06669892

7/26/2019 06669892

http://slidepdf.com/reader/full/06669892 1/6

Modelling and Identification of a Twin Hull-Based

Autonomous Surface Craft

Stefan Wirtensohn, Johannes Reuter, Michael Blaich, Michael Schuster, Oliver HamburgerInstitute of System Dynamics, University of Applied Sciences Konstanz

Konstanz, Germany

Email: {stwirten, jreuter, mblaich, schustem, ohamburg}@htwg-konstanz.de

Abstract— In this paper, the process and results of a parameteridentification task for a maritime unmanned surface vehicle arepresented. The system has been modeled using state of theart methodology, and the parameters have been estimated viaa weighted least square optimization approach. The requiredmeasurement data have been taken from various maneuvretrials. For solving the optimization problem, a Particle Swarm

programming approach has been used, which has reliably foundthe global minimum of the cost function. The results showexcellent agreement between measured and simulated data.

I. INTRODUCTION

The development of autonomous maritime vehicles has been

a vibrant research area over the last decades. First, these

activities were promoted for military use. Nowadays, there is

an increasing demand for civilian applications for unmanned

surface vessels (USV) as well. Typical tasks that USVs can

support are e.g. surveying, cleaning, or analytical tasks. A

major advantage of these typically rather small vessels is

their flexibility. They can operate in both, shallow and deepwater environments with minimum impact on the surrounding

area or population. Yet, they are usually large enough to

carry a sufficient amount of payload in order to be useful.

Further advantages are flexibility, safety, and not causing

any environmental harm. They can be fairly agile such that

operating in cluttered environment is possible. This makes

USV an appropriate choice e.g. for littoral research in biology

or limnology. For this reason, HTWG Konstanz has teamed up

with the Institute of Limnology from the department of biology

at Constance University and the Institute of Limnology from

the Baden-Wurttemberg State Environment Agency in order

to conduct research for developing a vehicle that can fulfill

the tasks described above. One particular goal among others

is to achieve very precise and robust motion control. The USV

should comprise excellent manoeuvrability, e.g. it should be

capable of turning on the spot and be able to autonomously

dock on to a battery charging station. The operating range

should be sufficiently long, and various safety mechanisms

should be implemented to guarantee a save return to the base.

In a previous project, the USV CaRoLIME (Catamaran Robot

- Locomotion In Maritime Environments) has been designed

and is used now as a starting point to design algorithms, and

to understand the system in more details. Moreover, various

sensors for IMU/GNSS navigation solutions as well as for

scanning the environment have been integrated. In this context,

modeling and identification tasks are of significant importance.

The parameterized model will basically have two areas of

use. First, it will be used for research in the area of model

based control. Newly developed strategies will be tested and

compared against standard controller designs. Second, for

hardware in the loop (HIL) and software in the loop (SIL)

test scenarios. In particular, the HIL test setup is consideredto speed up the development, since experience from previous

projects showed a lot of wasted time during non-functioning

test setups on Lake Constance. Furthermore, it will also allow

relevant testing even when the weather conditions are not

appropriate. To this end, a lot of effort has been put in the

area of modelling and identification. The results show that the

model is basically validated now and thus ready to be used for

the aforementioned purposes. The remainder of the paper is

structured as follows. In the next section, a detailed description

of the HTWG Konstanz water robot CaRoLIME is given.

Then, after a brief review of related work, the mathematical

model of the robot is introduced. The parameter identificationprocess is described in detail in section V, and the results are

discussed hereafter. The paper concludes with a summary and

a perspective on future working directions.

