40th Southeastern Symposium on System Theory TB1.4University of New OrleansNew Orleans, LA, USA, March 16-18, 2008

In-Situ Modeling of a High-Speed Autonomous Surface Vessel

MIDN 1/C Jonerik BlankBradley E. Bishop*

Weapons and Systems EngineeringUnited States Naval Academy105 Maryland Ave (Stop 14A)

Annapolis, MD 21402bishopgusna.edu

Abstract: This paper focuses on the development of a test security, and interdiction of unauthorized vessels inbed and methodology by which moderate-fidelity dynamics can territorial waters.be determined for a high-speed autonomous surface vessel (ASV). The ASV's inherent advantage for completing theseThe dynamics of planing craft are understood, but closed-form missions stems from their SPEAR (Stealthy, Penetrating,models are not available for controller design, and existing high- Enduring, Asymmetric, and Risk-free) characteristics. [4]fidelity simulators require a great deal of computation, making ASVs also gain advantage from their medium of operation,them impractical for reactive control systems. In this work, we the water-air interface, which makes them ideally placed todemonstrate a navigation system, its calibration and subsequent communicate with Autonomous Underwater Vehiclesuse for in-situ testing of the displacement mode dynamics of a (AUVs) as well as Unmanned Aerial Vehicles (UAVs). Thesmall ASV intended for planing operation. Initial results are Navy's keen interest in AUVs of late has been a key factorgiven for roll, pitch and thrust models. in accelerating the development ofASVs.

The current project being undertaken is an extension ofprevious work done in [5,6]. Although capable of extremelyIndex Terms -Autonomous surface vessel, modeling and hig spes h otwsol aal fatnmu

identification. high speeds, the boat was only capable of autonomousmotion and navigation at relatively low speeds. This was

I. INTRODUCTION because the extremely simple model of the system was onlyvalid for situations where the boat was not hydro-planing.

The last decade has seen great progress in the field of The current project aims to better model the boat system,autonomous vehicles. From the search robots used in the seen in Figure. 1.World Trade Center rescue efforts to the Predator UnmannedAerial Vehicle (UAV) used to strike al-Qaeda leaders inYemen in 2002, autonomous vehicles have made a significantimpact on the way that military and emergency operations areplanned and carried out today. [1,2] While autonomous andsemi-autonomous ground and aerial vehicles have been in thespotlight of late, significant developments are being made inthe field ofAutonomous Surface Vessels (ASVs).

The development of the modem ASV has beenaccelerated by several important factors; a major one being thecurrent Global War on Terror. Because the threat to today'ssurface vessels is asymmetric in nature and thus cannot becountered effectively by simply outgunning the enemy,interest has been focused on a force of much smaller and morehighly maneuverable ships intended to protect aircraft carriers approximately 81TOmm in lengthand other large vessels both when they are in port and whenthey are at sea. Failure to protect these assets can result in The new mathematical model, still in its early stages,catastrophes such as the attack on the USS Cole. [3] A swarm has been obtained using a novel method. Instead ofof ASVs surrounding a carrier and carrying out constant assuming that the boat system conforms to specificsurveillance would be ideal for such a job. established archetypes and therefore simply measuring

ASVs can be used for a variety of additional missions that constants to fit the equations, the model has been obtainedwould be cheaper and safer for machines to perform than using sensor measurements from the custom on-board dsPIChumans. These missions include port surveillance, port NayBoard, a custom in-house sensor suite containing: three

gyroscopes, for yaw, pitch and roll; three accelerometers for

978-1-4244-1807-7/08/$25.OO ©2008 IEEE. 347

TB1.4

each axis of acceleration; a magnetometer for heading Therefore, the offset is extrapolated from the calibrationinformation; and a GPS receiver. The dsPIC NavBoard is data, based on the recorded gyro rotation speed to acquireseen in Figure 2. The device was inserted into the vessel in more accurate data.such a way that accelerations and rotational rates could be Calibration on the gyro rate data was done bymeasured along / about the three main axes of motion for calculating the average difference between the gyro and thesurface vessels: surge, sway and heave (see Figure 3). differentiated encoder readings at steady state, then

offsetting the gyro data by that difference. The agreement~~~~~was much improved by this simple adjustment. This

