M O D E L L I N G M A N U A L C O N T R O L O F S T R A I G H T T R A J E C T O R I E S
W I T H A P E R S P E C T I V E F L I G H T - P A T H D I S P L A Y
Max Mulder
Delft University of Technology, Faculty of Aerospace Engineering, P.O. Box 5058, 2600 GB Delft, The Netherlands
e-mail: m.mulder@lr.tudelft.nl
Abstract. A perspective flight path display shows the flight trajectory to be flown in a synthetic three-dimensional world. The application o f such a display has important conséquences for a pilot because the guidance information is presented via spatial sources o f information. To understand pilot manual controi behaviour with a perspective display, it is essential to investigate the manner in which pilots use thèse oprical eues. The paper describes the approach chosen and discusses results o f one o f the experiments. Keywords. Perspective flight-path display, Manual controi, human operator modelling
1. I N T R O D U C T I O N
A perspective flight-path display, s h o w i n g t h e p l a n n e d trajectory t o t h e p i l o t i n a synthetic three-dimensional w o r l d ( F i g u r e 1), is not a new concept. Since t h e early 1950's i t h a s been h y -pothesized t h a t such a p i c t o r i a l display c o u l d m e a n , i n m a n y ways, a n i m p o r t a n t i m p r o v e m e n t i n informationtransfer t o t h e p i l o t . Its a p p l i c a -t i o n was i m p r a c -t i c a l , however, due -t o -technical l i m i t a t i o n s .
B a s i c a l l y , t w o developments i n technology m a d e the p i c t o r i a l display concept p r a c t i c a l . F i r s t , r a p i d i m p r o v e m e n t s i n c o m p u t e r technology m a d e sufficiently detailed real-time graphies possible. Second, the advance o f new p o s i t i o n i n g
Systems,
such as GPS ( G l o b a l P o s i t i o n i n g System) a n d MLS ( M i c r o w a v e L a n d i n g S y s t e m ) , p r o v i d e d t h e c a p a b i l i t y o f m e a s u r i n g the p o s i t i o n of the aircraft w i t h a sufficiënt u p d a t e rate.T h e a p p l i c a t i o n o f a perspective display i n t h e cockpit has i m p o r t a n t conséquences. I n a conven-t i o n a l cockpiconven-t conven-the p i l o conven-t m e n conven-t a l l y reconsconven-trucconven-ts conven-t h e aircraft's s p a t i a l a n d t e m p o r a l s i t u a t i o n f r o m a n u m b e r o f planar, i.e. t w o - d i m e n s i o n a l , displays. W i t h a perspective flight-path display this infor-m a t i o n is presented i n a spatial f o r infor-m a t [Theunis-sen a n d M u l d e r , 1995].
A t t h e Delft U n i v e r s i t y o f Technology, research
Fig. 1. The Tunnel-in-the-Sky display
is being conducted t o investigate t h e i m p l i c a t i o n s a perspective flight-path display has o n p i l o t ' s m a n u a l controi behaviour. T h e m a i n subject o f interest is n o t , however, whether such a display w i l l lead t o a n i m p r o v e d m a n - m a c h i n e interface. R a t h e r , t h e research i m p e t u s is t o détermine hous a pilot is able t o controi a c o m p l e x d y n a m i c System (the aircraft) along a spaceconstrained t r a -jectory, w i t h a perspective flight-path display as p r i m a r y source o f i n f o r m a t i o n . O n c e this ques-tion has been answered, a n a t t e m p t c a n be m a d e to represent t h e i m p o r t a n t characteristics o f t h e
p i l o t i n a m a t h e m a t i c a l model
T h i s paper describes one of the experiments w h i c h have been conducted. T h e intent is to show clearly the m a n n e r i n w h i c h the research issues are ap-proached. Section 2 discusses the d e c o m p o s i t i o n of the p r o b l e m i n t o different subsets. T h e n re-sults f r o m a cue-inventory are presented i n sec-t i o n 3. In order sec-to invessec-tigasec-te some of sec-the hy-potheses f o l l o w i n g f r o m this cue-inventory, an ex-p e r i m e n t has been conducted. Section 4 describes the setup of t h i s experiment w h i l e sections 5 a n d 6 discuss the t i m e - d o m a i n a n d frequency-domain results f r o m the experiment respectively. F i n a l l y , section 7 contains a discussion of the approach followed a n d conclusions.
2. T O W A R D S A C O N T R O L - T H E O R E T I C M O D E L O F P I L O T M A N U A L C O N T R O L
B E H A V I O U R W I T H A P E R S P E C T I V E F L I G H T - P A T H D I S P L A Y
I n [ M u l d e r , 1995] the m e t h o d o l o g y of the research project has been discussed. B e l o w , the m a i n points of interest are briefly repeated.
2.1. Research goal
O u r goal is to u n d e r s t a n d a n d , u l t i m a t e l y , to m o d e l the m a i n characteristics o f p i l o t m a n u a l control b e h a v i o u r w i t h a perspective flight-path display. T h e p a r t i c u l a r research interests are es-p e c i a l l y the information-transfer between the p l a y a n d the p i l o t , i n c l u d i n g the influences of dis-p l a y design variables a n d the effects of a d d i t i o n a l display symbology.
2.2. Modelling approach
T h e p i l o t ' s task is to follow the reference trajec-tory, a t y p i c a l guidance task. B a s e d o n the char-acteristics of the reference trajectory, the guidance task can be d i v i d e d i n t o a n u m b e r of phases (or sub-tasks):
1. to m a i n t a i n a straight section o f the trajec-tory,
2. to m a i n t a i n a curved section of the trajectory, 3. to control a t r a n s i t i o n between a straight a n d a curved section of the trajectory a n d vice versa.
In other words, or, f r o m a system-theoretical p o i n t of view, f o l l o w i n g the p l a n n e d trajectory leads to m a i n t a i n i n g a series of different system steady-states (or references) a n d c o n t r o l l i n g transitions between these steady-states. T h e m o d e l l i n g
at-tempts are s t r u c t u r e d a c c o r d i n g to t h i s decompo-sition p r i n c i p l e .