II . THE USV CAROLIME

CaRoLIME is a twin-hull USV (autonomous service craft)

for rivers and inland waters and has been set up based on

a small commercially off-the-shelf recreational vessel. Thus,

Fig. 1. Autonomous surface vehicle CaRoLIME on Lake Constance

978-1-4673-5508-7/13/$31.00 ©2013 IEEE 121

7/26/2019 06669892


the shape of the hulls had to be taken as is. The propulsion

is achieved by using electric trolling motors in a differential

setup, see Fig. 1. IMU sensing devices comprise of three mutu-

ally perpendicular mounted automotive grade accelerometers

and gyroscopes. Thus, acceleration in 3 degrees of freedom

and turning rates around yaw, pitch and roll angles can bemeasured. Further, a u-Blox LEA 6T GPS receiver and a

compass module pni V2xe are utilized. The navigation state

is based on a strap-down solution utilizing an Error State

Kalman Filter [1]. The software for controls and navigation

is distributed among various computers having an Ethernet

communication backbone. The sensors are connected to the

electric control units via serial interfaces, such as CAN, USB,

SPI, and RS232. Thus, a fairly complex distributed control

system is set up. Unification of the various protocols and

integration into one processor board is ongoing and obviously

desired for robustness and mandatory for commercial use.

III . RELATED W OR K

Here, a brief overview of related work is given mainly

subject to vessels that are of similar type like the CaRoLIME

USV. The MIT developed two twin-hull USVs (ACES [2] and

AutoCat [3]) for collecting bathymetry and hydrographic data.

The University of Rostock developed the measuring dolphin

MESSIN [4] for water monitoring. The catamaran Charlie was

developed in the SESAMO project from the CNR-ISSIA for

sampling the surface microlayer of the Antartica [5]. They

also did some modeling and identification for twin-hull USVs

with differential drive. Later they enhanced the vehicle by a

rudder-based steering system [6]. The Springer vehicle was

developed by the University of Plymouth (Plymouth, U.K.)for sensing, monitoring, and tracking of water pollution [7].

The Autonomous Systems Laboratory at the Instituto Supe-

rior de Engenharia do Porto (Porto, Portugal) developed an

autonomous catamaran ROAZ for rivers and estuarine environ-

ments. ROAZ was developed for enviromental monitoring like

bathymetry of riverbeds, estuaries, dam basins, and harbors.

Additionally, it was used as communication relay for under-

water vehicles [8]. The Instituto Superios Tecnico-Instituto de

Sistemas e Robotica (IST-ISR, Lisbon, Portugal) developed an

autonomous catamaran DELFIM for marine data acquisition

and as an acoustic relay for communication between a support

vessel and an autonomous underwater vehicle [9]. They also

carried out some work for a controlling and navigation systemfor trajectory tracking and path following [10]. Identification

and controls development for a wing-sailed catamaran was

carried out also at Standford University for the Atlantis project

TABLE I

TECHNICAL DATA

Length 2.5m

Width 1.2m

Mass 223.5kg

Additional Payload 120kg

Electric Motor Power (each) 600W

Supply Voltage Level 12

V

Fig. 2. Coordinate systems for the state variables

[11]. The Observer Kalman IDentification (OKID) method was

used for identifying a linear discrete time-invariant plant model

of fourth order. The input was generated using a human pilot

driving the system. The data obtained from the model where in

good agreement with measured data. Using this model, LQG

controlers were designed and tested with an electric trolling

motor. In [12], a simulated annealing method has been used to

identify the parameters of a fast container ship. More recently

Muske and coauthors [13] carried out maximum likelihood

estimation based identification for a small model boat. The

authors of this paper have tried to tailor their method for

the USV CaRoLIME, however, the results have not yet been

satisfactory.

IV. MODEL DERIVATION

A. Kinematic and Dynamic Equations

For modeling the approach developed by Fossen has been

utilized and is summarized briefly. The equation of motion for

a vessel is generally given by [14]

M ν + C (ν )ν + D(ν )ν = τ c (1)

For our USV roll, pitch and heave have only little influence

on the maneuver dynamics and are neglected here. Thus, the

velocity vector ν comprises of three states, surge, sway and

yaw angular rate as ν =

u v rT

. These quantities are

expressed in the body frame. A sketch of the used coordinate

system is provided in Fig. 2. τ c is the control input vector

providing forces in x, y directions as well as torque with re-

spect to yaw axis as τ c =

X Y N T

. In the literature, the

structures of the mass matrix M and Coriolis and centrifugal

matrix C are given as

M =

m − X u 0 0

0 m − Y v mxg − Y r0 mxg − N v J zz − N r

(2)

