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First published online December 28, 2007
Journal of Experimental Biology 211, 258-266 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.012625
Review, Biomechanics of Flight |
New experimental approaches to the biology of flight control systems
1 Department of Zoology, Oxford University, South Parks Road, Oxford, OX1 3PS,
UK
2 Department of Engineering Science, Oxford University, Parks Road, Oxford, OX1
3PJ, UK
* Author for correspondence (e-mail: graham.taylor{at}zoo.ox.ac.uk)
Accepted 18 September 2007
Summary
Here we consider how new experimental approaches in biomechanics can be used to attain a systems-level understanding of the dynamics of animal flight control. Our aim in this paper is not to provide detailed results and analysis, but rather to tackle several conceptual and methodological issues that have stood in the way of experimentalists in achieving this goal, and to offer tools for overcoming these. We begin by discussing the interplay between analytical and empirical methods, emphasizing that the structure of the models we use to analyse flight control dictates the empirical measurements we must make in order to parameterize them. We then provide a conceptual overview of tethered-flight paradigms, comparing classical `open-loop' and `closed-loop' setups, and describe a flight simulator that we have recently developed for making flight dynamics measurements on tethered insects. Next, we provide a conceptual overview of free-flight paradigms, focusing on the need to use system identification techniques in order to analyse the data they provide, and describe two new techniques that we have developed for making flight dynamics measurements on freely flying birds. First, we describe a technique for obtaining inertial measurements of the orientation, angular velocity and acceleration of a steppe eagle Aquila nipalensis in wide-ranging free flight, together with synchronized measurements of wing and tail kinematics using onboard instrumentation and video cameras. Second, we describe a photogrammetric method to measure the 3D wing kinematics of the eagle during take-off and landing. In each case, we provide demonstration data to illustrate the kinds of information available from each method. We conclude by discussing the prospects for systems-level analyses of flight control using these techniques and others like them.
Key words: control, stability, bird flight, insect flight, flight simulator, photogrammetry, virtual reality, biomechanics, steppe eagle, Aquila nipalensis
1 Introduction
While we may now claim a reasonable understanding of many mechanical and
physiological aspects of animal flight control, we do not yet understand their
dynamical interaction. Hence, while we are able to describe the neuroanatomy
and physiology of certain feedback and feedforward pathways (e.g.
Burrows, 1996
), we do not as
yet have the tools to understand how these are tuned to produce a robust
control system, nor to examine the selection pressures and constraints that
have operated in their evolution. A central aim of future research must
therefore be to unite our understanding of the mechanical and physiological
aspects of animal flight control, in order to offer insight into their
evolution as interacting dynamical subsystems of the control system as a
whole. This will necessarily entail embedding the empirical results of
physiological studies within the theoretical framework of classical mechanics
and, in consequence, the structure of the models we use to analyse animal
flight dynamics will dictate the empirical measurements we must make in order
to parameterize them.
Our aim here is to consider how tethered- and free-flight experiments can be used to provide the sorts of empirical data needed to parameterize models of animal flight dynamics, without being too prescriptive about model structure. In so doing, we outline a programme of empirical research aimed at unpicking the complex interaction between physics and physiology that underpins animal flight control. After reviewing the state of the art in tethered-(section 2) and free-flight (section 3) experimental paradigms, we describe several new techniques we have developed in order to overcome the main limitations we identify in existing methodologies. We do not set out here to provide detailed results or analysis from any of these methods, but instead offer demonstration data to illustrate the kinds of measurements that can be made using these new experimental methods. We conclude by discussing the prospects for systems-level analyses of animal flight control in the light of the conceptual and methodological themes that we review (section 4).
