Copyright ©1996, American Institute of Aeronautics and Astronautics, Inc.

AIAA Meeting Papers on Disc, 1996, pp. 37-47A9635006, AIAA Paper 96-3474

Analysis and comparison of the motion simulation capabilities ofthird-degree-of-freedom flight simulators

Nicolas A. PouliotUniv. Laval, Quebec, Canada

Meyer A. NahonVictoria Univ., Canada

Clement M. GosselinUniv. Laval, Quebec, Canada

AIAA Flight Simulation Technologies Conference, San Diego, CA, July 29-31, 1996, TechnicalPapers (A96-35001 09-01), Reston, VA, American Institute of Aeronautics and Astronautics,

1996

We present results of a preliminary study aimed at determining the simulation realism which could be achieved using reduceddegree of freedom (DOF) flight simulator motion bases. The quality of motion produced by two different 3-DOF platformswas compared to that produced by a standard 6-DOF Stewart platform. The 3-DOF motion bases investigated include aspherical mechanism which allows only rotational motions, as well as a motion base capable of heave, pitch and roll motions.To compare the different motion bases, four characteristic maneuvers were simulated using a nonlinear model of a Boeing747. The aircraft motions were then simulated on nine different combinations of virtual motion platforms and motion basedrive algorithms. The motion cues (specific forces and angular velocities) produced in this manner were then graphicallycompared. The analysis revealed that, in most cases, a 3-DOF simulator is capable of producing motion simulation qualitycomparable to that produced by a 6-DOF Stewart platform. (Author)

Page 1

96-3474A96-35006

AIAA-96-3474-CP

ANALYSIS AND COMPARISON OF THE MOTIONSIMULATION CAPABILITIES OF

THREE-DEGREE-OF-FREEDOM FLIGHT SIMULATORSNicolas A. Pouliot*, Meyer A. Nanon* and Clement M. Gosselin*

*Departement de Genie Mecanique, Univ. Laval, Quebec, Qc, Canada, G1K 7P4^Department of Mechanical Eng., Univ. of Victoria, Victoria, B.C., Canada, V8W 3P6

email: pouliot@gmc.ulaval.ca, mnahon@sirius.uvic.ca, gosselin@gmc.ulaval.ca

AbstractThis paper presents the results of a preliminary studyaimed at determining the simulation realism whichcould be achieved using reduced degree of freedomflight simulator motion bases. More specifically, thequality of motion produced by two different three de-gree of freedom (3-DOF) platforms was compared tothat produced by a standard 6-DOF Stewart plat-form. The 3-DOF motion bases investigated includea spherical mechanism which allows only rotationalmotions, as well as a motion base capable of heave,pitch and roll motions. To compare the different mo-tion bases, four characteristic maneuvers were simu-lated using a non-linear model of a Boeing ?47. Theaircraft motions were then simulated on nine dif-ferent combinations of virtual motion platforms andmotion base drive, algorithms. The motion cues (spe-cific forces and angular velocities) produced in thismanner where then graphically compared. The anal-ysis revealed that, in most cases, a 3-DOF simula-tor is capable of producing motion simulation qual-ity comparable to that produced by a 6-DOF Stewartplatform.

1 IntroductionThe six-degree-of-freedom (6-DOF) Stewart plat-form is undoubtedly the most popular motionbase for commercial flight simulators1 However, itis a complex and expensive mechanism which isbest suited to full training simulators. Recently,there has been renewed interest in low-cost partial-training simulators which could be used for early pi-lot training, prior to the use of full-training simula-tors. As well, the advent of high-performance ImageGeneration (IG) systems2 has tended to decrease therelative importance of motion generation, therebyraising the issue of whether lower cost motion de-

vices might be appropriate even for full-training sim-ulators. Finally, there has recently been heightenedinterest in lower cost simulators for applications toroad vehicle simulation and entertainment.

Relatively little work exists in the area of the designof reduced-dof motion bases or in the evaluation ofthe quality of motion sensations which could be pro-duced by these devices3'4'5

The purpose of this paper is therefore to analyzethe simulation realism which can be achieved usingalternative motion base mechanisms, with only 3 de-grees of freedom. It is conjectured that this reducedmotion capability might provide a cheaper alterna-tive to existing designs (simplicity, reduced cost ofmanufacturing and operation) while still producinga good quality of motion simulation for large trans-port aircraft. In all, nine combinations of motionbase architecture and drive algorithms were evalu-ated using four different aircraft maneuvers. Theevaluation maneuvers used in this study were cho-sen to ensure that a limited number of maneuverswould provide a broad range of motions, includingboth low and high frequency accelerations in all de-grees of freedom.

2 Background Material2.1 Type of aircraft and modeling

The present work focusses on the simulation ofcommercial airliners, and the Boeing 747 has beenchosen as a typical example. This emphasis isdue to the fact that, due to their large inertia,the natural motion of these aircrafts lends itselfwell to motion simulations which are principallycomposed of low-frequency rotations (including tilt-coordination). Thus, high-frequency translationalaccelerations such as those required for the Simula-

Copyright ©1995by the AIAA, Inc.All rights reserved.

