6
Cooperation of coordinated teams of Autonomous Underwater Vehicles ? Vladimir Djapic * Wenjie Dong ** Daniele Spaccini *** Gianni Cario **** Alessandro Casavola **** Petrika Gjanci *** Marco Lupia **** Chiara Petrioli *** * SPAWAR Systems Center Pacific, San Diego, CA 92152 USA (e-mail: [email protected]). ** Department of Electrical Engineering, the University of Texas - Rio Grande Valley, Edinburg, TX 78539 USA *** Computer Science Department, University of Rome, “La Sapienza,” Italy and WSENSE s.r.l., Rome, Italy **** Department of Informatics, Modelling, Electronics and Systems, University of Calabria, Rende, Italy and Applicon s.r.l., Rende, Italy Abstract: This paper presents the initial stage of the development of an underwater localization system suitable for a flexible number of users. Multiple Autonomous Underwater Vehicles (AUVs) can work as a team and cooperate with other teams of AUVs without costly and acoustically active components, which saves energy and allows AUVs to remain silent. The main building blocks for such a system are: spiral wavefront beacon in conjunction with a standard (circular) acoustic modem, Chip Scale Atomic Clocks (CSAC), acoustic modems, state-of-the- art adaptive underwater networking and Cooperative Localization (CL) algorithms. Using the difference in time of arrival between the spiral wavefront and the modem circular wavefront, receivers will be able to determine the bearing to the source using only one hydrophone. Synchronizing vehicles Chip Scale Atomic Clocks (CSAC) with the beacon at the beginning of the mission and during the longer missions will ensure the vehicles ability to also calculate their distance from the beacon upon every message reception. Keywords: Spiral beacon, atomic clock, acoustic modem, cooperative localization, underwater networking. 1. INTRODUCTION Multi robot coordination and cooperation have a potential to significantly improve ocean exploration missions. For multiple AUV operations, coordination refers to AUVs keeping their formation and cooperation association to achieve specified mission objectives. Teams of coordinated autonomous underwater vehicles (AUV) can then cooper- atively work with other teams of coordinated AUVs. This vision for ocean exploration dates back two decades ago with Autonomous Ocean Sampling Network (AOSN), see (1); however, it is now a reality with several tech- nological advancements. The integration of this technol- ogy will result in reduced total ownership cost of the AUV. Although the cost of small AUVs has significantly decreased; if coordinated teams are employed, expensive sensors previously required for precise AUV navigation are no longer necessary. For example, costly fiber-optic or laser-ring gyros can be replaced with MEMS counterparts and a Doppler Velocity Log (DVL), often considered as a main navigation sensor for AUV navigation, needs be installed only on one AUV that serves as the main node for ? This work was supported by Office of Naval Research Global (ONRG) NICOP N62909-14-1-N259 grant and ONR 0601153N grant. the team of AUVs. Coordination can be accomplished with less sensor sophisticated AUVs with the aid of underwater communication and utilization of inexpensive, low power Chip Scale Atomic Clock (CSAC) (4) and decentralized distributed control and localization algorithms. Cooper- ation can be accomplished with advances in underwater networking schemes. Ongoing efforts are aiming at similar goals. For example, The widely scalable Mobile Underwater Sonar Technol- ogy (WiMUST) (2) system will be composed of many AUVs carrying hydrophones to acquire sub-bottom profil- ing acoustic data. Instead of traditional arrays of sensors, that are either stationary or towed by the ship forming the fixed geometry of the acoustic antenna, new and exciting technology advances that will be integrated into WiMUST will allow for rapid, on-the-fly, changes to the geometry of the acoustic antenna. This has the potential to drastically improve ocean surveying. A team of researchers from SPAWAR Systems Center Pacific (SSC PAC), the University of Rome, and the Uni- versity of Calabria has recently demonstrated the utility of using synchronized atomic clocks for one-way ranging, which can be used for navigation updates to a team of AUVs broadcasting only one acoustic message. This mes- sage can be sent by an AUV equipped with more advanced

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Cooperation of coordinated teams ofAutonomous Underwater Vehicles ?

Vladimir Djapic ∗ Wenjie Dong ∗∗ Daniele Spaccini ∗∗∗

Gianni Cario ∗∗∗∗ Alessandro Casavola ∗∗∗∗ Petrika Gjanci ∗∗∗

Marco Lupia ∗∗∗∗ Chiara Petrioli ∗∗∗

∗ SPAWAR Systems Center Pacific, San Diego, CA 92152 USA(e-mail: [email protected]).