2 Tethered-flight paradigms revisited
2.1 Conceptual overview
The great majority of experimental research on animal flight has been done
while the animal is tethered, and therefore – strictly speaking –
not flying. This somewhat paradoxical situation has arisen because it is often
necessary to tether an animal in order to make any measurements at all, but
the opportunity that tethering presents for measuring forces and moments
directly allows us to make a virtue out of a necessity. Moreover, given that
the forces and moments can be measured, it is then a relatively simple matter
to predict using equations of motion how the animal would have flown at the
instant the forces were measured, had it momentarily been released from its
tether (Taylor and Thomas,
2003; Taylor and
bikowski, 2005). Hence, while a tethered animal is not
strictly flying, tethered measurements can nevertheless be used to infer how a
tethered animal would have behaved in free flight, provided that we can deal
with certain difficulties implicit in the approach.
The central problem with tethering is that it breaks the dynamics of the mechanical system and thereby breaks the feedback loops that naturally operate in free flight. A tethered system cannot therefore exhibit closed-loop behaviour, unless special measures are taken to simulate free-flight conditions by modulating the stimuli that the subject receives appropriately, and for this reason such systems have often been referred to as `open-loop'. Nevertheless, the physiological component of a tethered animal's flight control system remains intact: its sensors continue to receive input, its controllers continue to process the resulting signals, and its effectors continue to produce a response. This implies that we should still be able to extract meaningful information about the closed-loop function of the physiological system in free flight from measurements we make in tethered flight. As we will now argue, however, the nature of the distinction between so-called open-loop and closed-loop tethered paradigms has not in the past been made sufficiently precise, and this has led to some confusion in the interpretation of tethered-flight results.
2.1.1 `Open-loop' tethering
Measurements made under tethered conditions are usually referred to by
biologists as open-loop, unless feedback is used to modulate artificially the
stimuli that the insect receives
(Srinivasan, 1977). It is
important to recognize, however, that measurements made under open-loop
experimental conditions are not the same as measurements made on an open-loop
control system. Open-loop control refers to actions made in response to a
command signal without reference to the system's output during the action. For
example, aerial pursuit behaviour in hoverflies appears to be initiated
open-loop, with no modulation in response to changes in the target's
trajectory through the initial stages of a pursuit (i.e. without using sensory
feedback) (Collett and Land,
1978). This differs fundamentally from the situation experienced
by an animal in tethered flight, because it is reasonable to expect that a
tethered animal will continue to treat as feedback whatever sensory input it
receives in those modalities normally used for closed-loop control. Hence,
while the experimental conditions used in tethered flight may in some sense be
open-loop, the controller itself is certainly not behaving as an open-loop
controller. Taylor and bikowski
(Taylor and bikowski,
2005) have therefore suggested using the term `broken-loop' to
refer to measurements made in tethered flight, in order to distinguish them
from measurements of open-loop control systems. Like the terms open-loop and
closed-loop, the term broken-loop is borrowed from the control engineering
literature, where it is used to describe a closed-loop control system that has
been interfered with in some way (e.g.
Tischler and Remple,
2006).
To illustrate the importance of the distinction between open-loop and
broken-loop systems, consider how a classical linear controller would respond
if its normal feedback loops were broken. A typical
proportional-integral-differential (PID) controller uses three kinds of
feedback to achieve a commanded state: (1) the measured difference, or error,
between the actual and commanded states of the system (proportional control),
(2) the rate of change of the error (differential control), and (3) the sum of
the error through time (integral control); see e.g. Dorf
(Dorf, 2005). All three kinds
of feedback are usually needed to achieve a swift but stable response without
steady-state error, so it is reasonable to assume that the same kinds of
sensory feedback will be used by flying animals, even if the control laws
themselves might not be linear. Now, a hypothetical flying animal attempting
to reach a commanded state different from its current one using a PID
controller would perceive a constant error if tethered, and would therefore be
expected to increase the magnitude of its response as a result of integral
control until the controller reached saturation. We would therefore expect an
animal in tethered flight to display a ramped, and possibly saturating,
control response. This differs fundamentally from an open-loop control
response, which does not change through time unless the command is
changed.
