17th European Annual Conference on Human Décision Making and Manual Control
TRACKING CURVED TRAJECTORIES WITH A TUNNEL-IN-THE-SKY DISPLAY Max Mulder *
* Delft University of Technology, Faculty of Aerospace Engineering, Control and Simulation Division P.O. Box 5058, 2600 GB Delft, The Netherlands E-mail:
[email protected]
Abstract: The tunneî-in-the-sky display is a viable candidate to become the primary flight display of future aircraft cockpits. The tunnel display shows the fiight trajectory to be flown in a synthetic three-dimensional world. Presenting the guidance information via spatial sources of information has important conséquences for a pilot. Hence, to understand pilot manual control behaviour with a perspective display, it is essential to investigate the manner in which pilots use thèse optical eues. The paper describes the approach chosen and discusses one of the experiments.
Keywords: Aircraft control, cockpit displays, information analysis, cybernetics.
1. T H E TUNNEL-IN-THE-SKY DISPLAY The volume of air transportation will show a considerable growth in the near future. New technologies are being developed with the dual objective of increasing the efficieney of
air traffic management and enhancing fiight safety. One of the expected measures is to increase the flexibilíty in air trame control by allowing curved approach profiles. Flying these - inherently more complex - curved approaches increases the pilot task demand load and requires enhanced levéis of situation awareness. Improving the presentation of information to the pilot by means of intuitive displays can alleviate these problems considerably (Oliver, 1990). A promising candidate to become the primary flight display of future cockpits is the tunnel-in-the-sky display (Fig. 1), which shows a spatial analog of the planned trajectory. Previous research indicated that the tunnel display has cer-
tain advantages over current flight displays in both the pilot manual as the supervisory task (Wilckens, 1973; Grunwald, 1984; Wickens, Haskell, & Harte. 1989; Theunissen, 1997). A perspective flight-path display, showing the planned trajectory to the pilot in a synthetic three-dimensional world is not a new concept. Since the late 1940's it has been hypothesised that such a pictorial display could mean, in many ways, an important improvement in information-transfer to the pilot. Its application was impractical, however, due to technical limitations. Basically, two developments in technology made the pictorial display concept practical. First, rapid improvements in computer technology made sufficiently detailed real-time graphics possible. Second, the advance of new positioning systems such as GPS (Global Positioning System) provided the capability of accurately measuring the position of the aircraft with a sufficient update rate.
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Fig. 1. The tunnel-in-the-sky display. The application of a perspective display in the cockpit has important consequences. In a conventional cockpit the pilot mentally reconstructs the aircraft's spatial and temporal situation from a number of planar, i.e. two-dimensional, displays. With a perspective flight-path display this information is presented in a spatial format (Mulder, 1995). At the Delft University of Technology a research project was initiated to investigate the applicability of a tunnel display for the pilot manual control task. In contrast to other studies the project goal was not to compare the tunnel display with current displays in terms of pilot performance, situation awareness, and workload. Rather, the objective was to obtain an understanding of how pilots use the tunnel display as their main source of information in the aircraft guidance task (Mulder, 1995). Once this understanding is achieved, an attempt can be made to represent the important characteristics of the pilot in a mathematical model. For this purpose, a methodology has been developed, labelled the cybernetic approach, which allows substantial insight into the effects of varying display designs on pilot behaviour (Mulder. 1999). Four main steps can be distinguished in the approach: (i) a description of the pilot tasks; (ii) an identification of the interaction characteristics of the pilot and the display,
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leading to theoretical implications; (iii) an experimental validation of these theoretical implications, and (iv) an attempt to describe the observed pilot behaviour in a mathematical model (Mulder & Mulder, 1998). The paper will discuss the characteristics of interaction and an experimental assessment of the pilot task of manually guiding the aircraft along a circular tunnel trajectory.
2. T R A C K I N G CURVED TRAJECTORIES The pilot's task is to follow a planned reference trajectory, a typical guidance task. Based on the characteristics of this reference trajectory, the guidance task can be divided into a number of sub-tasks (Mulder, 1995): (i) to maintain or track a straight section of the trajectory; (ii) to maintain or track a curved section of the trajectory, and (iii) to control a transition between a straight and a curved section of the trajectory. In other words, or, from a system-theoretical point of view, following the planned trajectory leads to maintaining a series of different system steady-states (or references) and controlling transitions between these steady-states. The research project has been defined according to these different pilot sub-tasks. In (Mulder, 1996; Mulder & Mulder, 1998) the
17th European Annual Conference on Human Décision Making and Manual Control behaviour of a pilot Controlling the aircraft along a straight section of the trajectory has been examined. In (Mulder & van der Vaart, 1998) the behaviour of a pilot Controlling the aircraft in a curve-interception manoeuvre is analysed. The current paper deals with the sub-task of Controlling the aircraft along sections of the trajectory that are circular, i.e. curved with a constant radius.