∗∗Department of Electrical Engineering, the University of Texas - RioGrande Valley, Edinburg, TX 78539 USA

∗∗∗ Computer Science Department, University of Rome, “LaSapienza,” Italy and WSENSE s.r.l., Rome, Italy

∗∗∗∗Department of Informatics, Modelling, Electronics and Systems,University of Calabria, Rende, Italy and Applicon s.r.l., Rende, Italy

Abstract: This paper presents the initial stage of the development of an underwater localizationsystem suitable for a flexible number of users. Multiple Autonomous Underwater Vehicles(AUVs) can work as a team and cooperate with other teams of AUVs without costly andacoustically active components, which saves energy and allows AUVs to remain silent. The mainbuilding blocks for such a system are: spiral wavefront beacon in conjunction with a standard(circular) acoustic modem, Chip Scale Atomic Clocks (CSAC), acoustic modems, state-of-the-art adaptive underwater networking and Cooperative Localization (CL) algorithms. Using thedifference in time of arrival between the spiral wavefront and the modem circular wavefront,receivers will be able to determine the bearing to the source using only one hydrophone.Synchronizing vehicles Chip Scale Atomic Clocks (CSAC) with the beacon at the beginningof the mission and during the longer missions will ensure the vehicles ability to also calculatetheir distance from the beacon upon every message reception.

Keywords: Spiral beacon, atomic clock, acoustic modem, cooperative localization, underwaternetworking.

1. INTRODUCTION

Multi robot coordination and cooperation have a potentialto significantly improve ocean exploration missions. Formultiple AUV operations, coordination refers to AUVskeeping their formation and cooperation association toachieve specified mission objectives. Teams of coordinatedautonomous underwater vehicles (AUV) can then cooper-atively work with other teams of coordinated AUVs.

This vision for ocean exploration dates back two decadesago with Autonomous Ocean Sampling Network (AOSN),see (1); however, it is now a reality with several tech-nological advancements. The integration of this technol-ogy will result in reduced total ownership cost of theAUV. Although the cost of small AUVs has significantlydecreased; if coordinated teams are employed, expensivesensors previously required for precise AUV navigationare no longer necessary. For example, costly fiber-optic orlaser-ring gyros can be replaced with MEMS counterpartsand a Doppler Velocity Log (DVL), often considered asa main navigation sensor for AUV navigation, needs beinstalled only on one AUV that serves as the main node for

? This work was supported by Office of Naval Research Global(ONRG) NICOP N62909-14-1-N259 grant and ONR 0601153Ngrant.

the team of AUVs. Coordination can be accomplished withless sensor sophisticated AUVs with the aid of underwatercommunication and utilization of inexpensive, low powerChip Scale Atomic Clock (CSAC) (4) and decentralizeddistributed control and localization algorithms. Cooper-ation can be accomplished with advances in underwaternetworking schemes.

Ongoing efforts are aiming at similar goals. For example,The widely scalable Mobile Underwater Sonar Technol-ogy (WiMUST) (2) system will be composed of manyAUVs carrying hydrophones to acquire sub-bottom profil-ing acoustic data. Instead of traditional arrays of sensors,that are either stationary or towed by the ship forming thefixed geometry of the acoustic antenna, new and excitingtechnology advances that will be integrated into WiMUSTwill allow for rapid, on-the-fly, changes to the geometry ofthe acoustic antenna. This has the potential to drasticallyimprove ocean surveying.

A team of researchers from SPAWAR Systems CenterPacific (SSC PAC), the University of Rome, and the Uni-versity of Calabria has recently demonstrated the utilityof using synchronized atomic clocks for one-way ranging,which can be used for navigation updates to a team ofAUVs broadcasting only one acoustic message. This mes-sage can be sent by an AUV equipped with more advanced

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navigation sensors (FOG gyros and DVL) and can containits x and y position. By virtue of receiving a message fromthe “master” AUV, other inexpensive AUVs can updatetheir position estimate.