37American Institute of Aeronautics and Astronautics

tion of military aircrafts would tend to be poorlysimulated by the alternative platforms consideredhere. A complete nonlinear model of the Boeing7476'7is used in the present work to predict aircraftmotion in response to a range of pilot inputs andrandomly generated turbulence while flying at lowaltitude.

2.2 Reference frames

The reference frames associated with the aircraft areshown in Fig. la. Let Ffa be the inertial reference

a) Aircraft's reference frames.

b) Simulator's reference frames.

Figure 1: Reference frames.

frame, fixed to the ground. By convention, the Zaxis points vertically downwards and the X axis isparallel to the active runway. A second referenceframe Fa is attached to the aircraft and has its ori-gin at the center of mass of the aircraft CGa. The Xaxis of Fa points longitudinally forward while the Zaxis points downward with respect to the aircraft.As a result, the Y axis points out the right wing.Furthermore, vector Sai is defined as the vector con-necting the origin of frame Ffa to the origin of frameFa, as illustrated in Fig. la. Finally, Euler angles-. T

f}a = (0,0, i/j) are used to specify the relative ori-entation of frame F0 with respect to inertial frame(Fja). Hence, the inertial position of a point of theaircraft whose position vector with respect to frame

Fa is given by [P]pa can be written as

where

cBcij)

—s8 Si cficd

(1)

(2)

and where c stands for cos and s for sin. The re-lationship between the time derivatives of the Eulerangles and the angular velocity vector of the aircraft,wa, is then written as

1 00 c$0 -s<h

(3)

A third reference frame, denoted Fpa, having thesame orientation as Fa is also defined, with its originat the center of the pilot's head. The vector connect-ing the origins of these two frames, S02, is illustratedin Fig. la. In the present study, this vector hasbeen assigned the value S%2 = {26.2, -0.465, -3.4}m, which approximately represents the pilot's headlocation in a Boeing 747.

The reference frames associated with the simulator'smotion base, are shown in Fig. Ib. An inertial ref-erence frame (F/s) is fixed to ground, directly belowthe center of the simulator's motion base, when thesimulator is in its neutral position. Moreover, framesFs and Fps are attached to the moving platform ofthe simulator with their origins respectively locatedat the geometric center of the simulator's movingplatform CP and at the center of pilot's head PH.The latter frames have the same orientation, whichis given by the simulator's Euler angles, using theconvention defined for the aircraft. Finally, vectorSsi is defined as the vector connecting the originof frame Fjs to the origin of frame Fs and vectorSS2 is defined as the vector connecting the origin offrame Fs to the origin of frame Fps. Other pointsand vectors shown in Fig. Ib will be defined later.

2.3 Washout filter algorithm

The purpose of defining a reference frame with itsorigin at the pilot's head is to allow the determina-tion of the angular velocities (w) and specific forces(/) to which the pilot is subjected. It is generallyaccepted that these cues plays a dominant role inhuman motion sensing activities8

It is recalled that the specific force is a vectorialquantity defined as the difference between the trans-lational acceleration vector (a) and the vector of

38American Institute of Aeronautics and Astronautics

gravitational acceleration (g), i.e., / = a-g. Hence,a body at rest under the action of the earth's grav-itational field is said to be experiencing an upwardspecific; force of 9.81m/.s2, i.e. in the negative direc-tion of the Z axis defined above.

Since the flight simulator motion base has a limitedrange of motion, it is not possible to exactly repro-duce the angular velocities and specific forces ex-perienced in the aircraft. Hence, motion generationalgorithms (a.k.a. 'washout filters') have been devel-oped to generate the best motion commands withinthe constraints of the motion system. The principlesof the washout algorithm used in the present workwill now be reviewed.

One of the most demanding tasks for a motion basewith limited motion travel is the reproduction of lowfrequency translational accelerations. For instance,a constant acceleration of lm/s2 along the X axissustained for 5 seconds would require a travel of 12.5meters. However it is also possible to slowly tilt thesimulator about its Y axis at an angle of approx-imately 6 degrees, while the visual display contin-ues showing horizontal flight conditions. The pilotwould then experience a specific force componentalong the X axis of 9.81-sin(6°) = lm/s2. Althoughthe Z component of the specific force experienced bythe pilot would then be reduced to 9.75m/s2, thischange should not be noticeable. The effectivenessof this process, known as tilt coordination, to simu-late low frequency translational accelerations, leadsto an increased importance of the rotational chan-nels in relation to the translational channels.

The washout filter (WF), which includes the above-mentioned tilt-coordination, receives as inputs theangular velocities and specific forces sampled at aparticular location in .the aircraft - referred to asthe washout location and denoted WFa and WFSon Fig. 1 - and outputs the optimum displacementvector (55i) and the Euler angles (/?g) that the sim-ulator's cockpit should assume. The WF also con-tinually tries to return the motion platform to thecentral location of its range of motion (the neutralpoint).