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A perspective fiight-path display shows the trajectory to be followed in a synthetic threedimensional world. The task of the pilot is to control the aircraft along this trajectory. To fulfil this task, the pilot estimâtes the state of the aircraft with respect to the trajectory and, based on this estimated state, décides upon and activâtes the necessary control actions. In order to understand the interaction between the pilot and the display it is essential to understand this state estimation process. This has been investigated from two different points of view. In (Mulder, 1994) it was examined what effects a spatial display could have on the control behaviour of a pilot: the HUMAN in the human-machine interface was taken to be the central element. Main questions that were addressed were the availability, the usefulness and the potential utilisation or informationprocessing of all sorts of spatial, or optical sources of information present in the real world and/or in a perspective display. In (Mulder, 1996; van der Hoek, 1997b; Mulder, 1999) the MACHINE side was the main issue. An attempt was conducted to make an inventory of ail spatial eues in a generic perspective flight-path display. Hère, irrespective of the human element, mathematical relations axe derived that express the state of the aircraft with respect to the référence trajectory in terms of these optica! cues: information-
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Fig. 2. A snap-shot of the tunnel image when flying through a curved tunnel section. Besides the éléments referred to in the text, ® shows the horizon line, © the fixed aircraft référence symbol and ® to © the frame numbers f. 3.2 Curved tunnel sections The analysis of optical information for the curvi-linear référence fiight condition along a circular trajectory begins with defining a generic tunnel. Fig. 2 shows the tunnel image corresponding with the situation considered here. The optical eues originate from the projection of the main éléments of the tunnel geometry - the frames © , the altitude pôles ® and the longitudinal Unes © Connecting the frames - on the viewplane. An important différence between the current situation and the case of straight tunnels, reported in (Mulder, 1996) is that, when looking farther into the tunnel, the tunnel geometry does not vanish to infinity but bends off towards one of the sides of the viewplane. A gênerai geometrical définition of a right curve is reported in (Mulder, 1999). It is assumed that the circular trajectory (radius i? ) is approximated by a concaténation of straight segments Si bridging an angular distance A $ , measured along the tunnel centercircle. The aircraft is positioned in the tunnel (tunnel width W , height H ) with an arbitrary position and attitude with respect to the tunnel centercircle. The downslope r of the trajectory is assumed zéro. t
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3.3 Information-transfer
interaction characteristics were put into a theoretical framework (Mulder, 1999). For the three subtasks specified in §2, this framework led to a substantial insight into what design variables of the tunnel display were important to consider experimentally.
3.3.1. Static optical eues Positioning the aircraft with an arbitrary position error and attitude with respect to the trajectory results in a tunnel image similar to that of Fig. 2. The primary static eues are described at the hand
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(b) The lateral tunnel cues (5)-(7).
Fig. 3. Two subsets of static optical cues in a curveé tunnel section. The (U,V) and (17', V') axes represent thefixedand rotated central viewplane axes, respectively. of Fig. 3 showing two subsets of cues resulting from the projection of the longitudinal (Fig. 3(a)) and vertical (Fig. 3(b)) éléments of the tunnel geometry . The following cues can be defined (Mulder, 1999): 1
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17th European Annual Conference on Human Décision Making and Manua (5)
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An important différence with the inventory of static cues for straight tunnels is that instead of only one infinity point and one set of splay angles, the curved trajectory yields similar quantifies but now for all tunnel segments sj. Fürther, because the circular trajectory is shown through a concaténation of straight segments, no pseudo-horizons (Mulder & Mulder, 1998) émerge in the display. Mathematical expressions are derived (van der Hoek, 1997b) that relate the optical cues to the aircraft state with respect to the circulai tunnel trajectory. For a formai mathematical description of the array of cues listed above, the reader is referred to (Mulder, 1999).