Another technology that will be utilized in our upcom-ing tests is spiral beacon technology. The United StatesNaval Research Laboratory in Washington, D.C. (3) hasdeveloped an underwater acoustic analogy using a systemthat consists of a coaxial set of spiral and circular warefront beacons. This system operates similarly to the VOR(VHF Omni Directional Radio Range) system used inaerial traffic. The VOR uses a beacon whose mix of twosignals informs the recipients of their bearing towards thebeacon. In the same way, the underwater acoustic analogyprovides a navigation aid to AUVs. Using this technologytogether with synchronized clocks enables both bearingand range from the “master” to be known at each AUV.

These technologies not only have great potential for pre-cise navigation of inexpensive AUVs but also significantlyaffect the endurance (mission time) of the AUVs as theydo not need to transmit acoustic messages for navigation.Transmission of an acoustic message is much more costlycompared to the reception of the message. It costs approx-imately 40 Watts for transmission and only 40 mWattsfor reception. Low power onboard navigation sensors andthe elimination of acoustic transmissions can enable AUVsto navigate underwater for weeks at the time and theirmission time can come closer to currently employed un-derwater gliders so AUVs can be utilized for glider type ofmissions with much greater precision.

The rest of the paper is organized as follows. Section 2explains our Distributed Kalman Filtering cooperative es-timation. In Section 3 we present our AUV assets and theSpiral Wave Front Beacon concept. Section 4 describesour acoustic modems, our underwater networking algo-rithms, and planned improvements. Section 5 providessimulation results and Section 6 describes the results fromthe previous representative experiments. Finally, Section 7discusses future research goals.

2. DISTRIBUTED LOCALIZATION ANDCOOPERATIVE CONTROL

Distributed estimation with the aid of local informationis challenging because information is not available at eachagent. When multiple AUVs are involved, state estimationat each vehicle with the aid of neighbors’ information isagain extremely challenging because underwater commu-nication is intermittent and low bandwidth. Distributedcontrol of multiple vehicles has many benefits. However,controller design is challenging. In this paper, we considerdistributed localization and distributed cooperative con-trol of multiple vehicles.

2.1 AUV Model

Define a fixed inertia coordinate frame (I-frame) and alsodefine a body frame (B-frame) for each vehicle, for vehiclej its position ηj = [xj , yj , zj ]

> is described relative to thefixed inertia frame and its orientation can be defined by aunit quaternion Qj = [q0j , q

>1j ]>. The linear and angular

velocity of the vehicle are denoted by vj and ωj . Thekinematics of vehicle j is

ηj =R(Qj)vj (1)

Qj =1

2

[−q>1j

q0jI3 + S(q1j)

]ωj (2)

where S is the skew-symmetric matrix such that S(u)v =u× v where × denotes the vector cross product, and

R(Qj) = I3 + 2S(q1j)2 − 2q0jS(q1j).

The dynamics of the vehicle can be written as

Mj νj + Cj(νj)νj +Dj(νj)νj +Gj(Qj) = Bjτj (3)

where νj = [v>j , ω>j ]>, Mj = M>j > 0 is a positive definite

inertia matrix (which includes the added inertia), Cj(νj) =−Cj(νj)

> is a skew-symmetrical matrix containing theCoriolis and centripetal term, Dj(νj) > 0 is a positivedefinite damping matrix containing drag and lift terms(and possibly skin friction and viscous damping), Gj(Qj)denotes the gravitational and buoyant forces, Bj is theinput matrix, and τj is the external input.

2.2 Problem Statement

For a group of the above vehicles, in order to accomplisha mission the state of a vehicle should be known. The firstproblem considered in this paper is as follows.

Distributed Localization: Each vehicle’s available in-formation is its own sensors’ information and the infor-mation received from its neighbors. Propose distributedestimation algorithms such that the state of each vehiclecan be estimated as accurately as possible.

Given a virtual leader which is moving with a desiredtrajectory ηd(t) = [xd(t), yd(t), zd(t)]> and a desired for-mation which is defined by constant displacement vectorspj = [pxj , pyj , pzj ]

> for 1 ≤ j ≤ m, the distributedcooperative problem considered in this paper is definedbelow.

Distributed Leader-follower Control: For a group ofvehicles, the information from a virtual leader is availableto one or more vehicles. We propose a distributed controllaw for each vehicle with the aid of its own information andits neighbors’ information such that the group of vehiclescome into desired formation and the centroid of themmoves along a desired trajectory, i.e.,

limt→∞

(ηj − ηi) = pj − pi, 1 ≤ i, j ≤ m (4)

limt→∞

m∑j=1

ηj − pjm

− ηd = 0 (5)

In the next subsections, we will present the solution to theabove two problems.

