The Atlantis Project: A GPS-Guided Wing-Sailed ...elkaim/Documents/elkaim...The Atlantis Project: A GPS-Guided Wing-Sailed Autonomous Catamaran GABRIEL HUGH ELKAIM Autonomous Systems

The Atlantis Project: A GPS-GuidedWing-Sailed Autonomous Catamaran

GABRIEL HUGH ELKAIMAutonomous Systems Lab, Computer Engineering, University of California, Santa Cruz,

Santa Cruz, CA 95064 USA

Received September 2006; Revised January 2007

ABSTRACT: An autonomous catamaran, based on a modified Prindle-19 day-sailing Catamaran, was built totest the viability of GPS-based system identification for precision control. The catamaran was fitted with severalsensors and actuators to characterize the dynamics. Using an electric trolling motor, and lead ballast to matchall-up weight, several system identification passes were performed to excite system modes and model thedynamic response. LQG controllers were designed based on the results of the system identification passes, andtested with the electric trolling motor. Line following performance was excellent, with cross track error standarddeviations of less than 0.15 meters. The wing-sail propulsion system was fitted, and the controllers tested withthe wing providing all forward thrust. Line following performance and disturbance rejection were excellent,with the cross track error standard deviations of approximately 0.30 meters, in spite of wind speed variations ofover 50% of nominal value.

INTRODUCTION

This paper details the progress of the Atlantisproject, pictured in Figure 1, which began with theconception of an unmanned, autonomous, GPS-guided, wing-sail-propelled sailboat. The Atlantisproject has been very much a ‘‘systems’’ approach,with substantial innovations in the areas of wind-propulsion, overall system architecture, sensors,system identification and control.

Functionally, the Atlantis is the marine equiva-lent of an unmanned aerial vehicle, and wouldserve similar purposes. The Atlantis project hasbeen able to demonstrate an advance in controlprecision of a wind-propelled marine vehicle fromtypical commercial autopilot accuracy of 100 metersto an accuracy of better than one meter. This quan-titative improvement enables new applications,including unmanned station-keeping for navigationor communication purposes, autonomous ‘‘dock-to-dock’’ capabilities, emergency ‘‘return unmanned’’functions, and many others still to be developed.

The wind-propulsion system is a rigid wing-sailmounted vertically on bearings to allow free rota-tion in azimuth about a stub-mast. Aerodynamictorque about the stub-mast is trimmed using a fly-ing tail mounted on booms joined to the wing. Thisarrangement allows the wing-sail to automatically

attain the optimum angle to the wind, and weathervane into gusts without inducing large heelingmoments. Modern airfoil design allows for anincreased lift-drag (L/D) ratio over a conventionalsail, thus providing increased thrust while reduc-ing the overturning moment.

The system architecture is based on distributedsensing and actuation, with a high-speed digitalserial bus connecting the various modules together.Sensors are sampled at 100 Hz, and a central guid-ance navigation and control (GNC) computer per-forms the estimation and control tasks at 5 Hz.This bandwidth has been demonstrated to be capa-ble of precise control of the catamaran. The distrib-uted architecture is both more robust and less ex-pensive than systems that employ a high-speed,and often analog, star-configuration topology withcentralized sensor interpretation and actuation.

The sensor system uses differential GPS (DGPS)for position and velocity measurements, augmentedby a low-cost attitude system based on accelerome-ter- and magnetometer-triads. Accurate attitudedetermination is required to create a synthetic posi-tion sensor that is located at the center-of-gravity(CG) of the boat, rather than at the GPS antennalocation.

Experimental trials recorded sensor and actuatordata intended to excite all system modes. A systemmodel was assembled using Observer/KalmanSystem Identification (OKID) techniques. An LQGcontroller was designed using the OKID model,

NAVIGATION: Journal of The Institute of NavigationVol. 53, No. 4, Winter 2006Printed in the U.S.A.

237

using an estimator based on the observed noisestatistics. Experimental tests were run to sail on aprecise track through the water, in the presence ofcurrents, wind and waves.

SYSTEM DESCRIPTION

In order to experimentally validate the conceptspresented in this research, a prototype system wasbuilt based on a heavily modified Prindle-19, day-sailing catamaran. The catamaran was 7.2 m long,3 m wide, and was originally equipped with a slooprig sail with 17 m2 of sail area. Directional controlis based on rudders at the end of each hull, andretractable centerboards approximately 1

2 m behindthe main crossbeam. Several sensors and actuatorswere installed within the hulls, and the entire sail-ing system (mast, boom, main and jib sails) wasreplaced with a vertical self-trimming wing (wing-sail) suspended on spherical roller bearings.