3.3.2. Dynamic optical cues The dynamic optical cues are essential in the perception of two important referents of curvi-linear motion, i.e. theflight-pathangle and the yawrate. Whereas the yaw-rate can in principle be estimated with static cues, the flight-path angle can not. In (Mulder, 1999) it is shown that there are two, essentially identical forms of dynamic optical cues. First, there are the derivatives of the static optical cues, labelled the indirect dynamic cues. Second, there are the direct dynamic cues originating from the global optie flow field. The derivatives of the static cues provide information about the flight-path, the yawrate and the radius of the curvi-linear motion. A yaw-rate error can be perceived as the translational velocity of the complete tunnel geometry on the viewplane. It can be hypothesized, although the perspective projection atténuâtes some of the error magnitudes, that for curvatures which are not extremely shallow the yaw-rate error is especially salient at larger viewing distances. The flight-path angle error is conveyed by
Fig. 4. The optieflowfield for a curvi-linear motion condition with a yaw-rate that is too small and a flight-path angle error to the left. The circle shows the direction of the velocity vector with respect to the World. The thin lines, the dash-dot line and the dashed line show the theoretical flow pattern, the locomotorflowline and the reversai boundary respectively. (the following state is plotted: Kt—2000 [mj; W = H =45 [m]; V =70 [m/s]; e = - 5 ° , ib =0°; 0=0°;
was being controlled more actively when the tunnel was rotated. The non-significance of the rotation effect in ail other cases allows the rotation measure to be discarded from further analysis, limiting the expérimental conditions to 10 (velocity (2 levels) and display (5 levels)). The means and 95% confidence limits of ail eight experiment dépendent measures (ail subjects) averaged over the 10 expérimental conditions are illustrated in Fig. 7. As one can see from this figure, the higher velocity condition leads to lower pilot control activity ( à ) , higher aircraft roll angle and roll rates (é , 4> ) lower heading angle (ip ) and yaw-rate (r ) errors, and to somewhat higher values of the lateral position error measures (X — S. X — R). These effects can be partly attributed to the different aircraft handling characteristics for the two velocity conditions, and the fact that especially the amplitudes of the dynamic optical eues are a linear fonction of the velocity of motion. Results indicate that heading angle tracking accuracy is superior for the splay-only display (C). Position error performance is also quite good with this display, but only in terms of the STD (X - S). Comparing Figs. 7(e) and 7(f) reveals that the use of this display leads to the largest bias of ail displays in Controlling the lateral position relative to the centercircle. e
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Fig. 7. The means and 95% confidence limits of the experiment dépendent measures (ail subjects). In thèse figures the insets show the two velocity conditions (70 & 110 [m/s]). The codes of the five displays are shown at the bottom. So, although pilots smoothly fly through the tunnel with this display, they adopt a consistent and most probably unperceivable bias towards the outer side of the curve. This bias also occurs for the other displays but to a significantly less extent, especially when no tunnel contour is presented at ail (displays D and E ) . These data support the hypothesis that the tunnel frames compénsate for the position error bias caused by the optical splay information. The results further support the hypothesis that when no tunnel contour is available the accurate control of the roll angle becomes more important in order to maintain the right yaw-rate (Figs. 7(b) and 7(c)). Flight path control détériorâtes with these displays ( D and E ) , caused by the lack of splay information and the ineffectiveness of the information conveyed by the tunnel frames for this purpose. Finally, frame irregularity shows to be of only minor importance when splay information is available. When the splay cues are not available performance decreases rapidly when the
frames are put in random order. Although not shown in Fig. 7 it are thèse conditions where the rotation of the tunnel geometry as a whole had the largest - but not significant - positive effect on pilot path-following performance.
6.
CONCLUSIONS
The experimental data show that the primary cues used by pilots to control the aircraft along curved tunnel segments, are the optical splays conveyed by the longitudinal tunnel contour lines. The use of splay angles and especially the splay angle rates leads to smooth trajectory following, but, due to the introduction of perceptual biases, not with the best performance. The optical density information conveyed by the tunnel frames forms a second piece of information used by pilots. Control with frame-only displays is less smooth, more jerky, but has the advantage of much smaller perceptual biases leading to improved pathfollowing performance. The combination of
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17th European Annual Conference on Human Decision Making and Manual Control both sets of cues in the baseline generic tunnel geometry yield the best performance. Rotation of the tunnel geometry with the datum aircraft roll angle does in general not lead to increased path-following performance. Although the roll angle itself is controlled more accurately, the virtues of tunnel rotation for performance only occurs in the informationpoorest tunnel geometries.
7. A C K N O W L E D G E M E N T S
University of Technology, (to be published) Mulder, M., & Mulder, J . A. (1998). Tunnel Size in a Tunnel-in-the-Sky Display: A Cybernetic Analysis. Proceedings of the
Seventh IFAC/IFIP/IFORS/IEA Symposium on Analysis, Design and Evaluation of Man-Machine Systems, Kyoto Japan, September 16-18, 335-340. Mulder, M . , & van der Vaart, J . (1998). Curve Interception with a Tunnelin-the-Sky Display: Pilot Timing Strategies. Proceedings of the Seventh
IFAC/IFIP/IFORS/IEA Symposium on Analysis, Design and Evaluation of Man-Machine Systems, Kyoto Japan, September 16-18, 341-346.
The author wishes to acknowledge AJ van der Hoek, M.Sc. student, whose graduation thesis work provided the basis for this paper.
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