2.3 Solution to the Distributed Localization and DistributedLeader-follower Control problems

The dynamics of an AUV is nonlinear. For distributedestimation, we discretize the system in (1)-(3) to thefollowing discrete-time system.

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x(k) =A(k)x(k − 1) +B(k)ω(k − 1) +G(k)u(k) (6)

where x is the state of the system, u is the control input,and w is the noise and uncertainty.

Assume there are m sensors. The measurement of sensori about this UAV is

yi(k) =Hi(k)x(k) + vi(k) (7)

where

E(w(k)w>(j)) =Q(k)δkj

E(vi(k)v>i (j)) =Ri(k)δkj

E(vi(k)v>i (j)) = 0

E(w(k)v>i (j)) = 0.

Between sensors, there is communication. The communica-tion between any two sensors can be described by a graphG = {A,V} where the node set A denotes the labels ofm sensors and the edge set E denotes the communicationbetween sensors. for simplicity, it is assumed the com-munication is bidirectional. Therefore, the graph G is abidirectional graph. Two sensors are said to be neighborsif there is communication between them.

For sensor i, its neighbors are formed a set and is denotedby Ni.

Next, we present an algorithm on how to estimate the stateof an AUV with the aid of neighbors’ information.

Let x−i (k) and x+i (k) be the prior and posterior estimatesof x(k) to incorporating the measurement y(k) by sensori, respectively. Also we let xi(k) be the estimation ofxi(k) after all information has been incorporated. Forsensor i, we let the vector y∗i denote the collection ofits measurement yi and its neighbors’ measurement yj forj ∈ Ni and Hi denote the collection of its measurementmatrix Hi and its neighbors’ measurement matrix Hj forj ∈ Ni. Also, let R∗i denote the collection of the varianceRi of its measurement noise and the variance Rj of itsneighbors’ measurement noise for j ∈ Ni. since the controlinput u(k) is not available for each sensor, it should beestimate at the same time. Let ui(k) be the estimate ofu(k) by sensor i.

We propose the following three-step distributed estimationalgorithm:

Distributed Estimation Algorithm:

For sensor i,

• Time update:

x−i (k) =Axi(k − 1) +G(k)uj(k)

ui(k) =−∑j∈Ni

bij(ui(k − 1)− uj(k − 1))

−bi0((ui(k − 1)− u(k − 1))

−ρ sign[∑j∈Ni

bij(ui(k − 1)− uj(k − 1))

−bi0((ui(k − 1)− u(k − 1))]

P−i (k) =AP+i (k − 1)A> +BQB>

where bij > 0, ρ is a sufficiently large positiveconstant, bi0 > 0 if u(k) is available to sensor jotherwise bi0 = 0.

• Measurement update:

x+i (k) = x−i (k) +K∗i(k)(y∗i(k)−H∗i(k)x−i (k))

P+i (k) = (I −K∗iH∗i)P−i (k)(I −K∗iH∗i)>

+K∗i(k)R∗iK∗i(k)>

K∗i(k) = P−i (k)H>∗i[H∗iP−i (k)H>∗i +R∗i]

−1

• Fusion:

xi(k) =∑s∈Ni

δ∑l∈Ni

δ + αx+s (k) +

α∑l∈Ni

δ + αx+i (k)(8)

where positive constants α and δ satisfy the con-straint α >> δ > 0.

Under some assumptions, it can be shown that the abovedistributed estimation algorithm can estimate the state ofan AUV and the estimates of different sensors can reachconsensus.

With the aid of the estimation algorithms proposed in thelast section, the state of each vehicle can be estimatedonline and is available for controller design. For simplicityof presentation, in the controller design it is assumed thatthe state of each vehicle is known.

For the vehicles in (1)-(3), we design distributed controllaws with the aid of its cascade structure in two steps foreach type of vehicles. In the first step, we design someintermediate controller such that (4)-(5) are satisfied. Inthe second step, we design real control inputs for eachvehicle with the aid of the results in the first step suchthat (4)-(5) are satisfied.

Step 1: We design an intermediate controller for eachvehicle.