There exist several variations of WF algorithms9

but its classical form has been used here due to itswidespread use in commercial simulators. A com-plete description of this algorithm can be found inNahon et al, 19929 while Fig. 2 illustrates the al-gorithm, as used in the present work. However, thedashed-line block denoted as HF emulator is an ad-dition developed for the purposes of the present workonly, and will be described in a subsequent section.Consequently, boxes 13 to 17 should be non-existentin the conventional classical WF algorithm.

As can be seen in Fig. 2, the washout algorithm isbroadly divided into three parallel channels of mo-tion. The upper channel (translational), consistingof boxes 1 to 4, scales the input specific forces (/oa),typically by scale factor of 0.5, transforms the result-ing vector into the ineitial reference frame and thenadds the gravity vector. This produces the acceler-ation vector (ac) which must be filtered to extractonly its high frequency component (a,i) in order toassure that the simulator will remain near its neutralpoint. Finally, (asi) is integrated twice to obtain therequired displacements of the platform (Ssi). Thelowest channel (rotational), consisting of boxes 7 to10, is similar to the translational channel but actsupon angular velocities. Hence box 10 only carriesout a single integration, thus producing a set of Eu-ler angles (fih)- The central channel, consisting ofboxes 5 and 6, represents tilt-coordination. Box 5 re-ceives the scaled specific forces and extracts their lowfrequency components which are then transformedby box 6 into tilt angles (/?TC)- Box 6 also includesa rate limiter to ensure that the tilt-coordinationwill occur slowly enough to keep the effect realistic.The sum of j3h, and PTC provides @s, the orientationof the simulator, which is then used to compute thematrices Qs and Rs.

Figure 2: Washout filter algorithm layout.

3 MethodologyIn this work, aircraft simulation software developedat the University of Toronto Institue for AerospaceStudies (UTIAS) to drive a full scale six-degree-of-freedom simulator10was used off-line on a worksta-tion. Some of the algorithms included in the soft-ware were modified in order to simulate the three-degree-of-freedom motion bases evaluated in thiswork. Indeed, it, is possible to artificially reducethe simulator's number of DOF by inhibiting, forinstance, all the translations while keeping the ro-tational motion, thus emulating the behavior of athree-DOF spherical simulator.

39American Institute of Aeronautics and Astronautics

Figure 3 summarizes the various steps which wererequired in order to produce the results. The pri-mary inputs consisted of two standard text flies. Thefirst file gives the initial conditions which are neces-sary in order to solve the differential equations offlight. The second file is a complete time historyof the aircraft's control inputs (elevator deflection,throttle position, wheel angle, etc.) for the entiresimulated maneuver and with a sampling frequencyof 20 Hz. The aircraft model, with the help of threemajor modules (engine model, turbulence genera-tion and ground model) then outputs the simulatedflight history to a file. The accelerations and angularvelocities thus obtained are then fed directly into thevestibular model and into the WF algorithm. Thevestibular model, described in detail in Reid and Na-hon, 198510, is use to determine wether conclusionsbased on pilot sensations would differ appreciablyfrom ones based on motion time histories. As de-picted in Fig. 3, the WF transforms the flight historyinto the simulator motion time history, according towhich degrees-of-freedom are currently available.

Finally, the simulator specific forces and angular ve-locities arc fed into the vestibular model, which pro-cesses both the aircraft and simulator flight historiesto produce the pilot sensations time-histories.

ers started with the cruise conditions. These initialconditions are summarized in Table 1. A brief de-

Table 1: Initial conditions files content.

-5 Simulator's•g o •§ uvailabli:S ^ S DugfL'es of fi-ceiln H

Aircraft'scommandinput file

Initialcondition

file

£J "§ s iWashout Hltci i i i . —— . f1 — ̂ Mathematical model I t Flight — '

i — 1| ill' aircraft [ History -, —

r| —— •Simulation

Histoiy

VcstihularMoJol

J ||AircraftResults

J1

SimulationResults

Figure 3: Layout of the methodology.

The methodology described above produces resultswhich can be used to compare the quality of the mo-tion simulation obtained with a 3-DOF simulatorwith that obtained with a 6-DOF simulator. Ad-ditionally, the results obtained with both types ofsimulator can also be compared with the real flyingexperience.

3.1 Evaluation maneuvers

Since it would not be possible to test an exhaustiveset of aircraft flying sequences, a limited number ofmaneuvers had to be selected. Four characteristicmaneuvers were used to perform the comparison be-tween the simulators. These maneuvers were chosento exercise the full range of simulator DOFs.

The first maneuver started with the initial condi-tions referred to as runway conditions while the oth-

I.C. FILE:Speed (m/s)Altitude (m)Engine EPR

runway50.04.671.02

cruise212.562801.10

scription of each of the four maneuvers follows.

Take-Off Maneuvre (TOM): This maneuver be-gins at a speed of 50 m/s on the runway with thethrottle lever at 15% of maximum power. Afterthree seconds, the throttle is abruptly set to 100%and the aircraft accelerates. At t=lls, when rota-tion speed is reached, the nose is lifted and soonafter, the aircraft takes off at a steady pitch angleof 10 degrees. Finally, six seconds later, a suddenfailure occurs on the right outboard engine and thepilot eases the elevator to keep the plane level. Themaneuver ends at t=25s.