M a i n t a i n i n g a certain state of the s y s t e m against disturbances is s i m p l y a r e g u l a t i o n task. T o m o d e l this task, t w o w e l l k n o w n m o d e l l i n g m e t h o d o l o -gies can be a p p l i e d : T h e classical a p p r o a c h , re-s u l t i n g i n a m u l t i - c h a n n e l verre-sion o f M c R u e r ' re-s crossover-model [ M c R u e r et a l . , 1965], a n d a n op-timal control approach, u s i n g the O p t i m a l C o n t r o l M o d e l ( O C M ) of K l e i n m a n et a l . [ K l e i n m a n et a l . 1969]. T h e t r a n s i t i o n phase between t w o different steady-states can be m o d e l l e d u s i n g a n extension to the conventional O C M , i.e. the O p t i m a l C o n -t r o l a n d P r e v i e w M o d e l ( O C P M ) , w h i c h has been described i n [ M u l d e r , 1995].
In the f o l l o w i n g , the discussion w i l l be restricted to the regulation task o f f o l l o w i n g straight sections of the t u n n e l trajectory.
3. O P T I C A L C U E S I N A S T R A I G H T T U N N E L S E G M E N T
3.1. General
A perspective flightpath display shows the p l a n -ned trajectory i n a s y n t h e t i c t h r e e - d i m e n s i o n a l w o r l d . T h e task o f the p i l o t is to c o n t r o l the air-craft a l o n g this p a t h . T o fulfil his task, the p i l o t estimates the state o f the aircraft w i t h respect to the trajectory a n d , based o n the estimated state, decides u p o n a n d activates the necessary c o n t r o l action(s). I n order to u n d e r s t a n d the i n t e r a c t i o n between the p i l o t a n d the display i t is essential to get grip of this state e s t i m a t i o n process. T h i s has been investigated f r o m two different points of view.
In [ M u l d e r , 1994] i t was e x a m i n e d w h a t effects a s p a t i a l display has o n the c o n t r o l b e h a v i o u r of a pilot: T h e man i n the m a n - m a c h i n e interface was taken to be the central element. M a i n questions that were addressed were the a v a i l a b i l i t y , the use-fulness a n d the p o t e n t i a l u t i l i z a t i o n o f a l l sorts of s p a t i a l , or o p t i c a l sources o f i n f o r m a t i o n present i n the real w o r l d a n d / o r i n a perspective display. In [ M u l d e r , 1996] the machine side was the m a i n issue. A n a t t e m p t was m a d e to m a k e a n i n v e n t o r y of a l l s p a t i a l cues i n a basic perspective f l i g h t - p a t h display. Here, irrespective o f the h u m a n operator, m a t h e m a t i c a l relations are derived t h a t express the state of the aircraft w i t h respect to the ref-erence trajectory i n t e r m s of these o p t i c a l cues. O b v i o u s l y , m o s t o f the available cues w i l l p r o b -ably be neglected b y the operator for reasons o f their p e r c e i v a b i l i t y thresholds or s i m p l y because
XTE/TAE -5 [deg] 0 [deg] + 5 [deg]
- 5 [ m ]
0 [ m ]
+5 [m]
Fig. 2. Distortion of the symmetry of the tunnel display
they are t o o far-fetched for the operator t o be rec-ognized as p o t e n t i a l sources o f i n f o r m a t i o n . S o m e of the cues, however, are so evident a n d c a n be so easily perceived f r o m the display t h a t i t is m o s t probable that they are used b y the operator. It are these p a r t i c u l a r cues w h i c h are t h e m a i n sub-ject o f investigation.
3.2. Straight tunnel sections
In t h i s paper, the discussion w i l l be restricted t o sections of the trajectory that are straight a n d infinitely l o n g . F u r t h e r m o r e , wind-effects are ne-glected. A s has been discussed i n [Mulder, 1995], i n case o f no p o s i t i o n errors (and relatively s m a l l aircraft a t t i t u d e angles) the t u n n e l image w i l l b e symmetrie. A n y déviation f r o m the trajectory leads t o a d i s t o r t i o n o f this s y m m e t r i e c o n d i t i o n ( F i g u r e 2 ) . T o m i n i m i z e the discrepancy between the a c t u a l a n d the p l a n n e d trajectory, the opera-tor m u s t m a i n t a i n a s y m m e t r i e t u n n e l image. In [ M u l d e r , 1996] i t is shown t h a t there are m a n y o p t i c a ! cues i n t h e display t h a t are directly related to t h e déviation o f the aircraft p o s i t i o n a n d a t t i -tude f r o m the référence trajectory. F o r example, the aircraft h e a d i n g error, or Track-Angle-Error
(TAE), c a n be perceived f r o m t h e t r a n s l a t i o n of t h a t p a r t o f the t u n n e l w h i c h is located at a large
distance f r o m t h e v i e w p o i n t , as was observed i n [ G r u n w a l d a n d M e r h a v , 1976] a n d [Theunissen, 1994]. I n t h i s paper t h e discussion w i l l be re-stricted t o t h e o p t i c a l cues related t o a p o s i t i o n error.
3.3. Optical cues
T h e l a t e r a l a n d v e r t i c a l p o s i t i o n errors c a n b e es-t i m a es-t e d u s i n g a large n u m b e r o f o p es-t i c a l cues o f w h i c h the most salient ones are i l l u s t r a t e d i n F i g -ure 3. F i r s t o f a l l , we have the relative l a t e r a l displacements e,j a n d o f the t u n n e l frames i a n d j located at distances D,- a n d Dj ( w i t h Dj = Di + AD, a n d A D the fixed distance be-tween t w o successive frames). C h a n g e s i n these relative l a t e r a l displacements f r o m t h e zero-error c o n d i t i o n are a f u n c t i o n of l a t e r a l p o s i t i o n error X o n l y ( i n a p p r o x i m a t i o n ) :
Scij = +KX
\ DiDj ) (1)
(2) w i t h « a display constant dépendent o n the field-of-view o f t h e perspective p r o j e c t i o n a n d the size of the display screen.