= 0 ~~~~~~~experimentation also enabled usto determine the best rangeof motion for the vessel that can be accurately measured bythe sensors. Encoder data and uncalibrated gyro data areshown in Figure 4.

fi . _ ~~~~~~~~~~~150r- - - - - - - -1 - --- ---; -|-__- - - ---

Figure 2: NavBoardbasedonthe dsPIC processorand equippedwithPthree t trate gyros, a three-axis accelerometer, a magnetometer, a GPS receiver and a gyrO

XigBee radio communication system. ecor(D 100 - - - - - - - |- - - - - - - - - -

I Y' X 1 X ~~~I I I

IY(swayI I I I

pitch |L1

I If IB/J ~~~I Ir I

_? ~~~~I lfI III

50 - I I I I

H iNy iz U C1~~~~~~~~~~~~~~0 - - - - - - ----1- - - - - -TI- - - - - -1- - - - - - - -

XIsurge) 1Time (s)

Iroll Figure 4: instrumented angular rate (blue) and uncalibrated NavBoardI angular rate (red) for medium-rate yaw sample

Z (heave) Figure 5 shows encoder data, and calibrated gyro datalyaw

the same experiment. It demonstrates JUSt how much thecalibration improved the accuracy of the gyroscope's

Figure 3: Vessel axes and spin axesmesr en.

Calibrated pitch rate data for medium speed

11. SENSORCALIBRATION 20:0XX:TP0T8t);=000 ;0i;

I I ~ \

Beforeanymodeling couldbedoneusingthismethod, the 6sensors on the DSPic NavBoard needed to be calibrated. A ,0testing apparatus was built, consisting of a motor, with an 140-I I

IIII

integrated encoder, that could be spun at a specified rate. The U) 1200 - 4 +-- gyro- ---0

NavBoard was placed on the platform and spun on its yaw, ,,F 4: itme anua r (le a unclira encodepitch and roll axes, as well as with the axes tilted, at various ( f m - y sample

speeds. The gyro's readings were then plotted ajainst the c tderivative of the motor encoder's data in order to obtain 60t- - - - - -i - - - 4 - - - a- - - - - - - -

velocity plot. The gyro's readings were also integrated andplotted against the motor encoder data in order to obtain 20L 3 X ; ; ;Cer as

Bnerforemanymodlingaicoud btdoe uyrsingpths metho,ithwa °- -t~ - - - -

testingdappaatuser wasbultsonesisignofican mofstoer,ow itan I I I I I I I I I Iinltegrated encoer,taep

coudespnaaspemerr.Acifiedrate.

lTh

Ee(s20)-Nayoardwhaths plac canedonth epatorendinspun one ispeyawt--- - noepitch~ ~ ~ ~~~~~~~~~~~~~~~Fgran5olae,a:elswt h xstltd tvros 8 insruene anua rat (bue an caibae NaBor anuavelocityeplot.rThe gyro's wreadnspngwer als integatefasnd 40 - (e)foeimrteywsmlplote agint he otr ncoerdaa i ode toobai2348__

TB1.4

III. MODELINGTABLE I: LEFT ROLL TRANSFER FUNCTION (TF)

After the calibration phase, the basic dynamics of the boat PROPERTIESwere modeled by documenting responses to known # Poles Zerodisturbances in the water. For example, boat response to a 1 -0.0246 +1- 0.1665i -0.017disturbance in roll was determined by placing the boat in a 2 -0.0222 +1- 0.1649i -0.0058water tank, pushing down on one side of the boat, and letting 3 -0.0230 +1 0.1605i -0.0196go. The resulting motion of the boat was analyzed inMATLAB in order to obtain a roll model for the vessel: the 4 -0.0249 +1 0.1636i -0.0014accelerometers provided accurate pose information before the Note that, for purposes of determining these transferrelease, and the rate gyros coupled with the accelerometers functions (and all others in this work), the standard time unitwere used to determine the roll response of the vessel. Similar was approximately 1/70th of a second, which was the sampletests were conducted to determine the boat's response to time for the dsPIC NavBoard. The time domain responsedisturbances in pitch, as well as the boat's response to from these transfer functions is therefore defined oneffective thrust (push forward). M\ATLAB's System samples, instead of seconds, for future control purposes.Identification Toolbox was used to obtain models for the As can be seen, all the transfer functions were fairlysystem response to the various disturbances. similar, with somewhat variable gains but nearly identical