Turn-Entries Maneuvre (TEM): In this 40 sec-onds maneuver the aircraft, flying at cruise condi-tion, first rolls right, then left, and then right again.The maximum bank angle in each roll is approxi-mately 40°. The pilot adjusts the elevator to keepthe aircraft's altitude almost constant and the throt-tle lever is set at 55% of maximum power for theentire maneuver.

Throttle Impulse Maneuvre (TIM): The pi-lot, initially flying at cruise condition with 55%power, suddenly increases the throttle setting tomaximum power while adjusting the elevator to keepthe aicraft's altitude constant. Seventeen secondslater the throttle is set to idle until the end of themaneuver, at time 40 seconds.

Turbulence Area Maneuvre (TAM): This ma-neuver begins with the aircraft trimmed for cruisecondition, when a patch of turbulence is encoun-tered. The pilots makes no corrective control inputs.The controls therefore remain in the same state asif the plane were cruising in still air for a durationof 25 s.

3.2 Location of washout:

The original washout filter software taken from Reidand Nahon, 198510,always performed the washoutcalculations using values of specific forces existingat the location in the aircraft corresponding to thecentroid of the motion base. However, the presentwork also investigated alternative washout locations.As shown in Fig. 1, the location of WFn (and WFS),at which washout is performed, is defined with re-

40American Institute of Aeronautics and Astronautics

spect to the pilot's head by means of the vector Ro.Preliminary tests indicated that, it was imperativethat the vector Ro be identical in both the aircraftand the simulator (i.e. that -WFa and WFS be inthe same location relative to the pilot's head). At-tempts to use other configurations invariably led tothe generation of unwanted spurious translationalaccelerations.

However, in order to compute the hydraulic cylin-der lengths, the kinematics transformation softwarerequires the position of the centroid of the mo-tion base, denoted by Cp on Fig. 1, to be speci-fied. To accomplish this, even when washout mightnot be performed at Cp, vector Rwfs, must becalculated according to Rwfs — Ssi — Ro whereSj2 = (-0.02, -0.465, -1.783)?™, expressed in frameFs. This value for Ssz represents the pilot's headlocation relative to the centroid of the moving plat-form for the UTIAS flight simulator.

Three locations for the washout filter were thus eval-uated in the present work:

-. T@PH: The pilot's head. In this case, Ro - (0,0,0)and RwfJ = Sj2. The benefit of this scenario is thatno spurious translational accelerations are generatedat the pilot's head.©CP: The centroid of the moving platform. In thiscase, RoT = S%2 and Rwf* = (0,0,0). This isthe usual convention, as used in Reid and Nahon,198510.@CG: The center of gravity of the moving plat-form and cockpit. For the UTIAS simulator,

-. Tthis location has been approximated as Ro =(-0.02, -0.4G5, -0.483)m. The benefit of this lo-cation is that it tends to minimize the dynamic ac-tuation forces, since off-center rotations are not gen-erated.

3.3 Alternative motion base architectures:

In the present work, the three different motion basearchitectures were simulated and compared. Thelast two use a particular combination of three de-grees of freedom which could be emulated using areal six degree-of-freedom simulator.

STW: The first architecture is the conventionalStewart platform which possesses a full six degreesof freedom. It can translate along all three orthogo-nal directions independently, as well as rotate aboutthese same axes. A schematic representation of thismotion base is shown in the uppermost frame ofFig. 4. At a given time step, the washout filter algo-rithm produces Ssi and the orientation matrix Qs.

Figure 4: Different Motion Base Architectures.

SPH: The second architecture considered has onlythree degrees of freedom, consisting of rotationsabout three mutually perpendicular axes. The mid-dle frame of Fig. 4 shows a representation of whatthe motion base might look like. As it was high-lighted in the discussion of tilt-coordination, the ro-tational motion channels are particularly importantin the simulation of large transport aircraft. Sincethe platform is only capable of rotations, the onlyuseful ouput from the washout algorithm is the ori-entation matrix Qs. The linear displacements aresystematically set to zero and the location at whichwashout is performed (WFe) will then not be al-lowed to move with repect to the ground.

HPR: The third architecture also has three degreesof freedom but this time including translation alongthe vertical axis (heave). The other two degrees offreedom consist of rotations about the two horizontalaxes, namely the pitch (around the Y axis) and roll(around X axis). The notation HPR therefore standsfor Heave-Pitch-Roll. The last frame of Fig. 4 showsa representation of what this motion base might looklike. The point WFS will then move along a verticalaxis while the two rotations are performed about thispoint. In this case, the useful output of the washoutfilter are the Z component of Ssi and the roll andpitch components of fts-

41American Institute of Aeronautics and Astronautics

3.4 A HF emulator

In order to compensate for the loss of translationalmotion in the 3-DOF SPH and HPR architectures,a further modification of the washout algorithm,called a 'high frequency (HF) emulator', was eval-uated. Its purpose is to reproduce some of the highfrequency translational accelerations by command-ing an appropriate angular acceleration assumingthat the pilot's head is displaced from the centerof rotation by a non-zero vector Ro. The HF emula-tor, consisting of boxes 13 to 17 in Fig. 3, was thusimplemented into the washout filter algorithm, andis described below.