T h e same holds for t h e relative v e r t i c a l
Fig. 3. Position error eues in a straight tunnel section
ments m¡ a n d vy, w h i c h are a f u n c t i o n o f t h e vertical p o s i t i o n error V o n l y ( i n a p p r o x i m a t i o n ) :
* = - K W )
/Dj -Dj\ \ DiDj ) ova = +KV (3) (4) Note that i n t h e f o r m u l a s stated above, the dévi-ations are f o r a l l possible pairs o f t u n n e l framesi a n d j. A s one c a n see, however, the a p p l i
-cability o f these cues détériorâtes fast when the distances i n v o l v e d b e c o m e larger. T h e
t e r m r a p i d l y decreases t h e a m p l i t u d e s of the dis-placements below threshold.
T h e second set o f cues resuit f r o m t h e l o n g i t u d i -n a l li-nes co-n-necti-ng t h e i -n d i v i d u a l t u -n -n e l frames. T h e angles t h a t the projections o f these lines m a k e w i t h the h o r i z o n are also m e r e l y a f u n c t i o n o f lat-eral a n d v e r t i c a l p o s i t i o n error o n l y : V X (5) Ui = W W (5) V X (6) U>2 =
w
+w
(6) V X (7) U>3 = +w
+w
(7) V X (8) W4 = +w w
(8) w i t h W the (square) t u n n e l w i d t h .A t h i r d eue results f r o m t h e i m a g i n a r y line
Con-necting the intersections of the a l t i t u d e pôles w i t h the b o t t o m o f the t u n n e l frames. T h e resuit is a n angular eue w h i c h changes a l m o s t i d e n t i c a l l y w i t h the latéral p o s i t i o n error:
W5 = - 2 *
W (9)
T h i s eue w i l l be neglected i n t h e f o l l o w i n g , be-cause i n t h e displays used i n t h e e x p e r i m e n t de-scribed below the a l t i t u d e pôles are n o t presented.
3.4. Discussion
T h e linear a n d angular o p t i c a l eues discussed above are b o t h a f u n c t i o n o f v e r t i c a l a n d l a t e r a l p o s i t i o n error only. T h e r e are t w o f u n d a m e n t a l différences between these cues.
F i r s t o f a i l , w h e n the aircraft m o v e s t h r o u g h the t u n n e l , t h e t u n n e l frames t r a n s l a t e t o w a r d s t h e perceiver, w h i l e t h e l o n g i t u d i n a l lines connecting the frames appear t o d o n o t . T h i s i s a n i m p o r -t a n -t fac-t, since -t h e m o -t i o n o f -t h e -t u n n e l frames c o u l d prevent a n accurate e s t i m a t i o n o f the o p t i -cal displacement eues: T h e p i l o t c o n s t a n t l y has t o shift attention towards a n e w set o f frames. T h e angular eues, however, o n l y change because o f a changing p o s i t i o n error, m a k i n g a shift i n
Fig. 4. Display A (X = 10 [m], TAE = -5 [deg], W = 45 [m])
Fig. 5. Display B (X = 10 [m], TAE = -5 [deg], W = 45 [m])
t i o n forwards a n d backwards i n t o the t u n n e l i m -age unnecessary.
Second, as one c a n see f r o m t h e formulas stated above, i t is clear t h a t a l a t e r a l a n d a vertical p o s i t i o n error b o t h determine a n y one o f the four a n -gles. T h i s is i n contrast t o t h e fact that a change i n t h e relative l a t e r a l (vertical) displacements o f the t u n n e l frame lines is o n l y a f u n c t i o n o f t h e lateral (vertical) p o s i t i o n error. I n other words, the angular cues are coupled a n d the linear cues uncoupled w i t h respect t o t h e l a t e r a l a n d vertical p o s i t i o n errors. T h i s is also a n i m p o r t a n t fact. T h e c o u p l i n g o f the angular cues means that a n y change i n a n y o f t h e four angles c a n be t h e re-sult o f b o t h a v e r t i c a l a n d a l a t e r a l p o s i t i o n error. T h e linear cues, o n the other h a n d , are uncoupled a n d o n l y change w i t h i n t h e same d i m e n s i o n (i.e. l a t e r a l o r vertical) as t h e o c c u r r i n g p o s i t i o n error.
3.5. Hypotheses and experiment justification
T h e discussion above shows t h e virtues a n d dis-advantages o f the two p r i m a r y sets o f cues t o esti-m a t e a p o s i t i o n error o n a straight section o f the t u n n e l display. T o e x a m i n e the usefulness o f b o t h sets a n d t h e extent t o w h i c h t h e above m e n t i o n e d characteristics influence t h e i r relative usefulness, a n experiment h a s been conducted.
T h r e e displays were defined, w h i c h are a l l abstrac-tions o f the basic tunnel-in-the-sky display:
1. D i s p l a y A, s h o w i n g o n l y t h e l o n g i t u d i n a l lines connecting the t u n n e l frames (Figure 4 ) ,
2. D i s p l a y B, showing only t h e tunnel frames
themselves ( F i g u r e 5),
3. D i s p l a y C, a c o m b i n a t i o n o f displays A a n d
B ( F i g u r e 6).
Fig. 6. Display C (X = 10 [m], TAE = -5 [deg], W = 45 [m])
It is clear that i n d i s p l a y A o n l y t h e angular cues are available, w h i l e i n d i s p l a y B o n l y t h e linear displacement cues are present 1. F r o m display C,
b o t h sets of cues c a n b e perceived. F u r t h e r note that i n a l l displays t h e aircraft a t t i t u d e , i.e. p i t c h angle 0, r o l l angle § a n d h e a d i n g a n g l e2 \b can a n d
w i l l be perceived i n i d e n t i c a l fashion.