The ramped and possibly saturating broken-loop control response that we
predict will be observed in tethered flight is, however, consistent with the
familiar observation (Dudley,
1992) that tethered-flight responses tend to be exaggerated over
those exhibited in response to similar disturbances in free flight
(Taylor, 2007). Previously,
this has been treated as an experimental artifact – which in some sense
it is (Dudley, 1992) –
but the observation almost certainly also provides useful information on the
nature of the animal's controller, which a systems approach should be able to
identify. Far from being mere artifacts, the exaggerated responses observed in
tethered flight are in fact useful data when interpreted correctly. This comes
as some relief in the light of the earlier observation that most previous
experimental work on animal flight physiology has been done under broken-loop
conditions.
2.1.2 `Closed-loop' tethering
Measurements made under tethered conditions in which feedback is used to
modulate artificially the stimuli that the insect receives are usually
referred to as closed-loop (Srinivasan,
1977). Making measurements under closed-loop conditions does not,
however, ensure that the closed-loop dynamics will be correctly identified
unless great care is taken to match the dynamics of the artificial feedback
loop to the free-flight dynamics it simulates. Closed-loop control refers to
actions made in response to a command signal with reference to how the
system's state differs from the commanded state through the course of the
action. For example, insects classically exhibit an optomotor response in
which they will turn to follow a moving wide-field pattern so as to stabilize
their visual field. This natural tendency to stabilize the visual field by
turning in free flight can be simulated artificially in tethered flight by
modulating the visual stimuli that the insect receives using the measured
torque as feedback (Srinivasan,
1977). The resulting closed-loop experimental conditions are
certainly closer to free flight than the broken-loop experimental conditions
discussed in the previous section. Nevertheless, the situation is still
abnormal, not least because only one of the six degrees of freedom of free
flight (typically either roll or yaw) and only one of the sensory modalities
(typically vision) is usually employed in the experimental feedback loop.
Incorporating only one degree of freedom in the experimental feedback loop
is especially problematic for lateral motions, which display strong coupling
between their different degrees of freedom in free flight. Such coupling
arises partly as a result of inertial coupling, and partly because asymmetries
in lift tend to be associated with asymmetries in thrust or drag. This makes
it extremely difficult to generate a roll moment without also generating a yaw
moment, and vice versa, so that a banked turn in an aircraft, for
example, is typically achieved by coordinating the rudder (which nominally
controls yaw) with the ailerons (which nominally control roll) so as to
counteract adverse yaw. Furthermore, Newton's Second Law tells us that the
rate of angular acceleration of an object in response to an applied torque
depends on its moment of inertia, but no attempt is usually made to match the
gain of the artificial feedback loop to the animal's mass distribution
properties [but see Wehrhahn and Reichardt
(Wehrhahn and Reichardt, 1975)
for a notable exception]. It is therefore unlikely that the experimental
feedback provided in most closed-loop experiments matches kinematically, let
alone dynamically, the feedback that would have been obtained in free flight.
While closed-loop paradigms undoubtedly come closer to simulating natural
free-flight conditions than broken-loop measurements, this means that they
also come with a degree of uncertainty about what response is actually being
measured.
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) and
might be adapted for animal flight research. The difficulty with these kinds
of simulations, however, is that the finite bandwidth of the actuator hardware
necessarily impacts on the accuracy of the method. This is especially
problematic on the short timescales associated with animal flight. Hence,
while closed-loop experiments can indeed measure closed-loop dynamics, it is
technically difficult to ensure that these are the same as the closed-loop
dynamics of natural flight. Closed-loop experimental conditions therefore
offer no panacea for the more general problems of tethering, and while they
undoubtedly come closer to simulating free-flight conditions than broken-loop
tethering, we suggest that the certainty we have over how the feedback loop is
broken makes broken-loop measurements easier to interpret in the context of
animal flight dynamics.