poles. All of the results were underdamped with zeroes veryA. Roll disturbance on the left side. close to 0. Differences between the four transfer functions

System response to roll disturbance on the left side can be attributed to wave disturbances in the water tank in250 V F which the experiment was conducted. Since the tank was

I angle input relatively small, there were issues with waves reflecting off200.|1t|| | roll rate the sides of the tank, which resulted in only the data shown

150IoL I I I I I j in Figure 6 being valid for modeling (as it was taken before-O / 0 || ||waves propagated back from the walls ofthe tank).100 ----- The zero locations determined by MATLAB are clearly

50- --zeoi reality. Part of this error could be from noise or/ \ inHe--~-rror, as the steady-state roll rate for the vessel is clearly

___ __ __________ _ ________- misalignment of the accelerometer, or from drift in gyro°_ 0 l readings after calibration (a well-understood phenomenon).

As such, we compare the dynamics with the zero adjusted toC: -50 ._ __ _0. We see in Figure 7 that the step responses ofthe modelsa -001 I I I I - 0 so modified are all very close, which suggests that the data

are accurate.-150 12

5.6 5.8 6 6.2 6.4 6.6 6.8 7 7.2 7.4 7.6 _im (s)

3Figure 6: Roll rate (red) and roll input angle (blue) for roll disturbance 4

experiment on the left side of the vessel. 86 - 1 ------ -- ---.--...---.

In this series of tests, the boat was placed in the water anddisplaced downwards into the water on its left side, held down 4momentarily and then let go. Readings from the z- and y-axis 22--------- ...------- ----- ------------------------accelerometers were used to determine the roll angle .displacement, which is seen in Figure 6 as a negative stepinput along with the roll rate response. The input and output -2 -----.---.--- I------------------------------were used in M\ATLAB's System Identification Toolbox inorder to obtain preliminary, linear transfer functions for theboat's response to roll disturbance. A wide variety of -6

parameters were used, and the final 'best fit' system that -8 1 0balanced accuracy and intuition was a second-order system 0 50 100 150 200 250with a single zero. Transfer functions, from angle ofrelease to Time (samples): 1/70th secroll rate, obtained over four different trials, are given by: Figure 7: Step responses for various transfer functions, from angle of

release to roll rate, with zero correction

1) 2.33(s+.017) 2) 1.91(s+.0058)s2+.049s + .2 + .044s +.028 B. Roll disturbances on the right side.

3) 1.93(s+.0196) A\ 1.92(s +.001) This series of tests involved placing the boat in thes2 +.4s.2 2+09s+07water and applying a momentary angular displacement on

s + .046s .026+ .097s +.027the right side of the vessel. The resulting motion was

349

TB1.4

measured using the NavBoard and transfer functions were numerators of the transfer functions) and in the poleobtained. Once again, the System ID Toolbox was once locations than was seen in the roll results, which is likelyagain used to obtain multiple experimental transfer functions, due to the more nonlinear nature ofthe pitch dynamics.from angle of release to roll rate:

1) 2.33(s+.019) 2) 2.12(s +.028) TABLE III: FRONT PITCH TF PROPERTIESs +.047s +.028 s2 +.049s +.028 # Poles Zero

3) 1.99(s +.0025) 4) 1135(s+-021) 1 -0.0316+10.1405i -0.0159s2 +.049s+.027 s2 +.039s+.024 2 -0.0311 +I-0.1292i -0.0142