First, assume that the high frequency accelerationwhich must be emulated is denoted by as\. Thisacceleration can be transformed into the simulatorreference frame according to a = Q^«si • Since anangular acceleration can only produce linear acceler-ations which are perpendicular to Ro, the followingtransformation is performed on a to remove the ac-celeration component along Ro:

a± = a — (a • R.o)Ro

(4)

The resulting vector now represents the componentof the original high frequency acceleration which canbe emulated. A corresponding angular accelerationcan then be calculated according to:

(5)pfolMKSj.x.Ro)!!

That value can be integrated once to obtainthen multiplied by the inverse of Rs matrix in orderto get the derivative of the Euler angles and theseare finally integrated, giving as a results a value for

The HF emulator is automatically disabled when us-ing the 6-DOF STW motion base. When the HFemulator is used with the 3-DOF SPH motion base,the vector Ro is set to (1.25, 0, 0), representinga center of rotation located behind the pilot, andallowing mainly Y and Z accelerations to be em-ulated. When the HF emulator is used with the3-DOF HPR motion base, Ro is set to (0,0,-1.25)since high frequency vertical accelerations need notto be emulated (they can be produced directly bythe motion base).

Table 2 summurizes the 9 different combinations ofmotion bases, washout filter locations and HF em-ulator that have been used in this study for eachof the 4 maneuvers. Thirty-six sets of results where

therefore generated and will be presented in the nextsection.

Table 2: Studied Architectures.

STW(6-DOF)SPH(3-DOF)HPR(3-DOF)

@PH••

@CP•••

@CG

••

+HF

••

3.5 Conservative assumptions:

Additional assumptions were made to ensure thatthis study would remain conservative. The first wasto assume that all three motion bases would have thesame range of motion capabilities for those DOFswhich were active. This assumption was dictatedby the need to allow a future comparison to be per-formed on a standard 6-DOF motion base. It shouldbe noted, by means of Table 3 from Reid and Nahon,198811, that a 3-DOF motion base could be designedto have a much wider range of angular travel thanthe Stewart platform.

Table 3: STW motion base travel limits.

LinearXYZ

Vmax^•rnax

±0.65 (m)±0.59 (m)±0.52 (m)0.80 (m/s)10.0 (m/s2)

Angular<£9$

^max

&max

±20.8(°)±21.3(°)±20.0(°)34.4(°/s)400(°/s2)

A second conservative assumption was to use thesame washout filter structure and coefficients for allmotion bases (except for the HF emulator, whereactive). This washout filter had been designed togive good performance on the 6-DOF motion basedescribed by Table 3. It should be noted, however,that the washout filter algorithm could likely be im-proved for operation specifically with the 3-DOFmotion bases.

4 Results fc Discussion4.1 Performance indicators

The 36 sets of results mentioned in the preceding sec-tion, produced using different combinations of eval-uation maneuver, motion base architecture, washoutfilter location and high frequency emulator, wereevaluated in a number of ways. The initial resultswere generated as time-histories of different param-eters. These included pilot control inputs; aircraft

42American Institute of Aeronautics and Astronautics

and simulator positions, velocities and accelerations;pilot vestibular model responses; and motion baseactuator lengths. From these results, twelve graphswere then constructed: three for the components ofthe specific force /; three for the, the correspondingsensed specific forces af; three for the componentsof the angular velocity w; and three for the sensedangular velocities sH>. On each graph, three curveswere plotted: the first representing the aircraft's val-ues, the second denoting the simulator's values, andthe third giving the difference between the first two.In all cases, the conclusions based on the vestibularmodel results do not differ appreciably from onesbased on motion time histories, and so only the lat-ter will be shown here.

These results were then examined visually. However,since this type of evaluation would clearly be sub-jective, complementary objective comparison tools,called the Performance Indicators were also devised.The first of these indicators, PI1, is intended toyield a single numerical value which describes theaverage error in the motion variables experienced bythe simulator pilot, while the second indicator, PI'2,describes the average error in the rate of change ofthe same variables. The two indicators are describedas Pli = WQ(A + B) where i 6 {1,2} and where:

These are then summed over the complete maneu-ver, of duration T, and normalized by T and by thesampling frequency T (20 Hz)—that is, by the totalnumber of elements in the summation.

The second performance indicator, P/2, aims toevaluate the difference between the derivative of thesimulator and aircraft specific forces (and angularvelocities), and is defined as:

A/fct A/Af"At At

At At

(10)

(11)

where, once again, the subscript k represents thecomponent X, Y or Z, being considered. Thus, thederivative of the specific force A/fc^Ai (or of theangular velocity, Awfcj/Ai) component is evaluatedat time t using a first backward difference, whereAt is \IT — 0.05 sec. The error in this quantityis taken as the absolute value of the difference be-tween aircraft's and simulator's values. These arethen summed over the duration of the maneuver andnormalized by (FT — 1) since the summation nowbegins at t = At

A

B

PHX

+ +

(6)

(7)

Thus, each performance indicator is a weighted av-erage of six component indicators, corresponding tothe 6 motion channels. Moreover, since translationalquantities have different unit dimensions than an-gular ones, all quantities were normalized by theircorresponding upper limits amax and u>max from Ta-ble 3.