2.2 New techniques for tethered flight
Many of the issues discussed in section 2.1, once recognized, can be dealt
with experimentally. This section describes the design of a virtual-reality
flight simulator designed to meet these requirements for work with insects
(Fig. 1). Our intention here is
to provide a conceptual overview of the simulator in order to illustrate how
its design overcomes these issues. The simulator has several key features,
which distinguish it from the current state of the art as has been developed
elsewhere. Firstly, it provides stimuli in all of the sensory modalities known
to be used in flight control. Secondly, it has a bandwidth broad enough to
match dynamically the free-flight motions of the insects it is designed for
work with. Thirdly, it is possible to vary stimuli in the different sensory
modalities independently to determine how they are combined by the insect's
controller to achieve effective flight control.
The virtual-reality simulator provides an immersive visual environment for
an insect tethered at the centre of a 1 m diameter acrylic sphere, whose
surface is painted to act as a rear projection surface
(Fig. 1). The projection system
is designed to allow simulation of any combination of translation and rotation
in a bright and realistic visual environment. Two customized data projectors
display synchronized sequences of binary images at 1024 pixels x 768
pixels and up to 8000 frames s–1 using Digital Light
ProcessingTM technology (Texas Instruments Inc., Dallas, TX, USA). This
is well in excess of the bandwidth of any insect's visual system
(Miall, 1978) and sufficient
therefore to allow projection of grayscale images by time-averaging of binary
images. The arc lamps used by the projectors are extremely bright (1500
lumens) and are run without flicker by a DC electronic ballast. Any suitably
rendered image sequence can be projected, so it is possible to display either
video recordings of natural environments or animated sequences generated on a
computer. At present, computer-generated sequences are rendered in 3D
animation software using an explicit computer-aided design (CAD)-based
representation of the flight simulator
(Fig. 2). Sequences are
preloaded onto RAM prior to projection, but it is also possible to project
images generated online, so that in principle the system may be run in a
closed-loop configuration. Aerodynamic stimuli are provided by a thin-walled
transparent suction tunnel inside the projection sphere, with an
electronically adjustable flow speed.
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The insect itself is rigidly tethered to a six-component force–moment
balance sufficiently sensitive to resolve the periodic forces generated by a
blowfly Calliphora erythrocephala through its wingbeat (Nano-17, ATI
Industrial Automation, Apex, NC, USA). The balance is attached to a movable
sting such that the insect can be rotated about its centre of mass by
attaching the sting to one of several different rotary axes driven by a
brushless motor with integrated position encoder. Each of these rotary axes is
servoed by a computerized motion controller, which can be programmed to
execute any given pattern of rotation in that axis, thereby providing static
adjustment of the insect's orientation as well as dynamic stimulation of
inertial sensors such as halteres. The motion of the rotary axes is
phase-locked to the data projectors using a transistor–transistor logic
(TTL) synchronization signal. Although it is only possible to generate a
limited set of inertial rotations in the simulator, these are appropriate to
the structures of most tractable models of unsteady flight dynamics. For
example, if the equations of motion used to analyse the data are linearized,
then any motion that the model can describe can be represented as a linear sum
of the characteristic natural modes of the system. Furthermore, it can be
shown that a set of four characteristic motions (flight at steady angle of
attack and sideslip, pitch oscillations, yaw oscillations, and coning
rotations at non-zero angle of attack and sideslip) is sufficient to
parameterize a non-linear model of unsteady rigid-body flight dynamics
completely (Tobak and Schiff,
1981). Pitch oscillations have already been studied by Taylor et
al. (Taylor et al., 2006) for
desert locusts Schistocerca gregaria in a more basic experimental
apparatus, but the new virtual-reality flight simulator is designed to
generate all four types of characteristic motion. This is an excellent example
of how the structure of a model used to analyse experimental data should
dictate the experiments that need to be performed.