122

7/26/2019 06669892


C =

0 −mr −mxgr + Y vv + γ

mr 0 −X uumxgr − Y vv − γr X uu 0

(3)

with γ = Y r + N v

2

The elements of matrices M and C contain the mass m,the moment of inertia J zz subject upright to the z-axis, xg

the x-coordinate of the center of gavity of the vessel in body

fixed coordiantes and five added mass coefficients. For a more

detailed description of the elements of the matrices please see

[14]. The damping matrix D is chosen as follows

D=−

X u + X |u|u|u| 0 0

0 Y v + Y |v|v|v| 00 0 N r + N |r|r|r|

(4)

with the linear drag coefficients X u, Y v, N r and the quadratic

drag coefficients X |u|u, Y |v|v and N |r|r.

B. Propeller ModelThe propellers can be controlled separately with an under-

laying control loop for the rotational speed of each propeller.

The dynamic of this underlaying control loop is much faster

compared to the other dynamics and is thus neglected. The

thrust force F can be expressed according to [15] by

F = K T ρ d4 p n |n|, (5)

with n the rotational speed, d p the diameter of the propeller,

and ρ the water density. K T is the nondimensional thrust

coefficient depending on the advance ratio J , given by

J = ua

n d p

. (6)

Here, ua is the inflow velocity of the propeller. This relation-

ship is usually highly nonlinear and is determined by open

water tests and approximated by complex series [16]. Based

on a typical propeller open water diagram, an almost linear

relationship between K T and J can be assumed, if n and

ua have the same sign. Therefore, a simplified expression

containing the parameters c1 and c2 can be derived [15].

K T = c1 − c2J (7)

Putting (6) and (7) into (5), F is obtained as

F = c1 ρ d4 p n |n| − c2 ρ d3 p ua |n|. (8)

For different operating maneuvers of an USV, the values of nand ua can change sign. Accordingly, c1 and c2 have different

values in different regimes. Thus, a four-quadrant model is

assumed as

c1c2

=

a1 b1

T n ≥ 0 ∧ ua ≥ 0

a1 0T

n ≥ 0 ∧ ua < 0a2 0

T n < 0 ∧ ua ≥ 0

a2 b2T

n < 0 ∧ ua < 0

. (9)

The four-quadrant model contains the constant parameters a1,

a2, b1 and b2. For the case n and ua have different signs, c2 is

set to zero. This simplification is done based on the assumption

that J is small in this modes compared to the other modes.

C. Propulsion

The propulsion concept in use is set up differentially with

two propellers, ref. to Fig. 2. The inflow velocity ua might

be different for the two propellers, particularly, if the robot

changes its orientation. This has to be considered when

calculating the control input τ c. Knowing the distance l, ref. toFig. 2, the inflow velocity for the starboard propeller (uaport )

and portside propeller (uastar ) are given by

uaport = u − l

2r and uastar = u +

l

2r

Thus, one has to calculate the thrust F port and F star of the

two propellers independently and finally get the input vector

as follows

τ c =

F star + F port 0 (F star − F port) l2

T (10)

V. IDENTIFICATION

By inspection of (2), (3), (4) as well as (9), it is found that

a number of 18 parameters have to be provided for the model.

14 parameters are used in relation to the ship dynamics and 4reflecting the actuator forces. Assuming m, J zz and xg to be

known, the parameter vector to be identified is obtained as

θ = (θ1,θ2)T (11)

with

θ1 = (X u, Y v, N r, Y r, N v, X u, Y v, N r, X |u|u, Y |v|v, N |r|r)

θ2 = (a1, a2, b1, b2).

A. Least Square Estimation

For identification, an off-line procedure has been used. Sincethe actual propeller speed is not measurable in our setup, it has

been estimated for each motor based on electrical current and

voltage measurements. The model (1) has been implemented

in Matlab/Simulink and stimulated by the estimated propeller

speed. For the actual identification process measurement data

of surge, sway and yaw angular rate are needed. The resulting

trajectories of a simulation then are compared to the measured

values by an error function

ek = ν sim(tk,ν m(0), τ c(tk), θ) − ν m(tk)