There are several main subsystems on theAtlantis, and all of them are connected to eachother via a high-speed serial network. The networkutilized is the Controller Area Network (CAN) bus,which was designed by Bosch electronics for robustcomponent communication in an automotive envi-ronment [1]. The entire wiring bus on the Atlantisconsists of four (4) wires: power (þ12V), ground,CAN_hi, and CAN_low. There are many advan-tages to this setup, but the ease of troubleshootingand flexibility of physical topology are at the fore-front of utility in this design.

Figure 2 shows the system as it ties togetherlogically and electrically on the CAN bus. Themain subsystems are: attitude system, anemome-ter, hullspeed, rudder angle, rudder actuator, GPS

receiver, and wing-sail. These subsystems commu-nicate to the main GNC computer that computesthe current estimate of the state, and returns therequired commands to the actuator in order toachieve control.

The attitude system, pictured in Figures 3 and 4,consists of a three-axis magnetometer, a two-axisaccelerometer, and a Siemens 515 microcontroller.It functions based on a novel gyro-free quaternionbased solution to the vector matching problem firstproposed by Whaba in 1966 [2]. The algorithm isdiscussed extensively in [3, 4, 5]. The attitude sys-tem is mounted alongside the Global PositioningSystem (GPS) antenna, inside a waterproof Pelicanbox on a wooden crossbeam at the forward staylocation (note that the wooden crossbeam wasadded for increased structural rigidity of the hulls,due to the stresses induced by the wing).

The GNC computer, shown in Figure 5, a Pentiumclass laptop, is placed in another waterproof case,

Fig. 1–The Atlantis, based on a Prindle-19 Catamaran, with aself-trimming wingsail. The Atlantis was designed to demon-strate a very high precision of navigation and control, evenin the presence of wind and waves. As shown here, testing inRedwood City harbor, January 2001, the Atlantis was able toachieve line following to better than 30 cm. 1�s under windpropulsion. The author and colleagues on board are humanballast to prevent capsizing during this initial test.

Fig. 2–Block diagram of the major subsystems of the Atlantis.Note that both power and CAN signals go through a slip ring atthe top of the stub mast in order to electrically connect the rotat-ing wing to the rest of the system.

Fig. 3–The Atlantis uses a low-cost attitude solution that isbased on a quaternion solution to Wahba’s problem, where thetwo observed vectors are Earth’s gravitation and magnetic fields.The solution produces 100 Hz. attitude data and is based onan Analog Devices 2-axis accelerometer and Honeywell 3-axismagnetometer.

238 Navigation Winter 2006

along with the Trimble Ag122 GPS receiver. TheGNC computer is equipped with an ESD parallelport dongle that allows communication over theCAN bus. A DC/DC converter insures that thelaptop draws power from the boat power busrather than its own internal batteries.

Inside the starboard hull, beneath the rearinspection cover, are two Infineon 505 microcon-trollers, one for the hullspeed and rudder anglesensor, and the other for the rudder actuator,pictured in Figure 6. There is a Standard Commu-nications Electronics marine through-hull speedsensor, pictured in Figure 7, in the bottom is thestarboard hull, and a LoHet magnetic field effectsensor between two magnets on the rudder hingeline to measure rudder angle. The actuator is afractional horsepower DC motor, with a lead screwassembly, constrained to rotate only in yaw, andan Infineon H-bridge mosfet drive for electroniccontrol of the motor.

Inside the stub-mast, a Mercotac slip ring allowsfor a full 360 degree rotation without twisting thefour wires that comprise the wiring harness ofthe Atlantis. The wing itself is built in three sectionsthat are assembled on site. The lower section con-tains an electronics pod with the batteries, ballast,and battery-charging electronics. A microcontrollerand DC motor are used to control the trailing edgeflap. It also contains the anemometer microcontrol-ler, with the Standard Communications Electronicsmarine transducer head, pictured in Figure 8,attached to the top of the electronics pod lid.

Within the wing are four actuators that areidentical to the rudder actuator, which actuate the

Fig. 4–A close-up of the low-cost attitude solution used on theAtlantis, and pictured in Figure 3. The ruler is there for scale,and shows that the entire board is less than 6 inches long and 4inches across. The microcontroller is an Infineon 515 processor,and the attitude is being relayed on the CAN bus.