T o analyze the usefulness o f the o p t i c a l cues f r o m the three displays, t w o a d d i t i o n a l variables were i n t r o d u c e d i n t h e experiment:
I T h e effect o f control channel: T h r e e control channels were a p p l i e d :
1 The angular cues could be estimated from the imaginary
lines connecting the tunnel frames' vertices. Results from a pilot questionnaire revealed, however, that this was not the case.
2 Since the reference heading angle of the tunnel is set zero,
the aircraft heading angle equals the track-angle-error.
(i) Roll: l a t e r a l t r a c k i n g only, t h e v e r t i c a l p o -sition error V was kept zero,
(ii) Pitch: v e r t i c a l t r a c k i n g only, the l a t e r a l p o -s i t i o n error X w a -s kept zero,
(iii) Dual: a c o m b i n a t i o n o f (i) a n d ( i i ) , i.e. b o t h the l a t e r a l as the v e r t i c a l p o s i t i o n er-rors h a d t o be m i n i m i z e d simultaneously. II T h e effect o f forward motion:
T w o situations were e x a m i n e d :
(i) No (forward) motion, i n w h i c h the l o n g i -t u d i n a l p o s i -t i o n o f -t h e aircraf-t was fixed, resulting i n a hovering t a s k3,
(ii) (Forward) motion, i n w h i c h the l o n g i t u d i -n a l p o s i t i o -n o f the aircraft was set free, re-s u l t i n g i n a conventional t u n n e l t r a c k i n g task.
These a d d i t i o n a l e x p e r i m e n t a l variables c a n be used t o e x a m i n e t h e usefulness o f the t w o sets o f p o s i t i o n e s t i m a t i o n cues according t o the follow-i n g a p r follow-i o r follow-i hypotheses:
I T h e presence o f f o r w a r d m o t i o n has n o effect on the p e r f o r m a n c e4 w i t h display A.
II T h e presence o f forward m o t i o n deteriorates performance w i t h display B.
III T h e a d d i t i o n o f a n a d d i t i o n a l control channel deteriorates performance w i t h display A. I V T h e a d d i t i o n o f a n a d d i t i o n a l c o n t r o l channel
deteriorates performance w i t h display B, b u t to a significantly less degree t h a n t h e perfor-m a n c e deterioration for the saperfor-me c o n d i t i o n o f display A.
T h e effects o f the independent variables m o t i o n a n d control c h a n n e l o n display C are expected t o be a m i x t u r e o f those effects o n displays A a n d B. Since display C is a c o m b i n a t i o n o f displays A a n d B, the relative virtues a n d disadvantages of the c o m b i n e d sets o f cues could compensate for each other.
4. E X P E R I M E N T 4.1. Goal of the experiment
T h e goal of the e x p e r i m e n t was t w o f o l d . F i r s t o f a l l , the v a l i d i t y o f the hypotheses stated i n t h e former section m u s t be e x a m i n e d . Second, the observed control b e h a v i o u r o f t h e subjects m u s t be described a n d e x p l a i n e d w i t h a m a t h e m a t i c a l
3 In the hovering task the lateral and vertical position
er-rors result in an apparent motion in a plane perpendicular to the tunnel centerline.
4 Performance is defined here as the accuracy with which
the reference trajectory can be followed (position errors).
m o d e l .
T e s t i n g t h e hypotheses does n o t d e m a n d m u c h i n -genuity i n the e x p e r i m e n t a l design. O n e c o u l d for instance define a conventional c o m p e n s a t o r y t u n nel t r a c k i n g task, measure a l l performance v a r i -ables o f interest, a n d d o a post-hoc analysis o f the empirical d a t a u s i n g s t a t i s t i c a l tests.
T h e efforts t o describe t h e observed b e h a v i o u r v i a a m a t h e m a t i c a l m o d e l , however, are n o t so s t r a i g h t f o r w a r d . B o l d l y , one c o u l d state t h a t m a k -i n g models -is relat-ively s -i m p l e , w h -i l e v a l -i d a t -i n g t h e m c a n be extremely difficult. N a t u r a l l y , t h e m o d e l v a l i d a t i o n c o u l d b e restricted t o u s i n g t h e e m p i r i c a l t i m e - d o m a i n d a t a o n l y . M o s t , i f n o t a l l , of the widely-used operator m o d e l l i n g techniques, however, have s h o w n their a p p l i c a b i l i t y especially i n the frequency-domain.
T h e frequency-domain d a t a , i.e. the operator frequencyresponse functions, c a n be h a r d t o o b t a i n . I n o u r s i t u a t i o n t h i s is especially t r u e b e -cause:
• t h e p i l o t is o p e r a t i n g i n closed-loop, w h i c h introduces a l o t o f subtleties i n t h e identifi-c a t i o n proidentifi-cedure,
• w i t h the t y p e o f displays discussed here, the p i l o t is essentially a m u l t i i n p u t , m u l t i -o u t p u t s y s t e m .
In order t o o b t a i n t h e f r e q u e n c y - d o m a i n d a t a , a n identification m e t h o d w i l l be used t h a t was devel-oped i n [Lunteren, 1976] a n d a p p l i e d i n [Paassen, 1994]. T h e a p p l i c a t i o n o f this m e t h o d h a s i m p o r -t a n -t consequences for -the d e f i n i -t i o n o f -t h e exper-i m e n t , as w exper-i l l b e dexper-iscussed exper-i n t h e next sectexper-ion. 4.2. Identification procedure
4.2.1. method. I n [Lunteren, 1976], a n o n -p a r a m e t r i c i d e n t i f i c a t i o n m e t h o d is develo-ped t o estimate p i l o t frequency-response functions i n closed-loop. A l t h o u g h a f u l l discussion o f t h i s m e t h o d is b e y o n d t h e scope o f t h i s p a p e r , t h e m a i n concepts w i l l b e briefly addressed.