In summary, the virtual-reality flight simulator we have developed enables
realistic simulation of all of the sensory stimuli known to be important in
the moment-to-moment control of insect flight, in order to allow the forces
and moments to be measured and modelled as functions or functionals of the
sensory input states. The simulator has some features in common with existing
facilities elsewhere, but differs in a number of important respects. For
example, other state-of-the-art facilities for visual stimulation either use
arrays of light-emitting diodes (Sherman
and Dickinson, 2003; Lindemann
et al., 2003), which offer excellent temporal resolution but are
constrained in luminance and ease of programming, or commercial LCD projectors
(Gray et al., 2002), which
offer excellent luminance and ease of programming but are constrained in
temporal resolution. Luminance is of particular importance, because the
response of the visual system is much slower under dim conditions. In
contrast, the virtual-reality simulator that we have developed combines
excellent temporal and spatial resolution with extremely high luminance,
convenience of operation and an almost unrestricted field of view for the
insect. Most importantly, it is unique in combining simulation of visual,
aerodynamic and inertial stimuli in a single apparatus, allowing measurement
of all six components of the forces and moments that the insect produces.
3 Free-flight paradigms revisited
3.1 Conceptual overview
However sophisticated tethered-flight paradigms may become, it goes without
saying that the natural state of flight is free flight. It does not follow,
however, that free flight is necessarily natural flight – in most
experimental situations, the subject will be trailing leadwires, carrying a
load, flying in a wind tunnel, or simply flying in a confined space.
Nevertheless, it is only possible to have the chance of identifying true
closed-loop dynamics in free flight, and for this reason free-flight paradigms
are likely to play an increasingly important part in our developing
understanding of animal flight control. The key difficulty from a flight
dynamics perspective is that the forces and moments cannot be directly
measured – only the animal's consequent motion. This is problematic
because although Newton's Second Law tells us that knowledge of mass and
acceleration is equivalent to knowledge of force for a moving particle, things
are more complicated for a solid body. For example, a measured roll
acceleration might reflect the direct application of a roll torque, but it
might also reflect a non-zero product of the angular velocity components about
the pitch and yaw axes if their moments of inertia are unequal. The issues of
coupling alluded to in section 2.1.2 therefore mean that it will not in
general be possible to treat different degrees of freedom separately.
Given that it is generally incorrect to infer the forces and moments in one
axis from the accelerations and angular accelerations in only that axis, there
is no substitute for using a physically complete set of equations of motion to
analyse acceleration data obtained in free flight. Hence, in contrast to a
designed tethered-flight experiment – in which the animal's response to
a prescribed stimulus can be measured and the parameters of the model fitted
separately – free-flight paradigms will generally require all of the
parameters of the model to be fitted simultaneously. This brings us into the
domain of system identification (Ljung,
1998). System identification has been used successfully for over
half a century to determine experimentally the dynamics of what in control
engineering is termed the `plant' of a control system – typically the
physical system being controlled, and in our case the animal's flight
dynamics. System identification is becoming increasingly common as a means of
modelling aircraft flight dynamics and control, as witnessed by the recent
publication of several texts on the subject
(Klein and Morelli, 2006;
Jategaonkar, 2006;
Tischler and Remple,
2006).
There are three general approaches to system identification: (a)
`white-box', where we know the physical model of the plant through sound
application of fundamental laws of physics and seek to estimate the physical
parameters of that model from measured data; (b) `grey-box', where we
postulate a model structure at the level of assuming, say, a first order
system with dead time, and seek to estimate its physical parameters; (c)
`black-box', where we seek to estimate both the model structure and its
parameters from data (Jategaonkar,
2006). In each case, the model structure and/or parameters are
identified using maximum likelihood methods, minimization of prediction error,
or other similar optimization procedures. Since a white-box approach is based
on a physical model of the system, there is little risk of over-fitting the
model with unnecessary parameters; with a grey-box or black-box approach, this
can be avoided by model reduction techniques and statistical control of the
overall type I error. It is common in the identification of aircraft flight
dynamics to use a white-box approach, as the basic underlying dynamic model of
a fixed-wing aircraft can be readily derived. By the same token, it should be
possible to use a white-box approach in the identification of the flight
dynamics of gliding animals. A white-box approach may not be feasible for
flapping flight, however, which is much more difficult to model theoretically,
and it is likely that a grey-box or black-box approach will be required in
such cases.