The component indicators which make up PI1 aredefined as follows:

FT

<=o

t=0

(8)

(9)

where the subscript k represents the component X,Y or Z, being considered. Thus, the absolute valueof the difference between a component specific force(or angular velocity) experienced in the aircraft andin the simulator is evaluated at each time step t.

4.2 Graphical examples:

Seven plots are now presented to illustrate the re-sults obtained. These are a condensed version ofthe plots previously mentioned, for the sake of com-pactness. Four curves now appear on each plot: afine dotted line which shows the aircraft's behavior;a coarser dotted gray line which represents the be-haviour of the 6-DOF Stewart platform; a black solidcurve showing the behaviour of the 3-DOF platformunder consideration; and finally, a dashed line whichshows the difference between the two simulators (6-DOF and 3-DOF). No angular velocity plots havebeen presented in this paper since most of the 3-DOF architectures considered produce exactly thesame motions as the 6-DOF platform: only the YAWaxis of HPR motion bases and the HF emulator pro-duced different angular time histories. Selected re-sults are now shown for each of the four maneuvers,in turn.

Take-Off Maneuver (TOM): Early in this ma-neuver, the aircraft is subjected to a relatively largeamplitude low frequency longitudinal acceleration asthe aircraft accelerates down the runway. Later inthe maneuver, at t — 17s a high frequency motionis apparent when the engine failure occurs.

Figure 5 shows the X specific force produced by the6-DOF STW@PH and the 3-DOF SPH@PH sim-ulations. Tilt-coordination begins at t = 3s in

43American Institute of Aeronautics and Astronautics

both cases. However, the tilt coordination rate limit(of 3°/sec) prevents both simulators from produc-ing an X specific force buildup which is as rapidas in the aircraft. When the nosewheel is rotated,(at t = Us), the tilt angle is further increased inboth simulators to produce a larger X specific force.The circled region highlights the weakness of theSPH@PH in producing a high frequency accelera-tion: while the STW@PH manages to quickly reducethe X specific force in the same direction as the air-craft (though not to the same extent), the sphericalmotion base is constrained by the low frequency na-ture of its tilt-coordination. This difference is clearlyvisible in the A.Fx curve.

Figure 5: Fx and Fz in the TOM.

In a separate test with the same maneuver, the Zspecific forces produced by a 6-DOF STW@PH mo-tion base and by the 3-DOF SPH+HF motion baseare also shown in Fig. 5. From this plot, it becomesclear that both simulators do a poor job of simulat-ing this channel of motion. The reason, well knownin flight simulation circles, is that tilt-coordination

cannot be called upon to produce any vertical ac-celeration. Furthermore, in the attempt to generatea longitudinal specific force, any platform will in-variably be constrained to generate positive (down-ward) values of Fz. The first circled region in thisplot shows a sudden deviation of the SPH+HF fromthe STW which is due to the position of the pilotwith respect to the center of rotation (Ro). As a re-sult of this displacement, when the tilt-coordinationprocess begins, the pilot is subjected to an upwardacceleration. The second circled region highlightsan area where the HF emulator produces a bene-ficial effect. These and other graphical results forthe TOM confirm that the spherical motion baseappears almost as effective as the Stewart platformin this maneuver. In particular, the SPH@PH andSPH@CG architectures produce results which areespecially close to the STW@PH curves. HPR ar-chitectures also performed relatively well, especiallyinto the Z linear channel of motion. However, theirweakness showed up when the Z angular channel isconsidered since no rotationnal motion is possible forthem, even if these are required by the engine-failuresimulation.

This analysis is confirmed, for TOM, by the valuesof the performance indices PIl and PI'2 as shownin Table 4. This table summarizes the objectiveanalysis by giving for each of the maneuver the top-three 3-DOF architectures and their correspondingPIl and PI2 values, as well as the best performingSTW motion base and the worst architecture.

Table 4: Performance Indicators results for severalarchitectures (PIl, PI'2).

TOM

TEM

TIM

TAM

Best 3-DOF

Best 6-DOFWorst 3-DOF

Best 3-DOF

Best 6-DOFWorst 3-DOF

Best 3-DOF

Best 6-DOFWorst 3-DOF

Best 3-DOF

Best 6-DOFWorst 3-DOF

SPH@PH(10.091, 0.190)SPH@CG(10.093, 0.192)SPH@CP(10.123, 0.214)STW@PH(10.112, 0.200)HPR+HF(10.307, 0.219)SPH@PH(13.724, 0.299)SPH@CP(13.782, 0.273)SPH@CG(13.755, 0.293)STW@CP(13.810, 0.276)HPR@CP(13.836, 0.277)SPH@PH(0.577, 2.035)SPH@CG(0.576, 2.073)HPR@PH(0.579, 2.051)STW@PH(0.579, 2.071)SPH+HF(0.589, 2.241)SPH@CP(1.019, 0.403)HPR@CP(1.045, 0.369)HPR+HF(1.052, 0.362)STW@CP(0.996, 0.353)SPH+HF(1. 084, 0.388)