Here tk ∈ [0, tn] is the discretized time, ν sim(tk) the

simulated velocity in body fixed coordinates from (1) and

ν m(tk) is the vector of measurements. For integration (1), the

initial values have been chosen to coincide with the values,

the measurements start with. Following [13] the cost function

J = 1

N

N k=1

eT kQ−1ek (12)

provides the combined weighted mean error subject to the

three signals in ν . N = tn/∆T is the number of data samples

in the measured and simulated signals, with ∆T the sampling

time. The errors of the components are weighted by the inverse

of the respective variance of the measurement error. Thus,

Q = diag(σ2

u, σ2

v , σ2

r)

123

7/26/2019 06669892


with σu = 0.05m/s, σv = 0.05m/s and σr = 1◦/s the

estimated standard deviations of the measurement errors of

surge, sway, angular rate respectively. These values have been

left constant during all trials. Note, that the high standard

deviation of the yaw rate measurement is not subject to sensing

inaccuracy but in order to reflect the disturbances imposed bywave motions.

Due to the large amount of parameters and the nonlinear

system dynamics, for identification a multi-step approach has

been used. First, the damping coefficients in surge direction are

determined via a coast down experiment. For this approach,

no other parameters, in particular no propeller parameters, are

needed. Using the obtained parameters and keeping the robot

fixated, the propeller parameters can be identified by a drag ex-

periment. In a last step, the remaining parameters are obtained

with data collected from zigzag and spiral maneuvres. The

complexity of the optimization problem requires also a solver

that is derivative-free and able to handle local minima. Best

results have been achieved using a particle swarm algorithm[17]. The Matlab implementation provided by Brecht Donckles

[18] has been found to work well for our purpose.

B. Identification of Surge Dynamics

Presuming an almost straight line motion, i.e. neglecting

sway and yaw rate, (1) simplifies to

(m − X u)u − X uu − X |u|u|u|u = X (13)

Since at this point in the identification process the propeller

parameters are not available, that would be necessary to

calculate τ cx, the following run-off experiment is utilized.

First, the robot is accelerated up to maximum speed, then

the propelling force τ cx is set to zero. Thus, deceleration

is caused by damping only. Using a simplifying assumption

from literature where the relation X u = −0.05m is commonly

used [14], the remaining unknown parameters are the damping

coefficients X u and X |u|u. Fig. 3 shows the result of the run-

off experiment for both measured and simulated data after the

estimation procedure. The data are in good agreement and

Fig. 3. Measured and simulated surge velocity during the run-off experiment.

The root mean square error (RMSE) was 0.02

m

s .

thus, the coefficients have been used during the remainder of

the identification process.

C. Identification of the Propeller Parameters

In order to get accurate estimates of the propeller parameters

a1, a2, b1, b2 in (9) the thrust force is measured while the robot

is tied to a poller. Thus, the inflow velocity ua is guaranteed

to be zero by design. Equation (9) indicates that both, pos-

itive and negative angular propeller rates are necessary. The

experiments were carried out at various propeller speed levels.

Determining a1 and a2 therefore is straightforward. To get the

remaining coefficients b1, b2 straight line motion with different

propeller rates have been performed. However, b2 is hard to es-

timate, since the robot becomes yaw instable during backward

driving. Thus, as an intermediate work around the assumption

b2 = b1 is made. Fig. 4 shows a comparison of measured

and simulated data after tuning the parameters. Again, a very

good agreement between measurements and simulation can beshown. However, the accuracy of the estimated parameter b2has not been determined yet, since no adequate maneuvres

have been carried out so far. This requires more tests, e.g.

braking maneuvres.

Fig. 4. Measured and simulated surge during straight line motion. Theobtained RMSE was 0.04m

s .

D. Identification of the Steering Dynamics

For identification of the remaining parameters, it would have

been desirable to generate motion patterns for the robot that

provide independent motion in sway and yaw rate. This would

force certain terms in the righthand side in (1) being zero

and an estimate of the active parameters would become more

straightforward. With the differential propulsion system used

so far, this is not feasible since rotation around the z-axis

without having sway velocity cannot be achieved. Therefore,

two motion patterns, zigzag- and spiral-maneuvre that have

coupled sway velocity and yaw rate have been performed.