We assume vj is a virtual control input and design acontroller for it. We propose that

vj =R(Qj)>vdj (9)

vdj =−ej − ρj tanhejε

(10)

ej =∑i∈N

aji(ηj − pj − ηi + pi) + bj(ηj − pj − ηd) (11)

Step 2: We design the real inputs for each type of vehicles.

We choose a desired angular velocity ωdj with the aid of

other requirements. Let νdj = [v>j , ω>j ]> and νj = νj − νdj ,

then

Mj˙νj + Cj νj = Bjτj −Gj −Djνj −Mj ν

dj − Cjν

dj (12)

We choose the control inputs

τj =B−1j [−K6j νj +Gj +Djνj +Mj νdj + Cjν

dj ] (13)

where K5j is a positive definite constant matrix.

With the above design procedure, it can be shown that thedistributed control laws in (13) ensure that (4)-(5) holdpractically, i.e.,

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(a) Bluefin 9 AUV (b) Riptide Micro AUVs

Fig. 1. SSC PAC’s AUVs.

limt→∞

‖ηj − pj − ηi + pi‖ ≤ ε, 1 ≤ i, j ≤ m (14)

limt→∞

m∑j=1

ηjm− ηd

≤ ε (15)

where ε is a small constant.

In the proposed controls, we assumed that the state of eachvehicle is measurable and is known exactly. If the stateof each vehicle is estimated with the aid of the proposeddistributed estimation algorithms, we can replace the statein the control algorithms with the estimated value.

3. AUV ASSETS AND SPIRAL BEACON

In the project and for its experiments we have several AUVassets available, briefly described in what follows.

3.1 Bluefin 9 AUV

SSC PAC has two Bluefin Sealion II AUV. Standard com-mercial off-the-shelf (COTS) Sealion II AUV is a 2-man-portable vehicle weighing in at about 60 Kg. As opposed tothe COTS Sealion II, a payload nose section was added forintegration of additional sensors into the existing Sealion IIUUV platform (Fig. 1(a)). The new payload nose will holda payload pressure vessel with a spiral beacon and acousticmodem. The Sealion II Standard Payload Interface (SPI)software was upgraded to provide capabilities comparableto the current Bluefin Robotics standard and will support“backseat driver” functionality so Distributed Localizationand Cooperative Control algorithms presented in Sec. 2can be implemented.

3.2 Spiral Wave Front Beacon

Spiral Wave Front Beacon uses a coaxial set of a spiralwave front beacon and a circular wave front beacon. Thecircular wave front beacon can be a classic beacon oreven an acoustic modem, while the spiral wave front canbe generated using a physical spiral beacon or a circulararray of beacons fired in a rotational manner in orderto synthetically create a spiral wave front. The differencein phase (or time) between the spiral wave front signaland the circular wave front signal informs the recipientof its bearing towards the beacon (See Figure 2). Theseparation between those two signals can be done in time,frequency or a mix of the two methods. Furthermore, in thesynthetic spiral method, a changing chirp signal in relationto bearing can be used (as it is normally used in scanningsonar and radar systems) to increase angular resolutionand robustness. The spiral beacon was recently receivedfrom DBTech Acoustics, LLC and it is being integrated.

Fig. 2. Representation of the acoustic localization fieldgenerated by the Spiral Wave Front Acoustic ModemBeacon (Tb carries bearing information and Tr carriesrange information.)

The bearing can be used to determine the position of arecipient. For example, if there are two spiral wave frontbeacons with known position, the position of a recipientcan be calculated with the aid of its bearings to the twobeacons. In our distributed estimation framework, thebearing of a recipient can be fused with other sensors’information to determine the position of the recipientwith the aid of the distributed Kalman filter algorithmsproposed in Section 2.

3.3 Riptide Micro AUVs

SSC PAC has three Riptide Autonomous Solutions MicroAUVs. Two of them are shown in Fig. 1(b). The microAUV is a new, highly flexible, open source autonomousundersea vehicle that provides users a state-of-the-art, lowcost development solution ideally suited for developers ofautonomous behaviors, power systems, subsea sensors, andnew payloads. The micro-UUV features open hardwareand software interfaces to provide users a reliable androbust platform to advance technology development. Thevehicle design is optimized for high efficiency with thebest hydrodynamic signature in its class. Sea Modemswith CSAC (presented in Sec. 4) and a MEMS IMUwill be added to the Micro AUVs for the developmentof Distributed Localization and Cooperative Control andunderwater networking algorithms.