44American Institute of Aeronautics and Astronautics

Turn-Entries Maneuver (TEM):This maneuveris the only one in which relatively large amplitudetranslational accelerations and angular velocities aregenerated in all three channels of motion for the en-tire duration of the maneuver. Figure 6 shows theFx motion channel as it is simulated by STW@CPand HPR@CP. The near-zero AFz curve shows thatthe 3-DOF simulation is almost identical to the 6-DOF simulation. Recall that the angular velocitiesproduced by both these simulators are identical ex-cept in yaw.

-0.50 I10

i20

I '30 40

Time (s)

-3.0

other hand, have no way of compensating for the lat-eral specific force produced by the bank angle. Onceagain, the Fz specific force was poorly reproducedin most cases, including the Stewart platform. Infact the simulator motion produced for this maneu-ver was nearly the same for all the 9 architecturesconsidered, and hardly differed for the 3-DOF and6 DOF simulators. Nevertheless, based on a visualinspection of their results, SPH@CP, SPH@CG andHPR@CP seemed to produce the best motion of the3-DOF motion bases, while the three spherical ar-chitectures garnered the best results in terms of theperformance indicators (see Table 4).

Throttle Impulse Maneuver (TIM): This thirdmaneuver takes place completely in a vertical planeand all the cues that the pilot senses are in thatplane. Moreover, this maneuver is the smoothestof the four studied here, and contains only low fre-quency motions. This therefore explains the excel-lent quality of simulation that was obtained with allthe simulators considered. Figure 7 shows the mo-tion produced by SPH@CG and STW@CP. It can benoted that all three curves are almost superposed forthe entire maneuver.

i.oo

Figure 7: Fx in the TIM.

Figure 6: Fx and Fy in the TEM.

The similarity between the performance of a 3-DOFsimulator and a 6-DOF simulator is again clearlyvisible from Fig. 6, where the SPH@CP architec-ture is used as a case in point. It is also clear fromthis figure that, during this maneuver, there is alarge difference between the amplitude of aircraft'slateral specific force (Fy) and that experienced inboth simulators. The aircraft tends to produce near-coordinated turns (i.e. the centripetal accelerationcompensates lateral component of the gravity vectorinduced by the bank angle). The simulators, on the

In fact this maneuver generates high frequency ac-celerations at only two times in its 40 seconds du-ration. These high frequency accelerations lead toa half-second delay which can be observed duringthe steep changes in Fx. However, the more seri-ous effect of these high frequency accelerations arethe sudden peaks (false cues) which are visible onthe Fx curves produced by both simulators. Noticehowever that the false cues produced by the Stew-art platform are almost three times worse than forthe 3-DOF SPH motion base. In fact, the sever-ity of these false cues is proportional to the lengthof Ro since they represent the translational accel-eration induced by the angular acceleration caused

45American Institute of Aeronautics and Astronautics

by the onset of tilt coordination. Thus, no suchpeaks were observed in the @PH simulations where\\Ro\\ = 0. These motion bases therefore tended toproduce the best results for the TIM, as verified bythe performance indicator values in the third columnof Table 4.

Turbulence Area Maneuver (TAM): Airline pi-lots who train in simulators consider that the mo-tion base's ability to adequately render HF acceler-ations such as turbulence or mechanical vibrationshas a strong influence on their overall perception ofrealism. Hence this fourth maneuver is crucial tothe evaluation of motion platforms with fewer than6-DOF. However, since these accelerations are ran-domly generated and not due to pilot inputs, thegeneral form of the simulated curve, such as its am-plitude and frequency, tends to be more importantthan obtaining an exact, replication of the aircraft'sbehavior. Figure 8 provides a good example of thissince both simulators generate an adequate likenessof the aircraft's longitudinal specific force Fx, eventhough neither is able to reproduce it exactly.

However, as for all other maneuvers, the verticalspecific force Fz is much more difficult to repro-duce. As an example, consider Fig. 8 which showsthe vertical specific force obtained with STW@CPand SPH+HF. In both cases, the motion producedin this degree of freedom has only about one third ofthe amplitude that was produced in the aircraft. Infact the amplitude obtained with the 3-DOF simula-tors without the HF emulator produced even smallerFz value and, in the worst case, with SPH@PH,the vertical specific force was basically zero. Fi-nally, considering all channels of motion, it appearedthat SPH+HF and HPR+HF, as well as SPH@CPor SPH@CG were best able to simulate the TAM,and with a realism equivalent to the 6-DOF Stewartplatform. Even though the performance indicatorvalues seemed to be less relevant in the evaluationof TAM, they are nevertheless presented in Table 4.