Fig. 5–Guidance, Navigation, and Control computer box, withthe Trimble Ag122 DGPS Receiver, A Pentium Class laptop, andDC-DC converter to power the laptop, and an ESD Parallel portCAN dongle. The entire box is sealed and has water-tight con-nections for Power, CAN, and the RF signal from the GPSantenna.

Fig. 6–Rudder actuator is made from a Pittman 24V DC Motorturning a lead-screw. The motor has a 512 line per revolutionquadrature phase encoder attached, and is directly attachedto the lead screw. With this arrangement, a slew-rate of over20 degrees per second was achieved.

Vol. 53, No. 4 Elkaim: The Atlantis Project: A GPS-Guided 239

trailing edge flaps and the tail. The momentbalance between the wing and the tail keeps thewing-sail at a constant angle of attack relative tothe wind. As long as the wind does not cross thecenterline of the boat, then the wing continues toprovide thrust in the correct direction for forwardmotion through passive stability of the wing-sailsystem. Should the wind cross through the center-line of the boat, then the position of the flap andtails must be reversed, which corresponds to tackingor jibing depending on whether the wind crosses thecenterline facing aft or forward, respectively.

The anemometer is used to measure the windspeed and direction relative to the angle of thewing-sail. Essentially, this is a measure of angle ofattack of the wing.

SYSTEM IDENTIFICATION METHODOLOGY

In order to control the Atlantis, a system modelneeded to be assembled. While several good model-ing techniques exist to model a powered boatthrough the water [6], they remain complicatedand difficult to calculate. In order to reduce themodel order, and obtain a model that would havesufficient fidelity for active control, several differ-ent methodologies were attempted. In order toformulate the equations of motion, the Atlantis isassumed to be traveling upon a straight line,conveniently assumed to be coincident with theX-axis, through the water at a constant velocity,Vx. The distance along that line is referred to asX, the along track distance. The perpendiculardistance to the line is referred to as Y, the crosstrack error, and the angle that the centerline ofthe Atlantis makes with respect to the desiredpath is defined as C, the angular error. Figure 9illustrates the mathematical model of the assumedpath of the Atlantis.

This first pass model is a simple kinematicmodel that assumes that the rudders cannot movesideways through the water. This places a kine-matic constraint upon the motion of the entire boat,and the linearized analysis produces the followingcontinuous time state-space equations:

Ywd

24

35

�

¼0 Vx 00 0 Vx

L0 0 0

24

35 Y

wd

24

35þ 0

01

2435u (1)

Fig. 7–Hullspeed sensor is located towards the rear of thestarboard hull, and is made by the Standard CommunicationsElectronics Corporation. Due to its location behind the center-board of the hull, the signal is quite noisy from the turbulence.

Fig. 8–A 3-cup annemometer is used to determine wind speedand direction. The unit is made by Standard CommunicationsElectronics, and has a two-pulse per revolution output forthe cups, and a quadrature analog signal for the direction ofthe weathervane. It was calibrated in a wind tunnel.

Fig. 9–The basic equations of motion for the Atlantis on thewater. A simplified model is used as a basis for understandingthe vehicle motion. Velocity is along the X-axis, with crosstrack error being measured in the Y-axis. The heading error ismeasured from the X-axis to the centerline, and defined as C.


Where Y, w, and d are defined as the cross trackerror, azimuth error, and rudder angle, and L isthe length from the C.G. of the boat to thecenter of pressure of the rudders. Note thatthese simplified equations of motion are insuffi-cient to control the boat to great precision, butare excellent for generating intuition for the sys-tem identification process. Equation 1, when castinto transfer function form, becomes a triple inte-grator, and cannot be stabilized by simple pro-portional control. In addition, the assumption ofconstant Vx is poor, since unless the wind can becontrolled, the velocity will always be dependenton the speed of the wind. Closer inspection ofEquation 1 shows that the errors in azimuth andcross track integrate not with time, but ratherwith distance traveled forward. What this meansis that if the boat is sitting still in the water, noamount of rudder deflection will cause the azi-muth to change. Likewise, when moving veryquickly through the water, only very small inputsare required to turn the boat through a consider-able angle.