4. UNDERWATER ACOUSTIC COMMUNICATION,NAVIGATION AIDING, AND NEW ADAPTIVENETWORKING ALGORITHMS AND POLICIES

The Control Engineering Group of the Autonomous Sys-tems Laboratory at the DIMES Department of the Uni-versity of Calabria has developed, in collaboration withApplicon s.r.l., a compact low-power underwater acousticmodem for AUV navigation and communication appli-cations (6). SeaModem is the commercial name of this

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Fig. 3. SeaModem stacked with BeagleBone and CSAC.

modem actually produced by Applicon s.r.l. It is a FSKunderwater acoustic modem well suited for shallow wa-ter communications. The working frequency band rangesbetween 25 to 35 KHz, with selectable data-rates of 750bits/sec, 1500 bits/sec and 2250 bits/sec. A UART in-terface is used to host the modem. SeaModem has twoexpansion connectors both pin-to-pin compatible with theLinux embedded platform BeagleBone developed by Bea-gleBoard.org Foundation. The BeagleBone board is anopen-source embedded PC based on an ARM Cortex CPUrunning a Linux operating system. The BeagleBone acts asa host and uses the integrated UART interface to commu-nicate with the modem. The integration with BeagleBonemakes the SeaModem a stand-alone system with all thefunctionalities of a Linux system. Moreover, new high-levelfunctionalities can be developed on the BeagleBone thatcan use the modem as a communication device. To avoidloss in accuracy due to the typical clock drifts arising in thestandard real-time clocks integrated in the DSP and em-bedded platforms, Seamodem hardware is being extendedwith a CSAC. CSACs have a very low drift will enable theSeamodem clock to remain synchronized for many hourswithout remarkable error in the range calculation. The SeaModem and CSAC are shown in Fig. 3.

4.1 New adaptive networking algorithms and policies

The Underwater Group of the Senses Lab at the Com-puter Science Department of the University of Rome “LaSapienza”, has developed, in collaboration with WSENSES.r.l., a novel framework named SUNSET, for “SapienzaUniversity Networking framework for underwater Simula-tion Emulation and real-life Testing,” enabling to seam-lessly simulate, emulate and test in real-life novel com-munication protocols (7). To fully support the AppliconSeaModem (Section 4) operations a new driver has beendeveloped in SUNSET to control and reconfigure the mo-dem, locally or via acoustic links. This driver allows to setthe transmission gain, the FSK modulation, the Viterbialgorithm for forward error correction, the guard periodand the chirp threshold, etc. SUNSET enables the conceptof Software Defined Communication Stack (SDCS), namedSUNSET-SDCS (S-SDCS) where different network proto-cols running at the same layer of the protocol stack canbe selected and used according to the network conditionsand application scenario in both autonomous and manualways. Special algorithm, named Policies, can be designedand developed to automatically switch among the differentprotocols to achieve higher performance of the overallsystem.

5. SIMULATION

5.1 Distributed Estimation

For aerial vehicles and surface vehicles, IMU and GPSreceivers are equipped. The integrated INS/GPS systemcan estimate the state of the vehicle with reasonableprecision. For a underwater vehicle, IMU is installed inthe vehicle. However, GPS signal cannot be received ifthe vehicle is under water. Due to the accumulated errorof IMU based estimation, the estimate based on IMUmeasurements is not accurate. To solve this problem,the proposed distributed estimation can be applied toimprove the accuracy of the state estimation with the aidof neighbors’ information.

Assume there are two surface vehicles (labeled as vehicle1 and vehicle 2) and one underwater vehicle (labeledas vehicle 3). The surface vehicles are equipped withIMU/GPS navigation systems. The state of each surfacevehicle can be estimated with the aid of their INS/GPSsystem with reasonable precision. The underwater vehicleis equipped with IMU based inertia navigation system. Itsstate can be estimated with the aid of the INS system.However, the estimation error becomes larger and largeras time goes. To improve the estimation accuracy of theunderwater, the proposed distributed Kalman algorithmscan be applied to estimate the state of the underwater withthe aid of neighbors’ information. Consider vehicles 1, 2,and 3 as three sensors labeled as 1, 2, and 3, respectively.The kinematics of vehicle 3 is defined by xy

ψ

=

[u cosψ − v sinψu sinψ + v cosψ

r

]+ w. (16)