These maneuvres are complementary, since during the zigzag-

maneuvres, components of ν are continuously changing, while

during the spiral maneuvre, the components of the velocity

vector remain constant most of the time. The errors between

simulated and measured data of both maneuvres have been

124

7/26/2019 06669892


Fig. 5. Propeller speed during zigzag maneuvre

combined by normalized summation. Therefore, the cost func-

tion becomes

J = 1

N 1

N 1k=1

eT 1kQ

−1e1k + 1

N 2

N 2k=1

eT 2kQ

−1e2k. (14)

As before, the particle swarm approach has been used to esti-

mate the remaining parameters of the model by minimization

of (14). The zigzag maneuvre is performed by swapping the

propeller speed values as soon as a change in orientation of

±20 degrees is reached. Figure 5 shows the propeller speed

associated with this maneuvre. From Fig. 6 it can be seen that

both measurements and simulated velocity trajectories are in

good agreement.

Fig. 6. Comparison of body fix velocities and yaw rate during zigzag

maneuvre (Surge RMSE 0.04ms , Sway RMSE 0.04ms , Yawrate RMSE 1.25◦

s )

The spiral maneuvre is executed by applying the propeller

speeds as shown in Fig. 7. Here, the maneuvre is started

with a narrow turning radius that is gradually increased up

to a straight line, followed by gradually turning in the other

direction. Again, the model is reflecting the vehicle dynamics

very well as can be seen from Fig. 8. Due to the fact that

for identifying the parameters, data from two significantly

Fig. 7. Propeller speed during spiral maneuvre

Fig. 8. Comparison of body fix velocities and yaw rate during spiral

maneuvre (Surge RMSE 0.05 ms , Sway RMSE 0.05ms , Yawrate RMSE 0.64

◦

s )

different maneuvres has been used, an overfitting is very

unlikely. In Fig. 9 the convergence of the parameters is shown.

As can be seen, after about 1000 iterations, the parameters

have reached their stationary values. Here, the values for the

best particle in each iteration are shown.

V I. DISCUSSION

The presented data show very promising results towards

the goal of having a reliable process for identification of

hydrodynamic coefficients established. It is important that no

additional manual tuning was necessary after the solution

for the coefficients of the optimization process was obtained.

Thus, an automatic setup seems to be feasible. It is worthwhile

mentioning that only few and simple maneuvres are required

which are not even overly exciting and thus wearing the

system, to evoke sufficient information regarding the vessel

dynamics in the measurement data. Technically, the particle

swarm method has been shown to be very reliable in finding a

minimum that provides a decent match between measurement

and simulation data. From the values of the coefficients shown

in Tab. II, the cross terms Y r and N v attract attention. They

125

7/26/2019 06669892


Fig. 9. Evolution of parameters during the optimization process

TABLE II

ESTIMATED PARAMETER VALUES AFTER IDENTIFICATION

X u Y v N r Y r N v−11.2kg −68.1kg −148.8kgm2 −172.2kgm −226.8kgm

X u Y v N r X |u|u Y |v|v−9.6Ns/m −132.24Ns/m −65.6Nms/rad −22.3Ns2/m2 0

N |r|r a1 a2 b1 b2

−56.6Nms2/rad2 0.0608 0.0241 0.142 0.142

seem to be rather large in comparison to the diagonal terms as

well as in comparison to data from the literature. The latter,

however, were obtained for large vessels. This issue will need

further attention in order to either find a physical explanation

or discard those values.

VII. CONCLUSION

In this paper, it has been shown how to obtain the hy-

drodynamic coefficients for a mathematical model of a slow

moving USV by using carefully designed experiments in

combination with a powerful optimization tool. These early

results suggest that a decent work flow is already established,

and the setup will therefore be adapted to other vessels, e.g.

the solar boat Korona of HTWG Konstanz. In regard to the

identification process, it has been observed that measuring

sway velocities are subject to some difficulties since usually

those values are small and in the range of the resolution of the

navigation solution. Thus, as a next step, the values obtainedhere could be regarded as an initial solution and then be further

improved by using a combined state observer - parameter

estimation approach, using e.g. the unscented Kalman Filter

or an expectation maximization approach. Furthermore, the

model is currently integrated into a HIL setup, and control

strategies based on this model are under development as well.