Thus, recharacterizing the variables of interest,to make the system velocity invariant, both theazimuth and cross track error are normalizedby velocity. The new variables of interest become yand ~w, with d remaining the same as previouslydefined. The new simplified equations of motionbecome:

~Y~wd

24

35

�

¼0 1 00 0 1

L0 0 0

24

35 ~Y

~wd

24

35þ 0

01

2435u (2)

where

~Y ¼ Y

Vx

~W ¼ WVx

(3)

Note that this causes the state transition matrix tobe constant. This concept of velocity invariance hasbeen tested extensively on GPS-controlled farmtractors [7], and shown to work very well. Func-tionally, this means that controller design isreduced to a single (non-gain-scheduled) controllerthat automatically adjusts for the changing velo-city based on decreasing input ranges as velocityincreases.

In order to gather data to perform a proper sys-tem identification of the Atlantis, a series of open-loop line-following tests were conducted in which ahuman driver, through the Guidance, Navigation,and Control (GNC) computer, caused the ruddersto either slew left or right at the maximum slewrate (25 degrees/s). Also, the driver commanded

the rudder slew rate to zero through the rudderactuator in order to track a roughly straight line.This ‘‘pseudo’’-random input was designed to applythe maximum power to the Atlantis through thecontrols and produce a rich output that wouldcontain information from all modes of interest. Atypical pass for system identification is pictured inFigure 10.

Once the System Identification process is com-pleted (and a state space representation of thesystem has been generated), a controller wasdesigned using a standard Linear QuadraticRegulator (LQR) methodology. The quadratic cost,as calculated below in Equation 4, minimizes theweighted sum of the outputs ( ymax and umax aredesign parameters).

J ¼X1k¼0

~xTk CT

1y2

max0 0

0 0 00 0 0

24

35C~xk þ~uT

k

1

u2max

� �~uk

0@

1A (4)

Note that the quantity ~xTk CT is nothing more than

yT which is [y w d]T. In other words, the cost that isbeing minimized by the LQR controller is theweighted sum of the square of the crosstrack errorand the input (rudder rate). This controller placesno penalty on either heading error or rudder angle;it only tries to reduce crosstrack error.

In terms of system identification, this becomesuseful as the inputs are scaled by velocity beforebeing assembled into the system identificationalgorithm. Thus, the identified system is onethat is the best model for the velocity invariantcontrol.

The system identification methodology used forthis work is the Observer Kalman IDentification

Fig. 10–A typical system identification pass. The input rudderangle slew rate, u, was input by a human driver attempting tokeep the Atlantis on a roughly straight line. Note that this passis over 700 meters long.


(OKID) [8]. Among its many advantages is aformulation that presumes a discrete-time, linearsystem. Since OKID’s development at NASA Lang-ley for the identification of lightly-damped space-structures, many advances on the basic theoryhave been published [9]. The following discussionis a summary of the OKID algorithm, and ispresented here for completeness.

Given a generic linear discrete-time state-spacesystem, the equations of motion can be written asfollows:

~xkþ1 ¼ A~xk þ B~uk

~yk ¼ C~xk þD~uk

(5)

Note that in the case of the Atlantis, ~uk isthe rudder slew rate, _d, and ~yk is, as before,[y w d]T. That is, the OKID will generate aset of [A, B, C, D] matrices that match theinput and output data.

It has been shown that the triplet, [A, B, C] isnot unique, but can be transformed through anysimilarity transform (i.e., the outputs are unique,but the internal states are not). However, thesystem response from rest when perturbed by aunit pulse input, known as the system Markovparameters, is invariant under similarity trans-forms. That is, for an initial condition of ~x0 ¼ 0, andfor the input ~u0 ¼ 1 and ~uk ¼ 0 for all k > 0, the sys-tem response is:

Y0 ¼ Du0

Y1 ¼ CBu0

Y2 ¼ CABu0

Y3 ¼ CA2Bu0

..

.

Yk ¼ CAk�1Bu0

(6)

These Markov parameters, [Y0 Y1 � � � Yk], are clearlyunchanged by any similarity transform, and arethus a unique representation of a linear time invari-ant system.

When these Markov parameters are assembledinto a specific form – the generalized Hankelmatrix of Equation 7 – this matrix can be decom-posed into the Observability matrix, a state tra-nsition matrix, and the Controllability matrix(Equation 8); thus the Hankel matrix (in a noise-free case) will always have rank n, where n is thesystem order.

Hðk� 1Þ

¼

C

CA

CA2

..

.