Identifying the dynamics of an animal's flight control system requires knowledge not only of the animal's motion but also of the control input which produces that motion. Furthermore, the control inputs we measure must be sufficient to excite all of the animal's modes of motion and the components of its motion that we measure sufficient for us to observe all of those modes. Once fitted, it is usual to validate the model by comparing its predictions of flight behaviour against validation data not used in the fitting of the model. Naturally, the accuracy of any such analysis rests on the accuracy of the kinematic data that are used to infer the dynamics. These may be collected either using instrumentation forming part of the measured system, such as onboard inertial measurement units and cameras, or using instrumentation external to the measured system, such as ground-based cameras.
3.1.1 Inertial measurement systems
The approach of getting the animal to carry sensors to measure its
kinematics is at present restricted to larger animals, for which the required
load forms a small enough proportion of body mass not to interfere unduly with
the flight dynamics. As a rough rule of thumb, we might aim for a system
constituting <10% of body mass. Birds were first made to carry inertial
sensors as early as 1982, in a wind tunnel study mounting accelerometers on
pigeons (Bilo et al., 1982).
However, it has only become possible to mount accelerometers on birds flying
freely without the constraint of trailing wires with the recent
miniaturization of data loggers
(Weimerskirh et al., 2005).
Accelerometer data have been used to answer a variety of behavioural and
biomechanical questions (Bilo et al.,
1982; Hedrick et al.,
2004; Weimerskirh et al.,
2005), but for flight dynamics purposes this needs to be combined
with information on rotation from angular sensors such as magnetometers and
rate gyros. As the smallest commercially available inertial measurement units
and data loggers providing these facilities have a combined mass of the order
of 0.05 kg, this presently limits us to animals with a body mass of the order
of 0.5 kg for studies of wide-ranging free flight. With the use of trailing
wires, smaller species of bird may also be considered, although this will
obviously constrain their flight dynamics. While it is impractical for insects
to carry inertial measurement systems at present, tiny induction coils
transducing position and orientation have been carried by blowflies flying
freely in a small flight arena with an applied magnetic field
(Schilstra and Van Hateren,
1999). Unfortunately, this technique is not well suited to flight
dynamics measurements because the insect is constrained by trailing wires, and
the instantaneous position and orientation data collected in this manner still
need to be differenced in order to extract velocity and acceleration.
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;
Hedrick and Biewener, 2007;
Hedrick et al., 2007).
Naturally, the fixedness of the measurement system constrains the flight
volume that can be covered, and for this reason all previous work has been
done indoors. Examples of moving measurements systems include pan-tilt mounted
cameras used to track insects flying around a large room
(Fry et al., 2000;
Müller and Robert, 2001).
A far greater flight volume can be covered if the external measurement system
follows the free-flying animal (Fry et al.,
2000), but the need to know the motion of the measurement system
introduces an additional source of measurement error that may not be tolerable
in flight dynamics studies. In any case, the most fundamental limitation of
using any kind of external measurement system for flight dynamics measurements
is that velocity, angular velocity and acceleration cannot be measured
directly. Instead, the kinematics must be estimated from the measured target
position and orientation using, for example, a numerical differencing
procedure or Kalman filtering. This amplifies the measurement error and
concomitantly reduces the useful bandwidth of the system, so that a very high
degree of spatial and temporal resolution is required in order to make
measurements suitable for flight dynamics modelling.
3.2 New techniques for free-flight analysis
In order to overcome some of the issues discussed in section 3.1, we have
developed complementary external and onboard measurement systems for analysing
the flight dynamics of free-flying birds of prey. The methods are described in
detail by Carruthers et al. (Carruthers et
al., 2007) and Taylor et al.