REFERENCES

[1] J. Wendel, Integrierte Navigationssysteme, 2nd ed. Oldenbourg Verlag,2011.

[2] J. E. Manley, “Development of the autonomous surface craft ACES,”OCEANS’97. MTS/IEEE Conference Proceedings, vol. 2, pp. 827–832,

1997.

[3] J. E. Manley, A. Marsh, W. Cornforth, and C. Wiseman, “Evolutionof the autonomous surface craft AutoCat,” Oceans 2000 MTS/ . . . , pp.403–408, 2000.

[4] T. Buch, C. Korte, and J. Majohr, “Navigation and automatic Controlof the Measuring Dolphin (MESSIN),” in Proc. 5th IFAC Conferenceon Manoeuvring and Control of Marine Crafts, Aalbourg, Denmark,August 2000, pp. 405–410.

[5] M. Caccia, R. Bono, G. Bruzzone, G. Bruzzone, E. Spirandelli,G. Veruggio, A. M. Stortini, and G. Capodaglio, “Sampling Sea Surfaceswith SESAMO,” Robotics & Automation Magazine, 2005.

[6] M. Caccia, G. Bruzzone, and R. Bono, “A Practical Approach toModeling and Identification of Small Autonomous Surface Craft,” IEEE

Journal of Oceanic Engineering, vol. 33, no. 2, pp. 133–145, Apr. 2008.[7] W. Naeem, R. Sutton, and J. Chudley, “Modelling and control of an

unmanned surface vehicle for environmental monitoring,” in UKACC International Control Conference, Glasgow, Scotland, August 2006.

[8] H. Ferreira, R. Martins, E. Marques, and J. Pinto, “Marine Operationswith the SWORDFISH Autonomous Surface Vehicle,” Power , no. May,2006.

[9] A. Pascoal, P. Oliveira, C. Silvestre, L. Sebastiao, M. Rufino, V. Barroso,J. Gomes, G. Ayela, P. Coince, M. Cardew, A. Ryan, H. Braithwaite,N. Cardew, J. Trepte, N. Seube, J. Champeau, P. Dhaussy, V. Sauce,R. Moitie, R. Santos, F. Cardigos, M. Brussieux, and P. Dando, “Roboticocean vehicles for marine science applications: the european asimov

project,” in OCEANS 2000 MTS/IEEE Conference and Exhibition, vol. 1,2000, pp. 409–415 vol.1.

[10] J. Alves, P. Oliveira, R. Oliveira, A. Pascoal, M. Rufino, L. Sebastiao,and C. Silvestre, “Vehicle and mission control of the delfim autonomoussurface craft,” in Control and Automation, 2006. MED ’06. 14th Mediter-ranean Conference on, 2006, pp. 1 – 6.

[11] G. H. Elkaim, “System Identification for Precision Control of a Wing-Sailed GPS-Guided Catamaran,” Ph.D. dissertation, Stanford University,Stanford, CA, 2001.

[12] A. Tiano and M. Blanke, “Multivariable identification of ship steeringand roll motions,” Transactions of the Institute of Measurement and Control, vol. 19, no. 2, pp. 19–63, April 1997.

[13] K. Muske, H. Ashrafiuon, G. Haas, R. McCloskey, and T. Flynn,“Identification of a control oriented nonlinear dynamic usv model,” in

American Control Conference, 2008 , 2008, pp. 562–567.[14] T. I. Fossen, Guidance and Control of Ocean Vehicles. Wiley, 1994.

[15] M. Blanke, “Ship Propulsion Losses Related to Automated Steeringand Prime Mover Control,” Ph.D. dissertation, Technical University of Denmark, Lyngby, Denmark, 1981.

[16] J. Carlton, Marine Propellers and Propulsion. Elsevier Science, 2011.[17] J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Neural

Networks, 1995. Proceedings., IEEE International Conference on, vol. 4,Nov/Dec, pp. 1942–1948 vol.4.

[18] Donckle, B, “Particle swarm optimization,” Oktober 2012. [Online].Available: http://biomath.ugent.be/ ∼brecht/downloads.html

126

06669892

Documents