CAa�1

26666664

37777775

Ak�1 B AB A2B � � � Ab�1B� �

ð8Þ

Hðk� 1Þ ¼ CAk�1O ð9Þ

That is, regardless of how far out one takes theHankel matrix (via parameters a and b), the rankof the Hankel matrix is always n, due to the factthat Controllability (C) and Observability (O) mat-rices can be at most of Rank n.

<ðCÞ � n ð10Þ

<ðOÞ � n ð11Þ

<ðHðk� 1ÞÞ � n ð12Þ

Because noise will corrupt the rank deficiency ofthe Hankel matrix (that is, for real noisy data,the Hankel matrix will always be full rank) theHankel matrix is truncated using a singular valuedecomposition (SVD) at an order that sufficientlydescribes the system. This truncated Hankel ma-trix is then used to reconstruct the triplet [A, B, C]in a balanced realization that ensures that thecontrollability and observability Grammians areequal. This is referred to as the Eigensystem Real-ization Algorithm (ERA); a modified version of thisalgorithm that includes data correlation is used toidentify the Atlantis. A more complete treatmentof the subject can be found in [10].

For any real system, however, system pulseresponse cannot be obtained by simply perturbingthe system with a pulse input. A pulse with enoughpower to excite all modes would likely saturatethe actuator or respond in a non-linear fashion.The pulse response of the system can, however, bereconstructed from a continuous stream of rich sys-tem input and output behavior. To see this, therecursion from Equation 5 is carried out (assumingfor simplicity that the initial state, ~x0, is 0):

Hðk� 1Þ ¼

Yk Ykþ1 � � � Ykþb�1

Ykþ1 Ykþ2 � � � Ykþb

..

. ... . .

. ...

Ykþa�1 Ykþa � � � Ykþaþb�2

26664

37775 (7)

y0 ¼ Du0

y1 ¼ CBu0 þDu1

y2 ¼ CABu0 þ CBu1 þDu2

y3 ¼ CA2Bu0 þ CABu1 þ CBu2 þDu3

..

.

yk ¼ CAk�1Bu0 þ CAk�2Bu1 þ � � � þ CABuk�2

þ CBuk�1 þDuk ð13Þ


These equations can be gathered into a matrixform (note that the OKID method is general formultiple input multiple output systems, which isto say that both Yk and uk can be vectors). Thesegathered equations result in a topelitz matrixform:

yk

..

.

y2

y1

y0

266666664

377777775¼

D CB CAB � � � CAk�1B

. .. . .

. . .. ..

.

D CB CAB

D CB

D

266666664

377777775

uk

..

.

u2

u1

u0

266666664

377777775ð14Þ

Note that the entries of this matrix are nothingother than the system Markov parameters, in anupper triangular form. Under normal circumstan-ces, there are not enough equations available tosolve for all of the Markov parameters. That is,given the input stream (uk) and the outputs (yk)for some span of time (k from 0 to r), we cannotsimply solve for the [D, CB, CAB, . . . , CAkB]Markov parameters.

Examination of Equation 14 shows that if forsome k, the quantity Ak ¼ 0, then the number ofunknown Markov parameters can be greatly re-duced, or truncated. Ak ¼ 0 for some k, however, isthe definition of asymptotic stability, which is sim-ply to say that the effect of an input k steps in thepast is negligible on the current outputs. The iden-tification process would be of little value if it couldonly work with asymptotically stable systems.

By adding an observer to the linear system equa-tions, the following transformation can take place:

where:

�A ¼ AþGC½ ��B ¼ BþGD�G½ �

~vk ¼~uk

~yk

� � (16)

Thus, the system stability can be augmentedthrough an observer, which has the effect of mak-ing Ap ^ 0 for some p that is sufficiently large.With that assumption, there are enough equationsto solve for the Markov parameters establishedthrough a least-squares solution [8]. It is useful tonote that the realization also provides a pseudo-Kalman observer. The observer orthogonalizes theresiduals to time-shifted versions of both input andoutput. Utilizing the separation lemma and theprovided Kalman filter, only the controller gainsneed be designed to implement a full-state-feed-back linear quadratic gaussian (LQG) controller.An improved version of the OKID process, whichincludes residual whitening [10], was used to iden-tify the sailboat dynamics from the experimentaldata.