B a s i c a l l y , for each p i l o t i n p u t s i g n a l a n i n d e p e n -dent reference (or, i n o u r case, disturbance) sign a l , u s u a l l y a s u m o f sisignusoids, has t o b e i sign t r o duced into t h e closed p i l o t / v e h i c l e l o o p . I n a w e l l -chosen e x p e r i m e n t a l setup, a l l variables o f inter-est t h e n c o n t a i n m u c h power at t h e frequencies o f the disturbance signals a n d o n l y l i t t l e power at a l l other frequencies. T h e operator's frequency-response f u n c t i o n c a n t h e n be e s t i m a t e d b y inter-p o l a t i o n a n d inter-p r o inter-p e r m a n i inter-p u l a t i o n o f t h e F o u r i e r coefficients o f the F F T - e d f r e q u e n c y - d o m a i n d a t a i n a m a n n e r described i n d e t a i l i n [Paassen, 1994].
Pilot
n l2H,
PX41
Aircraft
%3Fig. 7. Pilot model used in the identification process (lateral control channel). (In this figure, »i and »2 are the
two disturbances, 6„ is the pilot's lateral control signal (aileron), while the signal n i» the pilot remnant signal. The symbols <j> and X depict the aircraft's roll angle and lateral position error respectively. The pilot frequency-response functions are the two blocks Hp^ (inner loop) and HPX (outer loop).)
For a l l frequencies o f the référence sinusoids, a n e s t i m a t i o n i s o b t a i n e d o f the Operator frequency-response functions. I n this e s t i m a t i o n process, i t is assumed t h a t the Operator does n o t insert a n y noise i n t o t h e l o o p . Since this is not t h e case, the estimations c a n be biased a n d contain uncer-tainties. I n [Paassen, 1994] i t h a s been shown how a n a l y t i c expressions c a n be o b t a i n e d for the bias a n d variance terms o f the frequency-response functions.
4.2.2. Pilot Model. T h e control o f t h e l a t e r a l m o t i o n o f the aircraft requires the p i l o t t o close at least three feedback loops: F i r s t , serving as t h e most inner l o o p , t h e aircraft's r o l l a t t i t u d e is fed back. Second, t h e aircraft's heading angle serves as t h e m i d d l e l o o p , a n d finally the lateral p o s i t i o n is t h e outer l o o p . T h e same c a n b e stated for t h e control o f the aircraft v e r t i c a l m o t i o n .
T h u s , t o use t h e aforementioned identification m e t h o d , three independent i n p u t signais (for b o t h Channels) m u s t b e inserted t o estimate the three Operator feedback loops. I n m u l t i - l o o p tasks i t is often assumed, however, t h a t a l l p i l o t equaliza-t i o n is a p p l i e d equaliza-t o geequaliza-t a equaliza-tighequaliza-t a n d well-operaequaliza-ting inner l o o p . O u t e r loops are then f e d back us-ing s i m p l e gains. T h i s a s s u m p t i o n allows us t o decrease t h e n u m b e r o f i n p u t signais for each
Channel
f r o m three t o t w o : T h e first serves forthe e s t i m a t i o n o f the inner (attitude) l o o p , while the second w i l l b e used t o estimate t h e c o m -b i n e d m i d d l e / o u t e r loops. T h e c o m -b i n e d outer loop frequencyresponse function c a n then b e d i -v i d e d i n t o its m i d d l e - / o u t e r - l o o p components us-ing p a r a m e t r i c Operator models. T h i s is the ap-p r o a c h followed here. T h e resulting ap-p i l o t m o d e l is i l l u s t r a t e d i n F i g u r e 7.
4.2.3. Dual-axes tasks. W h e n b o t h t h e v e r t i c a l
as the l a t e r a l p o s i t i o n errors have t o be m i n i m i z e d
simultaneously, the
Operator
m o d e l consists o f s i x input signais a n d two o u t p u t signais. A p p l y i n g the aforementioned a s s u m p t i o n s , i.e. c o m b i n i n g the m i d d l e a n d outer loops, results i n a Operator m o d e l w i t h four i n p u t s a n d 2Outputs.
T h e identification m e t h o d c a n also c o m p u t e a l l P o t e n t i a l cross-couplings between t h e t w o Chan-nels. I n t h e f o l l o w i n g , however, i t is assumed t h a t i n dual-axes tasks t h e l a t e r a l a n d v e r t i c a l Chan-nels are controlled i n p a r a l l e l , neglecting a l l cross-coupling effects. P r e l i m i n a r y investigations have shown t h a t this is a safe a s s u m p t i o n .
4.2.4. Choice of input signais. T h e l a t e r a l a n d vertical c o n t r o l Channels are b o t h d i s t u r b e d w i t h two independent i n p u t signais each. T h e i n p u t signais were a l l c o m p u t e d as a s u m o f 12 sinu-soids. T h e a m p l i t u d e s o f thèse sinusoids for a l l 12 frequencies were d e t e r m i n e d b y t h e choice o f the i n p u t s i g n a l s p e c t r u m . These spectra s h o u l d b e chosen s i m u l t a n e o u s l y w i t h the System d y n a m i c s . 4.2.5. Choice of system dynamics. T h e Sys-t e m d y n a m i c s were Sys-the linearized d y n a m i c s o f a s m a l l business j e t , the C e s s n a C i t a t i o n I . F i g u r e 8 shows t h e s i m u l a t e d aircraft d y n a m i c s for the lateral c o n t r o l Channel a n d the i n s e r t i o n points o f the t w o l a t e r a l disturbance signais. A well-chosen c o m b i n a t i o n o f the
System
d y n a m i c s , t h e distur-bance signais' spectra a n d the intensity o f t h e dis-turbance signais, is c r u c i a l i n t h e e x p e r i m e n t . 4.3. Expérimental setup4.3.1. Design. T h e expérimental design w a s a 3 x 3 x 2 factorial design ( d i s p l a y , Channel,
ft.
ft„ft.