5 Conclusion fc Future WorkThis paper has investigated the potential of a vari-ety of 3-DOF motion platforms for the simulationof large transport aircraft motions. These platformscould be constructed and operated more econom-ically than the present standard Stewart platform.In addition, such platforms might be appropriate forlow cost procedures training simulators or for enter-tainment applications. Two basic architectures-one with three rotational DOFs, the other withheave, pitch and roll DOFs—were compared to theconventional Stewart platform. As well variations inthe washout location and the addition of a 'high fre-quency emulator' were considered. In all, nine plat-

Time (s)

Figure 8: Fx and Fz in the TAM.

form combinations were evaluated using four ma-neuvers. The comparison was mainly performed byvisual inspection of graphical results but objectivePerformance Indicators have also been devised andused as a backup comparison tool.

The analysis of the results revealed that, in mostcases, a 3-DOF simulator is capable of producing asimulation quality comparable to that obtained withthe 6-DOF Stewart platform. Based on the results,it is concluded that:

1. Three-DOF simulators represent a feasible al-ternative to 6-DOF motion systems since they canlead to a relatively good quality of simulation forlarge transport aircraft, such as the Boeing 747.Naturally, each of the motion degrees of freedomwhich was left unchanged (for example the angularvelocities in the case of spherical mechanisms) pro-duced identical motion histories. Maneuvers such

46American Institute of Aeronautics and Astronautics

as Throttle Impulse (TIM) or Turn Entries (TEM)produced very similar results for all of the simulatorssince they involve low-frequency motions which canbe well reproduced using primarily tilt-coordination.

2. The most effective, versatile and compliant 3-DOF architecture investigated here appears to beSPH@CG since it performed well in all four maneu-vers. In addition the HPR@PH and SPH+HF per-formed well enough to deserve further investigation.

3. The weak point of the 3-DOF simulators investi-gated here is, as could have been foreseen, their in-herent incapability to simulate high frequency trans-lational accelerations. Although the pilot can besubjected to high frequency specific forces if the vec-tor RO is non-zero, these motions are coupled to highfrequency angular accelerations. Thus, they cannotbe controlled independently, in particular when us-ing a conventional washout filter algorithm.

4. Performing the washout at the pilot's head re-moves the spurious cues generated by washout ar-tifices such as tilt coordination. However, it alsoobviates the possibility of using the HF emulator tosimulate high frequency translational accelerationsin the 3-DOF motion bases.

Future work will entail test sessions with airlinepilots on a real simulator (whose motion can beconstrained in order to simulate a 3-DOF system),as well as the design of a 3-DOF simulator. Itwould also be of interest, to develop a completelynew washout algorithm, which could be optimizedto achieve the best performance from a 3-DOF mo-tion base.

6 AcknowledgmentsThe work reported here was funded by the Natu-ral Sciences and Engineering Research Council ofCanada (NSERC) under a Collaborative ProjectsGrant.

[4] Yang, P.H, Waldron, K. J. and Orin, D.E., "Kinematics of a Three Degree-of-Freedommotion Platform for a Low-Cost Driving Sim-ulator", Proceedings of the 5th Symp. on Ad-vances iri Robot Kinematics, Portoroz, Slove-nia, June 1996.

[5] Repperger, D. W., "Study of supermaneu-verable flight trajectories through motion fieldsimulation of a centrifuge simulator.", Journalof Dynamic Systems, Measurement and Con-trol, Transactions of the ASME, Vol 114, No2, June 1992, pp 270-277.

[6] Leung, Y. M., "Solution of the General FlightEquations in Real Time", Master Thesis, De-partment of Aerospace and Engineering, Uni-versity of Toronto, 1985.

[7] Hanke, C. R. and Nordwall, D. R., "The Simu-lation of a Jumbo Jet Transport Aircraft, Vol-ume 11: Modeling Data", NASA CR-114494,Sept 1970.

[8] Gum, D. R., "Modeling of the Human Forceand Motion-Sensing Mechanisms", AFHRL-TR-72-54, June 1973.

[9] Nahon, M. A., Reid, L.D., Kirdeikis, "Adap-tive Simulator Motion Software with Supervi-sory Control", Journal of Guidance, Control,and Dynamics, Vol. 15, No 2, March-April1992, pp 376-383.

[10] Reid, L. D. and Nahon, M. A., "Flight Sim-ulation Motion-Base Drive Algorithms: Part1 - Developing and Testing the Equations",UTIAS no. 296, chapter 3, December 1985.

[11] Reid, L. D. and Nahon, M. A., "Response ofAirline Pilots to Variation in Flight SimulatorMotion Algorithm", Journal of Aircraft, Vol25, No 7, July 1988, pp 639-646.

References

[1] Crassous de Medeuil, C., "Evolution des sim-ulateurs d'avions civils.", Onde Electrique,VOL 68, No 6, Nov-Dec 1988, pp 35-41.

[2] Lapiska, C., Ross, L. and Smart, D., "Flightsimulation. An overview", Aerospace Amer-ica, Vol. 31, No 8, August 1993. pp 14-17, 33.

[3] Shiabev, V.M., "New concept of the motionsystem for the low cost flight simulator: De-velopment and design.", presented at the 1993AIAA FST Conference, 1993.

47American Institute of Aeronautics and Astronautics