An SVD of the aggregate velocity-normalizeddata for the Atlantis demonstrated a large dropin the magnitude of the singular values from thefourth to the fifth, indicating a system order, n, offour (Figure 11, left). In addition, modal singularvalues (Figure 11, right) of all catamaran modelsof order higher than four exhibited a two order-of-magnitude drop from the fourth modes to modeshigher than four. System reconstruction for theidentified dynamics also matches well, showingpredictive performance that matched within 0.1 mof cross track error, within 1.5 deg of headingerror, and within 4 deg for rudder angle. Note thatthese were open loop tests, without the Kalman

Fig. 11–The plot of the Hankel singular values of the system, showing that the experimental data is best representedby a 4th order system (left), and a singular value plot of the system modes showing again a large drop after 4 modes,again indicating that the system is 4th order (right).

~xkþ1 ¼ A~xk þ B~uk þG~yk �G~yk

~xkþ1 ¼ AþGC½ �~xk þ BþGD½ �~uk �G~yk

~xkþ1 ¼ �A~xk þ �B~vk

(15)


filter added in, which improved prediction greatly.Thus, using these results, the LQG controllerwas designed, and simulations carried out tovalidate the controller performance. Once satisfiedwith these simulations, experimental trials wereperformed in order to validate the concept.

The implementation of the identified controllerand estimator is fairly straightforward. From theOKID methodology, the linear system matrices [A,B, C, D] and the estimator G are extracted. Thecontrol gain matrix, K, is extracted from the LQRdesign (with the cost function in Equation 4).Abstractly, the controller is simply a mathematicalfunction that maps (with memory), a sequenceof system outputs to a set of control inputs. In thisspecific case, the first step is to normalize thecrosstrack error and heading error by the velocity(with a lower bound of 1 m/s to prevent noiseamplification) as shown in Equation 2.

Given that this implementation includes an esti-mator, the initial estimate of the state is set to 0(note that there are several methods for attempt-ing to find a better initial estimate for the state,such as taking the pseudo-inverse of the C matrixand multiplying it by the current measured out-puts). The initial control, u, is also set to 0.

At any given time-step, the control is calculatedfrom the current state estimate:

u ¼ � K½ �x (17)

and then the estimator is propagated forward onestep in time given the current control and mea-sured system outputs:

xþ ¼ AþGC½ �x� þ BþGD½ �u� G½ �~y (18)

where xþ is the future state estimate, x� is theprevious estimate, u is the actuator command, andy is the speed normalized sensor readings.

Note that the control portion of the propagation[B þ GD] could be implicity brought into the xk

term, but in this case was not due to saturationlimits imposed by the actuator hardware.

TROLLING MOTOR TESTS

While the wing-sail was still under constructionat Cris Hawkins Consulting in Santa Rosa, thesystem identification and controller tasks hadalready been completed. At this point, in order totest out the controllers, a MinKota electric trollingmotor was used to simulate the presence of thewing-sail and wind. This was done by mountingthe trolling motor at the sailboat center of gravity(CG), and turning the trolling motor such that itsdirection of thrust was canted off the centerline bymore than 40 degrees.

Since the dynamics of the catamaran are greatlyaffected both by the velocity through the waterand the displacement weight of the hulls, theAtlantis was ballasted with an additional 75 kg oflead ballast (in the form of batteries) to bring theall-up weight of the boat to the same as the weightas it would have had with the wing-sail installed.Also, in order to test the controllers at variousspeeds, the MinKota trolling motor was run with12, 24, and 36 V at approximately 65 A. Thischanges the speed of the boat through the water,simulating changes in wind velocity. In order tosimulate changes in wing direction, the MinKotatrolling motor was turned through various angleswhile the controller was regulating the path to aline.

In Figure 12, the Atlantis with the trolling motorcan be seen. The trolling motor is at the center ofthe boat, and the lead batteries provide the ballast.As pictured, the boat was run unmanned, with theGNC computer providing all navigation, at a speedof approximately 2 m/s (4 Kn). Of note is the factthat the anemometer is located at the front woodencrossbeam. This is only a temporary location, andmoving the sensor’s physical location is very easydue to the CAN bus architecture employed on theAtlantis.

Figure 13 shows a 500 m long typical autono-mous pass while under computer control. Notethat the computer regulates the path to the line,but that the turn is performed open loop with afeed-forward command. To the scale pictured inFigure 13, the recorded position data shows verylittle cross track error. This is in spite of the factthat the currents were changing, and the windand waves were all injecting disturbances into thesystem. In Figure 14, a close look at the errorsin the first part of the path shown in Figure 13

Fig. 12–The Atlantis on an unmanned trajectory being con-trolled by the identified LQG controller. Propulsion is from aMinKota trolling motor running at 12, 24, and 36 Volts. Themotor is canted off the center line to simulate off-center thrustas would be seen by the wing-sail.


reveals that the mean was less than 3 cm, andthe standard deviation was less than 10 cm.