•-ft.
ft =
ft
* 75
( J +Xty
S)
EL
s K3Fig. 8. Linearized System dynamics (latéral coiitrol channel). (In this figure, »i and ¿2 are the two disturbances, Sa is the pilot's latéral control
sig-nal (aileron). The symbols tj> and j> depict the aircraft's roll and heading angles, white X rep-résenta the latéral position error.)
m o t i o n ) , r e s u l t i n g i n 18 conditions ( T a b l e 1). E v -ery c o n d i t i o n was conducted 14 times: T h e first eight runs were used as t r a i n i n g runs a n d the last six runs were the a c t u a l measurement runs. T h e 18 conditions were f u l l y r a n d o m i z e d over a l l 252 (18 x 14) runs.
4.3.2. Setup. Subjects were seated i n a chair i n a darkened, noise-free r o o m i n front o f a 17 inch C R T m o n i t o r . T h e c o n t r o l m a n i p u l a t o r was a servocontrolled h y d r a u l i c sidestick w i t h c o n -ventional characteristics. T h e display update-rate was 20 H z . T h e t u n n e l was presented as a grey wireframe o n a b l a c k - a n d - w h i t e b a c k g r o u n d . A flight-path vector was n o t presented.
4.3.3. Subjects. T h r e e professional pilots c o l -l a b o r a t e d i n the experiment. R e s u -l t s o f o n -l y t w o pilots are available at t h i s t i m e .
4.3.4. Task. T h e task is s i m p l y to fly t h e aircraft as accurately as possible t h r o u g h t h e t u n n e l . I n other words: M i n i m i z e a l l o c c u r r i n g p o s i t i o n er-rors, despite t h e effect o f t h e disturbances a c t i n g on t h e vehicle.
4.3.5. Questionnaire. A f t e r c o m p l e t i o n o f t h e experiment, a l l subjects received a p i l o t question-naire i n w h i c h they were requested t o answer a
5 R = roll, P = pitch, D = dual.
c o n d i t i o n d i s p l a y c h a n n e l6 m o t i o n 1 A R ofF 2 A P off 3 A D off 4 A R o n 5 A P o n 6 A D o n 7 B R off 8 B P off 9 B D off 10 B R o n 11 B P o n 12 B D o n 13 C R off 14 C P off 15 C D off 16 C R o n 17 C P on 18 C D o n T a b l e 1 E x p é r i m e n t a l c o n d i t i o n s
n u m b e r of questions. T h e subjective results o f this questionnaire were used t o increase insight i n t o the observed, i.e. objective, overt c o n t r o l be-h a v i o u r .
5. T I M E - D O M A I N R E S U L T S
T h e performance variables o f interest were a l l recorded d u r i n g t h e measurement r u n s o f the ex-p e r i m e n t . Since t h e ex-p i l o t ' s task was t o fly as accu-rately as possible t h r o u g h t h e t u n n e l , t h e discus-sion w i l l be restricted t o t h e s t a n d a r d déviation o f the latéral a n d v e r t i c a l p o s i t i o n errors. T h e t i m e -d o m a i n results are e x a m i n e -d along t h e hypothè-ses of section 3. T h e s t a t i s t i c a l m e t h o d used was a conventional A N O V A followed b y a N e w m a n -K e u l s post-hoc analysis. A l t h o u g h i n d i v i d u a l dif-férences between subjects were f o u n d , t h e o v e i a l l trends were m o r e o r less équivalent. T h e results w i l l therefore be discussed u s i n g t h e d a t a o f one subject.
F i g u r e 9 shows the m e a n a n d s t a n d a r d déviation of the s i x measurements o f the s t a n d a r d déviation of the v e r t i c a l p o s i t i o n error V f o r a l l (vertical) conditions. Because i n t h e f o l l o w i n g a l l results are i l l u s t r a t e d b y t h e same g r a p h i c a l m e t h o d , a n e x p l a n a t i o n is given here. T h e lower p a r t o f t h e figure contains a s h o r t h a n d d e s c r i p t i o n o f t h e con-ditions. F i r s t of a l l , t h e figure is d i v i d e d i n three parts for a l l displays: A, B a n d C. Secondly, a ' . ' depicts t h e clean c o n d i t i o n (i.e. singleaxis v e r t i -cal control only, n o forward m o t i o n ) . T h e
5 4.5 4 3.5 3! 1-2.5 2 1.5 1 0.5 0
MBW+STO (S ran»)of vertical position (subisctA)
OaplayA +R •R DisplayB +R +R Display C *R *R +M +M 8 9 11 « Configuration #
MEAN+STD (6 rui») of lataral position (subject A) -t 1 r Qspiay A tP DisplayB t P DtaplayC +P tP 4 M 9 10 12 13 Configuration #
Fig. 9. Vertical position errors (subject A)
means t h a t the latéral control channel was added, resulting i n a dual-axis t r a c k i n g task. T h e '+M' means t h a t f o r w a r d m o t i o n was activated, while the '+R*, '+M' s y m b o l depicts t h e s i t u a t i o n t h a t b o t h a n e x t r a c o n t r o l channel as t h e forward m o -t i o n were a d d e d .
F r o m this figure i t is clear t h a t for display A the a d d i t i o n o f f o r w a r d m o t i o n has n o effect o n p i -lot performance, w h i l e the a d d i t i o n o f a n e x t r a control channel significantly (p=0.01) détériorâtes performance. T h è s e findings s u p p o r t hypothèses I a n d III.
For display B t h e results show t h a t there is a sig-nificant (p=0.01) effect of the a d d i t i o n of forward m o t i o n o n p i l o t performance, w h i l e the a d d i t i o n of a n e x t r a c o n t r o l channel has n o effect o n p i l o t performance. Thèse findings s u p p o r t hypothèses II a n d I V .