The measurement of three vehicles is as follows:

• For vehicle 1, the measurement is

y1 =[√

(x− x1)2 + (y − y1)2, ψ]>

+ v1 (17)

• For vehicle 2, the measurement is

y2 =[√

(x− x2)2 + (y − y2)2, ψ]>

+ v2 (18)

• For vehicle 3, the measurement is

y3 =[√

(x− x1)2 + (y − y1)2 ,√(x− x2)2 + (y − y2)2, ψ

]>+ v3

(19)

The communication digraph between vehicles is shown inFig. 4(a). The available information for vehicle 1 is themeasurement (y1, y2) and the estimation of the state byvehicle 2. The available information for vehicle 2 is themeasurement (y2, y3) and the estimation of the state byvehicle 3. The available information for vehicle 3 is themeasurement (y3, y1) and the estimation of the state byvehicle 1. The system in (16) is a nonlinear system. Weapply the proposed extended distributed Kalman filteringalgorithm. Figures 4(b)-5(b) show the tracking errors of(xj − x), (yj − y), and (ψj − ψ), respectively.

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1

3

2

(a) Communication direct graphbetween vehicles

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2−20

−15

−10

−5

0

5

10

15

20

time (sec)

x j−x (j=

1,2,3)

(b) Tracking errors of (xj−x) for1 ≤ j ≤ 3

Fig. 4. Communication direct graph and Tracking Error.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2−10

0

10

20

30

40

50

time (sec)

y j−y (j

=1,2

,3)

(a) Tracking errors of (yj −y) for1 ≤ j ≤ 3

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

time (sec)

ψj−ψ

(j=1

,2,3

)

(b) Tracking errors of (ψj−ψ) for1 ≤ j ≤ 3

Fig. 5. Tracking Errors.

6. FIRST IN-WATER RESULTS

Different in-field activities have been carried out in Oc-tober 2015 in waters south of Cartagena, Spain, duringthe TJMEX’15 campaign (Trident Juncture MCM EX-periment 2015). TJMEX15 experiments demonstrated theutility of using synchronized atomic clocks for one-wayranging which can be used for navigation updates toteam of AUVs broadcasting only one acoustic message.Several experiments have been performed to estimate theaccuracy of both two-way and one-way ranging estima-tion to localize underwater nodes. It can be seen fromTable 1 that both the ranging techniques achieves verygood results, with a minimum standard deviation of 0.11and 0.28 meters when using one-way and two-way ranging,respectively.

Table 1. Distance estimation using One-Wayand Two-Way travel time ranging.

Day One-Way (meters) Two-Way (meters)

Oct. 19 AVG=478.8, STD=0.11 AVG=478.7, STD=0.28

476

477

478

479

480

481

1000 1500 2000 2500 3000 3500 4000

Dis

tan

ce [

m]

Time [s]

Synchronize One-WayOne-Way RangingTwo-Way Ranging

Fig. 6. One-way and two-way ranging estimation.

7. CONCLUSION

Use of underwater vehicle groups and swarms for varioustypes of missions raises a need for such a system of under-

water vehicles to ensure high quality localization withouta need for costly components onboard every member ofthe groups or swarms. Synchronizing vehicles clocks withthe beacon in the beginning of the mission and duringthe longer mission (with either GPS, magnetometers, ore-field sensors) will ensure the vehicles ability to calculateits distance from the beacon upon every message reception.Bearing results from the beacons installed on some of theunderwater vehicles in the swarm, which can be equippedwith higher end navigation suites (DVL, costly IMUs), canachieve more accurate localization solution for the entireswarm. Our goal is to show that our assets, sensors, andalgorithms are reliable and have a chance to become astandard method to generate an underwater localizationfield for any number of underwater users whether those arevehicles, sensors, markers, loggers or divers. Not only willthe system enable localization for any number of users witha fixed update rate at a range limited by transmit powerand acoustic channel state, it will also increase autonomyfor energy critical systems and provide stealth capacity.

ACKNOWLEDGEMENTS

This work has been partially supported by the EU FP7 ICT project SUNRISE. We would like to thank Dr.Samantha Dugelay from Centre for Maritime Research& Experimentation for the invitation to participate inTJMEX’15 campaign and the engineering team and crewof Research Vessel Alliance for the support during theexperimentation.

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