Of interest, the azimuth shows a �20 degreebias for most of the path length of the run picturedin Figure 13, which is due to current. This canbe verified by looking at the velocity plot atthe bottom of Figure 14, where the top line is thehull-speed sensor, and the smooth lower line isGPS velocity. The difference in these two is current,and it can be seen in spite of the high frequencynoise of the hull-speed sensor (due to the placement

behind the centerboards). By calculation, the cur-rent was 0.62 m/s at an angle of 52 deg tothe Atlantis path, coming from the port side of theboat. This is a current speed that is close to 30% ofthe actual speed of the boat, and can be consideredquite a large disturbance.

WING-SAIL TESTS

In order to validate the performance of the con-trollers and all-up system, closed loop controlexperiments were performed in Redwood CityHarbor, California, on 27 January 2001. Thesetests were intended to verify that the closed loopcontrollers were capable of precise line followingwith the increased disturbances due to the wing-sail propulsion. No modifications were made to thecontroller design, and the tests were run on a daywith approximately 12 kn (or 6 m/s) of wind, withgusts up to the 20 kn (or 10 m/s) range. For atypical pass, the velocity of the Atlantis was againapproximately 2 m/s (4 kn), or approximately 50%of the true wind speed. Note that the Atlantis wasbuilt for precision, and not for performance. Highervelocities were well within the capability of thewing, but were not attempted.

Experimental data from the anemometer showsthe angle of the wind with respect to the wing(angle of attack) to vary þ/� 20 degrees from nom-inal. This demonstrates the requirement for aself-trimming wing; without the ability to trimquickly to a new angle of attack, the wing wouldremain stalled most of the time, and the thrustgenerated would be minimal. The ability to respondquickly to a new angle of attack by rotating intothe new trim condition allows the wing to absorbthese transient gusts and continue to provide fullthrust with a reduced heeling moment.

Qualitatively, the wing-sail performed even bet-ter than anticipated. With the tail centered, therewas no tendency for the Atlantis to heel whatso-ever, and the absence of aeroelastic instability (sailluffing) made the entire event very quiet. Uponturning the trailing edge of the tail in the directionof desired travel, the Atlantis smoothly acceleratedto speed and quietly continued on her course. Evenlarge gusts simply caused the Atlantis’ wing toquickly stall and, with only a slight shudder, repo-sition to a new angle of attack (as evidenced by theyarn tufts on the wing surface).

More impressive was the ability to sail pointedvery high into the wind. Upon analyzing the data,it was demonstrated that the Atlantis was capableof sailing to within 25 deg of the true wind direc-tion. At one point, a conventional sailboat cameabout behind the Atlantis and started luffing a full15 degrees off the wind from where the Atlantiswas making headway. This is clearly a result of

Fig. 13–The trajectory as recorded by the Ag122 DifferentialGPS receiver while under computer control. Note that feedbackcontrol is only used on the straight line segments. Turns areaccomplished by open-loop feed-forward commands. To theresolution of this image, cross track errors are less than onepixel wide.

Fig. 14–Close up of the first section pictured in Figure 13, show-ing very precise control while under trolling motor propulsionand autonomous control. The mean of the path is less than3 cm., and the standard deviation is less than 10 cm. Note thatthe presence of a current is indicated by a constant headingerror (middle) as well as a mismatch between the GPS velocityand the hull speed sensors (bottom).


the improved aerodynamics of the rigid wing, anda vindication of the self-trimming arrangementover a conventional sail. While further experimen-tal studies are required to quantitatively measurethe performance increase of the wing-sail, currentresults indicate very promising discoveries ahead.

Figure 15 shows a satellite picture of the harborwhere both the trolling motor and wing-sail testswere performed. The white dots are from a previ-ous year, when the Atlantis was conventionallysailed with a sloop rig, and was sailed by a humancaptain. The black dots indicate the various closedloop control passes from the recent tests. Note thatthe white trace has a curving, ‘‘human,’’ look to it,whereas the black trace looks like a ruler wasplaced upon the photograph and a line drawn.Qualitatively, the computer control simply does notlook like a human pilot.