T h e c o m b i n a t i o n o f displays A a n d B, i.e. display C, shows b a s i c a l l y t h e same trends as those for display B. F u r t h e r m o r e , for three o f the four con-ditions, p i l o t performance was superior w i t h this display. T h e performance détérioration due t o the a d d i t i o n o f f o r w a r d m o t i o n is s u b s t a n t i a l l y lower t h a n t h a t of d i s p l a y B, while the performance dé-térioration due t o t h e a d d i t i o n of t h e r o l l control task vanishes. T e n t a t i v e l y t h e n , one could state that the linear displacement eues are d o m i n a n t over the angular eues, a suggestion t h a t was sup-p o r t e d b y the results f r o m the sup-p i l o t questionnaire. T h e same conclusions can b e d r a w n when the performance o f the latéral control channel is e x a m -ined ( F i g u r e 10). A g a i n , the results for displays A a n d B s u p p o r t hypothèses I - I V , a l t h o u g h the performance détérioration for display A was sig-nificant o n l y at t h e p = 0 . 0 5 level. D i s p l a y C ,
how-Fig. 10. Latéral position errors (subject A)
ever, shows a m i x t u r e o f the effects o f f o r w a r d m o t i o n a n d t h e a d d i t i o n o f a c o n t r o l channel i n the sensé t h a t b o t h effects were f o u n d significant (p=0.01).
In conclusion, one c o u l d state t h a t t h e t i m e -d o m a i n -d a t a s u p p o r t t h e a p r i o r i hypothèses o f the experiment. T h e effects o f f o r w a r d m o t i o n and control channel are clear for displays A a n d B, while the results f o r display C are a m i x t u r e of the effects o f its components. A final note is t h a t the performance décréments due t o t h e a d d i t i o n of an e x t r a c o n t r o l c h a n n e l are generally larger i n the vertical channel t h a n i n the latéral channel, except for display C. T h i s c o u l d b e a t t r i b u t e d to the fact t h a t the v e r t i c a l c o n t r o l channel was j u d g e d significantly m o r e difficult t o c o n t r o l t h a n the latéral c o n t r o l channel. I n order t o f u l l y ex-p l a i n t h e causes for t h e ex-performance décréments one should take t h i s task difficuHy aspect i n t o ac-count, as w i l l b e shown i n the next section.
6. F R E Q U E N C Y - D O M A I N R E S U L T S T h e identification procédure results i n estimâtes of the inner- a n d outer-loop p i l o t frequency-response functions. T h è s e frequency frequency-responses can be c o m b i n e d w i t h the System d y n a m i c s , a l -lowing the c o m p u t a t i o n of the inner- a n d outer-loop crossover frequencies a n d phase m a r g i n s . A s has been stated above, i n the i d e n t i f i c a t i o n o f the dual tasks i t was assumed t h a t n o cross-coupling effects between t h e t w o control channels exist. F i g u r e 11 shows the outer-loop crossover frequen-cies a n d phase m a r g i n s for the v e r t i c a l p o s i t i o n t r a c k i n g task. T h è s e variables were c o m p u t e d ac-cording t o t w o approaches. F i r s t o f a i l , one c o u l d
0.91 0.8 0.7 0.6 | 0 . 5 0.4 0.3 0.2 0.1
PITCH CHANNEL outer loop crossover frequen cy (Subject A)
Display A +R +R +M +M Display B +R •FI • M *M Display C +R +R +M +M 8 9 11 12 configuration # 14 15 17 18 PITCH CHANNEL outer loop phase margin (Subject A)
Display A +R DisplayB +R +M +M Display C +R *R 8 9 11 12 14 15 configuration #
Fig. 11. Pitch channel outer loop crossover frequency and phase margin (subject A)
? ° 4
# 3 0
ROLL CHANNEL outer loop crossover frequency (Subject A)
Display A •P *P DisplayB +P +P +M +M Display C • P +P 4M +M 1 3 4 6 7 9 10 12 13 15 16 18 configuration #
ROU. CHANNEL outer loop phase margin (Subject A)
- i r ~ r - i r-f-t r - T T r-r-i r - — t 1— Display A • P DisplayB +P Display C +P 9 10 12 13 configuration M
Fig. 12. Roll channel outer loop crossover frequency and phase margin (subject A)
estimate the frequency-response functions for a i l six measurement runs for a i l conditions, result-ing i n s i x crossover frequency estimations a n d s i x phase m a r g i n estimations for each o f the 18 con-ditions. T h e circles i n the figure show the means and the v e r t i c a l line segments the s t a n d a r d dévi-ations of these s i x estimdévi-ations. T h e second ap-p r o a c h was to flrst o b t a i n a t i m e - d o m a i n average of the t i m e histories over a l l s i x measurements a n d then, u s i n g the averaged set o f t i m e histories, es-t i m a es-t e es-the crossover frequency a n d phase m a r g i n . T h i s results i n a single estimate of the variables o f interest for a i l 18 conditions, d e p i c t e d b y a cross i n the figures. N o t e t h a t generally the crosses are equal or close to the estimated means.
One can see t h a t the f r e q u e n c y - d o m a i n results generally follow the t i m e - d o m a i n r e s u l t s6. F o r
dis-6 Note that, theoretically, a higher crossover frequency
gen-erally implies a better performance and is usually
accom-p l a y A, the a d d i t i o n o f a n e x t r a c o n t r o l channel decreases the crossover frequency, a l t h o u g h the phase m a r g i n remains m o r e or less constant. A n e x p l a n a t i o n for t h i s tesult w i l l be given later since it requires knowledge of the b e h a v i o u r o f the p i -lot i n the other channel. D i s p l a y B shows a sig-nificant effect o f f o r w a r d m o t i o n w h i l e display C follows the trends of display B. T h e i m p r o v e d performance w i t h display C over display B is re-flected b y significantly higher crossover frequen-cies and lower phase m a r g i n s .