3 -0.0289+/- 0.1422i -0.0472TABLE II: RIGHT ROLL TF PROPERTIES 4 -0.0288 +/- 0.1366i -0.0104# Poles Zero1 -0.0234 +/- 0.1648i -0.0193 D. Pitch disturbances on the rear ofthe vessel.2 -0.0243 +/- 0.1672i -0.0278 In this series of tests, the pitch disturbance was applied

to the rear of the vessel. Pitch rate in response to the3 -0.0244 +/- 0.1628i -0.0025 disturbance was measured and the corresponding transfer4 -0.0194 +1- 0.1537i -0.0214 functions were obtained, from angle of release to pitch rate:

These transfer functions were very similar to one another 4.64(s +.015) 3.27(s+.039)and to the results from the left-side tests above, as expected. 1) 2__.044_______ 3.27(s+.039)' s2 +~~~~+.044s+.018 s2 + .051is+.018C. Pitch disturbances on thefront ofthe vessel. 3) 5.51(s +.0065) 4) 1.65(s - .1 1)

This series oftests involved pushing down on the front of s2 +.068s+.019 s2 +.048s+.019the vessel momentarily, letting go, and observing the pitch rateof the vessel, with the results again used to obtain transfer TABLE IV: REAR PITCH TF PROPERTIESfunctions from angle of release to pitch rate: # Poles Zero

1 -0.0220 +-0.1323i -0.015l) 17.02(s+.016) 2) 27.13(s+.14) 2 -0.0257+0.1317i -0.03912 2.-030257021-0213162s-0.039S 2 +.063s +.021 S2 +.062s+.018 3 -0.0339 +1- 0.1325i -0.00653) 13.52(s+.047) 4) 7.95(s +.01) |4 -0.0242 +-0.1374i 0.1098

s2+.058s +.021 s2+.057s +.019150 The transfer functions for this set of trials did not match

__\_1 those from the previous pitch tests as closely as was23 expected. This difference is most likely attributable to the

100 ', - nonlinear response, where the wetted surface and totalimmersed volume for the rear deflection was significantlyhigher than that for the front deflection, placing the vessel

O502yA\\ l farther into the nonlinear region of the dynamics. Asdemonstrated here, pitch response is typically linear only in

l', < a small region near the equilibrium. This also offers someexplanation for the deviation of response 2 from the front-pitch tests: the initial angle for this test was larger than thatof the others, and the effect can be seen in both the

50: \ / 0 l amplitude and the frequency of the response.

-100 5010000E. Response to deceleration in the water.0 50 100 1502se 250 In this test, the boat was placed in the water, pushed

with a constant force in the x direction from the rear, andFigure 8: Step responses for various transfer functions, from angle of release then let go and allowed to decelerate in the x direction, as

to pitch rate for front-end displacement, with zero correction seen in Figure 9. The input force was estimated (within ascale factor) from the change in velocity applied to the

These transfer functions had similar poles, and were all vessel by the push. The output ofthe generated system was(again) underdamped with zeroes close to 0. Once again, the the x-acceleration of the vessel in g's. The transfer functionnonzero zero locations were corrected, and the step responses from (estimated) force to surge (x) acceleration wasplotted (as seen in obtained, as was the step response, which is shown in Figure

Figure 8, above). There is a larger variation in both the 10 Note that the response shows slight overshoot incorrected gain (shown as the multiplicative factor in the

350

TB1.4

acceleration, which is possible depending on the speed of the thrust response characteristics. These data will be used goingvessel (as it nears and potentially passes hull speed). forward in developing control for the vessel. The techniques

developed for this modeling are quick, efficiently and

Transfer function: 2.93(s +.14) accurate, and can be implemented on low-cost hardware ins+ .22s + .0 9 order to obtain simplified models of complex systems.

