari | An open knowledge base for italian language in a collaborative perspective[END_REF], and, on the other hand, we will experiment on the development of methods for the "leaking" of the Semantic Roles associated to WN senses in VerbNet to the corresponding Italian verb senses and syntactic structures.

Table 1 :

 1 Table 1 for verbs and Table 2 for nouns. Results of Lexical Match for basic sense representation of verbs.

	Lexical Match	P	R	F1
	Verb SYN -all pairs	0.41 0.29 0.34
	Verb SYN -≥ 0.1	0.42 0.26 0.32
	Verb SYN -≥ 0.2	0.54 0.11 0.18
	Verb SYN -max score	0.59 0.19 0.29
	Verb SREL -all pairs	0.38 0.32 0.35
	Verb SREL -≥ 0.1	0.40 0.27 0.32
	Verb SREL -≥ 0.2	0.53 0.11 0.18
	Verb SREL -max score 0.60 0.20 0.30
	Verb -rand	0.15 0.06 0.08

Table 2 :

 2 Results alignment of Lexical Match for basic sense representation of nouns.

Table 3 :

 3 Results for Lexical Match alignment with extensions with BabelNet data.

	Lexical Match	P	R	F1
	Noun SYN+BABEL -all pairs	0.47 0.66 0.56
	Noun SYN+BABEL -≥ 0.1	0.58 0.40 0.47
	Noun SYN+BABEL -≥ 0.2	0.69 0.12 0.21
	Noun SYN+BABEL -max score 0.69 0.44 0.55

Table 4 :

 4 Results for Similarity Score based on MWN.

	Similarity Measure	P	R	F1
	Verb -all pairs	0.12 0.69 0.20
	Verb -≥ 0.1	0.33 0.19 0.24
	Verb -≥ 0.2	0.41 0.13 0.20
	Verb -max score	0.34 0.14 0.20
	Verb -rand	0.15 0.06 0.08
	Noun -all pairs	0.20 0.64 0.21
	Noun -≥ 0.1	0.42 0.28 0.33
	Noun -≥ 0.2	0.51 0.18 0.27
	Noun -max score	0.38 0.30 0.34
	Noun -rand	0.17 0.12 0.14
	Similarity Measure	P	R	F1
	Verb -all pairs	0.10 0.9 0.19
	Verb -≥ 0.1	0.47 0.25 0.32
	Verb -≥ 0.2	0.66 0.16 0.26
	Verb -max score	0.42 0.20 0.27
	Verb -rand	0.15 0.06 0.08
	Noun -all pairs	0.12 0.94 0.21
	Noun -≥ 0.1	0.52 0.32 0.40
	Noun -≥ 0.2	0.77 0.21 0.33
	Noun -max score	0.42 0.38 0.40
	Noun -rand	0.17 0.12 0.14

Table 5 :

 5 Results for Similarity Score based on WN 3.0.

Table 5 )

 5 , almost all aligned sense pairs of the gold are retrieved, outperforming both the Lexical Match and the similarity with MWN. As for the filtering methods, figures for verbs and nouns show that the simple cut-off thresholds provide better results with respect to the maximum score. Such a better performance of the simple cut-off thresholds with respect to the maximum score is due to the fact that aligning senses by means of semantic similarity provides a larger set of alignments and facilitates the identification of multiple alignments, i.e. one-to-many. As for verbs, the best the best F1 score (F1=0.32) is obtained when setting the cosine similarity to 0.1, though Precision is less than 0.50. When compared with threshold value of 0.1 of the Lexical Match and similarity with MWN, the similarity with WN 3.0 yields the best Precision (P=0.47 vs. P=0.42 for Verb SYN, P=0.40 for Verb SREL and P=0.33 for similarity with MWN). Similar observations can be done when the threshold is set to 0.2. In this latter case, similarity with WN 3.0 yields the best Precision score with respect to all other filtering methods and the Lexical Match results obtained with maximum score (P=0.66 vs.

	P=0.59 for Verb SYN, P=0.60 for Verb SREL and P=0.41
	for similarity with MWN).
	The results for nouns are different though in line with those
	for verbs. Apparently, the similarity with WN 3.0 has better
	results for F1 only with respect to similarity with MWN and
	lower values with respect to all Lexical Match sense config-
	urations and filtering methods, including the no threshold
	score of the basic sense descriptions (respectively, F1=0.55
	for SYN, F1=0.54 for SREL, F1=0.21 for similarity with
	WN 3.0). However, when maximizing the Precision for the
	similarity with WN 3.0 (threshold 0.2), the algorithm pro-
	vides better performances (F1=0.33) with respect to Lexical
	Match on the same filtering method, minimizing the drop of
	Recall (R=0.21; +0.09 with respect to SYN+BABEL with
	same threshold; + 0.08 with respect to SREL; +0.05 with
	respect to SYN, respectively).

Table 6 :

 6 Results for automatic alignment merging the best results from Lexical Match and Sense Similarity.

	SYN+SimWN30 02	0.61 0.38 0.47
	Noun -SYN+BABEL+SimWN30 02 0.67 0.61 0.64

Table 7 :

 7 Accuracy on the extracted VSFs with respect to the La Repubblica repository

For additional details on the Senso Comune model see details see[START_REF] Vetere | Senso Comune, an open knowledge base for italian[END_REF],[START_REF] Oltramari | Senso Comune: A collaborative knowledge resource for italian[END_REF].

Lexemes covering about 90% of all spoken and written texts in Italian. See[START_REF] Oltramari | Senso Comune: A collaborative knowledge resource for italian[END_REF].

Full details on MWN are reported in[START_REF] Pianta | Multi-WordNet: developing an aligned multilingual database[END_REF].

http://wordnet.princeton.edu/glosstag.shtml

http://www.d.umn.edu/ tpederse/text-similarity.html

http://ixa2.si.ehu.es/ukb/

We use Google Translate API.

Experiments on the use of VSFs for improving the alignment of verb senses are described in[START_REF] Caselli | Aligning verb senses in two italian lexical semantic resources[END_REF].

A subset of these verbs have been taken from[START_REF] Jezek | Capturing coercions in texts: a first annotation exercise[END_REF]