F i g u r e 12 shows the outer-loop crossover frequen-cies a n d phase m a r g i n s for the l a t e r a l p o s i t i o n t r a c k i n g task. F r o m the lower h a l f of this figure it is i m m e d i a t e l y apparent t h a t the a d d i t i o n o f a n e x t r a c o n t r o l c h a n n e l results i n a h i g h l y significant decrease i n phase m a r g i n for a i l conditions. T h e crossover frequencies, o n the other h a n d , show
panied by a smaller phase margin and vice versa.
that they are h a r d l y affected b y the control channel d i m e n s i o n . These findings are quite the o p p o -site of those o f the p i t c h channel analysis. A n e x p l a n a t i o n for the dual-axes results is obvious: T h e o r e t i c a l l y , i n a d u a l axes task the p i -lot has to d i v i d e his a t t e n t i o n over two channels, increasing his information-processing t i m e delay, w h i c h forces the p i l o t to sacrifice crossover fre-quency (and thus performance) to m a i n t a i n suffi-cient phase m a r g i n (i.e. s t a b i l i t y ) . F o r the v e r t i c a l control channel this was indeed the case. T h e lat-eral control channel, however, was regarded (sup-ported by the results of the p i l o t questionnaire) to be m u c h easier t o control t h a n the difficult p i t c h channel d y n a m i c s . T h u s , the lateral d y n a m i c s provided the p i l o t s the o p p o r t u n i t y to m a i n t a i n a relatively h i g h performance (i.e. crossover fre-quency) by s i m p l y sacrifying their phase m a r g i n . C o n c l u d i n g , one can state t h a t the frequency-d o m a i n analysis can reveal some of the uncertainties t h a t c o u l d arise f r o m e x a m i n i n g the t i m e -d o m a i n -d a t a o n l y . Instea-d o f a t t r i b u t i n g a l l ob-served trends i n the e m p i r i c a l d a t a to the indepen-dent variables of the e x p e r i m e n t , the frequency-d o m a i n frequency-d a t a revealefrequency-d t h a t part of those trenfrequency-ds are h i d d e n i n the e x p e r i m e n t a l setup itself.
7. D I S C U S S I O N / C O N C L U S I O N S A perspective flight-path display shows the trajec-t o r y trajec-to be flown i n a syntrajec-thetrajec-tic trajec-three-dimensional w o r l d . T h e aircraft's state is presented b y means o f a large n u m b e r o f s p a t i a l sources of i n f o r m a -t i o n resul-ting f r o m -the perspec-tive d i s -t o r -t i o n of the geometrical shape of the t u n n e l . In order to control the aircraft t h r o u g h the t u n n e l , the p i l o t must estimate the aircraft's state using these op-t i c a l cues.
T h e experiment described was designed to e x a m -ine some of the hypotheses resulting f r o m a cue-inventory of p o t e n t i a l o p t i c a l cues for a p o s i t i o n error. T h e hypotheses addressed the a v a i l a b i l i t y a n d relative usefulness of t w o sets of cues for a po-sition error: L i n e a r displacement cues caused b y the relative displacements of the i n d i v i d u a l t u n n e l frames a n d angular cues r e s u l t i n g f r o m the l o n g i -t u d i n a l lines connec-ting -the -t u n n e l frames. T h e results s u p p o r t e d the a p r i o r i hypotheses very well. It is s h o w n t h a t performance using the a n -gular cues o n l y (display A), t h o u g h independent of the f o r w a r d m o t i o n t h r o u g h the t u n n e l , deteri-orates fast when b o t h axes have to be controlled simultaneously. T h i s can be a t t r i b u t e d to the fact that the v e r t i c a l a n d l a t e r a l p o s i t i o n errors are
shown v i a the angular cues i n a coupled m a n n e r . Performance w i t h o n l y the linear displacement cues (display B) showed a n opposite effect. D u e to the u n c o u p l e d presentation o f the l a t e r a l a n d ver-t i c a l p o s i ver-t i o n error, ver-the d u a l axes ver-task h a d o n l y m i n o r effect o n p i l o t performance. T h e f o r w a r d m o t i o n t h r o u g h the t u n n e l , o n the other h a n d , d i d significantly deteriorate performance. T h i s c a n be explained b y the fact t h a t the t u n n e l frames m o v e towards the p i l o t , forcing h i m / h e r to constantly shift attention to a new set of frames.
T h e conventional t u n n e l display, c o m b i n i n g b o t h sets of cues (display C), resulted i n the best per-formance for a l l conditions. T h e effects of the independent variables o n performance w i t h this display showed a m i x t u r e of b o t h aforementioned trends, b u t to a significantly lesser degree. T e n -tatively one c o u l d state t h a t the a d d i t i o n of b o t h sets of cues led to a more robust performance. T h e results f r o m the f r e q u e n c y - d o m a i n analysis fully support the t i m e - d o m a i n d a t a . M o r e o v e r , it is shown that part of the observed performance effects c o u l d be a t t r i b u t e d to the different a d a p t a -t i o n of -the subjec-ts -to -the d y n a m i c s of -the sys-tem to be controlled. T h i s allows a m u c h better insight into the observed performance characteristics. It is expected t h a t the future m o d e l l i n g efforts, i n -c l u d i n g a p a r a m e t r i -c analysis of the identified op-erator frequency-response functions, w i l l substan-t i a l l y increase substan-t h i s insighsubstan-t.
T h e d u a l approach followed allows for a m o r e sub-stantial analysis of the observed m a n u a l c o n t r o l behaviour. A n i m p o r t a n t disadvantage of the ap-proach, however, is t h a t i t requires a h i g h l y ab-stracted design a n d definition of the e x p e r i m e n t a l variables of interest, r e d u c i n g the transfer o f the results to the 'real w o r l d ' .
8. A C K N O W L E D G E M E N T S
T h e author w o u l d l i k e to t h a n k guru René v a n Paassen for his s u p p o r t concerning the identifica-t i o n procedure. F u r identifica-t h e r , identifica-the a u identifica-t h o r w o u l d l i k e identifica-to t h a n k E r i k T h e u n i s s e n for the use o f the D E L -P H I N S t u n n e l display software.
9. R E F E R E N C E S
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XVth European Annual Conference on Human Decision Making and Manual Control (1996)