Figure 16 is, once again, a closer look at a bird’seye view of a set of computer controlled traces. Thecontrol system regulated about the lines in betweeneach ‘‘start’’ and ‘‘end’’ pair, and the turns in be-tween were performed open-loop in a feed-forwardsense. Figure 17 presents a close-up of the firstpath of the regulated control, and looks at the crosstrack error, azimuth error, and velocities. Notethat the dark line in the top of the velocity graph(the bottom panel of Figure 17) is the wind speed,and can be seen to vary well over 50% of nominal.

The mean of the cross track error is less than3 cm, and the standard deviation is less than30 cm. Note that this is the Sailboat Technical

Error (STE), the sailing analog of Flight TechnicalError, that is, the difference between the measuredposition and the reference position. Previous char-acterization of the coast-guard differential GPSreceiver indicated that the Navigation SensorError (NSE) is approximately 36 cm, thus the TotalSystem Error (TSE) is less than 1 m [3].

Figure 18 presents the aggregate of all controlledsailing runs overlaid one upon the other. Alongwith bounds indicating 61 m, the differences inpath length have to do with the location of theshore, and the desire not to run aground. Depend-ing on the path chosen, longer or shorter distanceswere traversed. At no time does the controlled

Fig. 15–Satellite photograph of harbor where the Atlantis wassailed under computer control. The white dots are data recordedfrom a human sailor using a conventional sloop rig. The blackdots show the data from various closed loop computer controlledsegments. Note how straight and ‘‘unnatural’’ they are. Simply,they do not look human.

Fig. 16–Birds eye view of Atlantis under computer control,propelled by the wing-sail. Path regulation happens betweeneach ‘‘start’’ and ‘‘end’’ pair, with the curves in between beingperformed open-loop with a feed-forward command.

Fig. 17–Close up of one of the control segments displayed in Fig-ure 16, showing a mean of less than 3 cm., and a standard devi-ation of less than 20 cm. Note that in this case, there was no sys-tematic current, though the wind can be seen to vary more than50% of nominal on the top line of the bottom plot.


performance of the system exceed the one meterbound. As a basis for comparison, the specificationsfor the top-of-the-line AutoHelm autopilot indicatea cross track accuracy of 0.05 nmi, or 92.6 m.

CONCLUSION

It has been demonstrated that with the combinedadvances in GPS technology, and the advent of lowcost sensors, an unmanned sailboat can be builtthat can navigate with unprecedented levels ofaccuracy. By utilizing a novel wing-sail propulsionsystem, the difficulties of actuating a sail havebeen overcome, and high authority control can berealized. A demonstrated Sailboat Technical Error(STE) in line following of less than 0.3 m (1 � r)was achieved in challenging conditions. Combinedwith a Navigation Sensor Error (NSE) of 0.36 m,this yields a Total System Error (TSE) of lessthan 1 m.

FUTURE WORK

While this project represents a great deal ofprogress on the concept of unmanned sailing ves-sels, there remains much more to do in order tomake the Atlantis more than an academic researchplatform. Control has been demonstrated on simplestraight line segments. However, more complicatedtrajectories are required than simple lines. Fur-thermore, these segments must be linked togetherin some smooth manner in order to create a viablemission for an autonomous sailing vessel.

While tacking and jibing are very simple with arigid self-trimming wing-sail, trajectory generation

must occur whenever the desired waypoint is un-reachable due to wind direction, which includestacking and jibing when necessary.

Lastly, due to the nature of automatic control,rearward sailing is only slightly more difficult thanforward sailing. With this ability, station keepingbecomes a viable maneuver, and one that shouldbe most useful.

We are currently working with the Atlantis atUC Santa Cruz to make the Atlantis more robust,with improved sensors, better integration, and toextend her capabilities to further demonstrate theviability of this craft.

ACKNOWLEDGMENTS

The work in this paper was the result of researchsponsored by University of California, Santa Cruz.The initial part of this research was conductedunder a birdseed grant from the Stanford Office ofTechnology Licensing (OTL). The author gratefullyacknowledges both the OTL and the PrincipalInvestigator (and Thesis Advisor), Dr. BradfordParkinson, of Stanford University for support andsharing the data.

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Fig. 18–Aggregate plot of computer controlled sailing passes,with lines at 61 meter bounds, overlaid on top of one another.The differences in path length have to do with distance to shore,and the desire not to run aground. The controller keeps theAtlantis well within the one meter bound, and shows a standarddeviation of less than 30 cm.