In more advanced phases of testing, the boat will beTABLE V: FORCE DISTURBANCE TF PROPERTIES placed in the water and various maneuvers conducted with

the motor running; these include sharp turns at slow speedsPoles DC gain Zero and high speeds. These data will be analyzed to determine a-0.1084 +1- 0.0856i 22.0826 -0.1439 comprehensive model of the system. Noise rejection,

especially in regards to slamming of the hull in uneven seasSystem response to a force in the x-direction and hull vibration due to the prop, is a significant issue that

force will require careful consideration. After sufficiently detailed

x-acceleration models are obtained for the boat in motion, a controller will0.250 C Xi I I l be designed and implemented for high speed motion.2 ~ ~ I I V

o 0.2 0 H r 7) f T j V. ACKNOWLEDGEMENTSLLl

ca 0.15 ------ t-- - - t The authors would like to thank Mr. Joseph Bradshaw oftheUnited States Naval Academy's Weapons and Systems

0.1 - - - ---- -- t Engineering Department's Technical Support Division forhis help with the dsPIC NavBoard and various other

< 0.05 -A----- --a---- ----a--- hardware needs. Additionally, the authors would like tothank Midshipman Allan Elsberry for his help with the

0 - Systems ID Toolbox and some additional M\ATLAB code.I I I I Finally, we acknowledge the support of ONR under the

-0.05 National Naval Responsibility in Naval Engineering (NNR-6.2 6.4 6.6 68 7 72 74 767lme8(s) NE) Program (Grant N0014-03-1-0160).

Figure 9: X-acceleration (red) and force (blue) for force disturbance VII. REFERENCESexperiment

25 [1] JOM Magazine (no author listed), Remote-Controlled Robots SearchWorld Trade Center Rubble, 53(12)(2001), pp. 4-7

.................. [2] USA Today (no author listed), U.S. kills Al-Qaeda suspects in Yemen,Available: http://www.usatodaylcom/news/world/2002-11-04-yemen-explosion x.htm, last visited 10 November 2007

[3] Global Security (no author listed), USS Cole Bombing, Available:http://www.globalsecurity.org/military/systems/ship/images/ddg-

^ 15 -67 cole-hole-clos usnavyO I-jpg last visited 26 March 2007[4] Israeli Weapons (no author listed), Protector Unmanned Naval Patrol

Vehicle, Available: http:Hwww.israeli-E weapons.com/weapons/naval/protector/Protecto.html, last visted 26

10o March 2007[5] Reed, C. M, Bishop, B. E. and Waters, J., "Hardware Selection and

Modeling for a Small Autonomous Surface Vessel," Proc. of the 2006IEEE Southeastern Symposium on Systems Theory, March 6-7, 2006.

[6] Reed, C. M, Bishop, B. E. and Waters, J., "Design of an AutonomousSurface Vessel," Proc. of the 2006 World Maritime TechnologyConference, London, UK, March 2006, CD-ROM.

[7] T. VanZwieten, Dynamic Simulation and Control of an Autonomous0 10 20 30 40 50 60 Surface Vehicle, Available: http:Hwww.oe.au.edu/-ananth/Tannen-

Time (samples): 1/70thsec Thesis.pdf last visited 27 April 2007Figure 10: Step response for force-surge acceleration transfer function [8] J 'int last visted2 April 2007

[]JOint Unmanned Systems Test, Experimentation, and Research (noauthor listed), Autonomous Surface Vessel, Available:

IV. CONCLUSIONS AND FUTURE WORK http://jouster.me.edu/proje ts.php?pro-jectid=4, last visited 27April 2007

In this work, we have demonstrated the efficacy of the [9] A. Leonessa, J. Mandello, Y. Morel and Miguel Vidal, Design of aSmall, Multi-Purpose, Autonomous Surface Vessel, IEEE Xplore

dsPIC NayBoard for in-situ testing of surface vessel dynamics. [10] H. Xi, Feedback Stabilization of High-Speed Planing Ves,sels by aWhile all of the tests here were carried out in displacement Controllable Transom Flap, IEEE Journal of Oceanic Engineering 31mode, the same methods will be used to determine moderate- (2006), pp. 421-43 1.fielt dyamc duin plnn motion.* .Th wor codce [11] MRV International, LLC, SOLUTIONS FOR FLEET, COASTAL &resulted in the calibration of the instrumentation used for POR SEURT, Avalablvsie:2Mach00measurement, and the modeling of the vessel's pitch, roll and

351