(Taylor et al., 2007),
respectively: here we provide a brief summary of the techniques used, together
with preliminary data to demonstrate the kinds of measurements that can be
made. These data are offered by way of illustration only, and it is not
intended that any detailed conclusions be drawn from them: the system
identification approach that we have outlined above requires large datasets
and a great deal of mathematically involved analysis, which falls outside the
scope of this review.
3.2.1 Onboard measurement techniques
Miniature inertial measurement units (IMUs) providing 3D information on
orientation, angular velocity and acceleration have only recently become
commercially available. We used an MTx/MTi unit (XSens Technologies B.V.,
Enschede, The Netherlands) together with a custom-built logger (M. Bacic,
Department of Engineering Science, Oxford University) to record at 100 Hz the
instantaneous 3D orientation, angular velocity and acceleration of a trained
male steppe eagle Aquila nipalensis weighing 2.5 kg. A pair of
miniature PAL wireless video cameras were fixed rigidly to the IMU and used
simultaneously to record the eagle's head and tail movements, using a
ground-based video receiver recording to MiniDV. The video data were later
deinterlaced to provide sequences at 50 frames s–1. The
instrumentation was carried on the eagle's back and was worn on a removable
harness made of webbing material and Velcro straps: the total load carried in
the experiments we describe here was <0.25 kg, or 10% of body mass, but we
have since managed to reduced the combined weight of the instrumentation to
<0.1 kg.
Fig. 3 shows the kind of information that is available on tail kinematics during flight, while Fig. 4 shows a typical set of inertial data recorded during coastal soaring. The inertial data are shown alongside synchronized video footage of the eagle from a handheld camcorder and from a rearward-facing onboard camera. The view of the body recorded by the onboard camera is stationary throughout, confirming that the instrumentation remained steady with respect to the bird during the manoeuvre. Unfortunately, the IMU heaves with the scapular region on which it is seated during flapping, so that at present we are only able to apply the technique successfully to gliding flight, during which the IMU remains steady on the bird. Together, these data demonstrate that it is possible to use an inertial measurement system to record the body kinematics of a large bird in wide-ranging free flight, while simultaneously recording parameters of its wing or tail kinematics using the onboard video. Given a sampling frequency of 50 Hz for the input measurements (from the onboard cameras) and 100 Hz for the output measurements (from the IMU), the bandwidth over which we can identify the response of the bird ranges up to a theoretical maximum of 25 Hz. This is much broader than the bandwidth we have observed the eagle to make control inputs over, and the technique therefore permits identification of its frequency response over the full range of input frequencies that it employs.
3.2.2 External measurement techniques
Independent validation of the response properties identified using onboard
instrumentation is possible by making use of a ground-based external
measurement system. This has only recently become feasible with the
development of ruggedized high-speed digital video cameras, which allow
stereo-photogrammetric measurements to be made under field conditions with
sufficient spatiotemporal resolution to extract usable flight dynamics
parameters. The disadvantage of this approach is that the bird must be close
to the cameras during the measurement, which limits the duration of the flight
record that can be obtained. Since the lowest frequency that can be identified
is inversely related to the length of the flight record, this means that
high-speed video data can only be used to identify the response of a bird at
higher frequencies. As such, the method is complementary to the onboard
instrumentation techniques that we have developed, which can be used to obtain
flight records lasting many tens of minutes and therefore offer better
resolution at lower frequencies.
The photogrammetric method uses a pair of synchronized Motionscope M3
cameras (Redlake Imaging Inc., Tucson, AZ, USA) giving 1280 pixel x 1024
pixel resolution at 500 frames s–1. Using manual tracking of
approximately 70 recognizable natural features of the plumage of the wings,
head and tail, and using self-calibrating bundle adjustment calibration
techniques we have been able to reconstruct the 3D position of each of these
points on the bird as it comes in to perch on its handler's arm.
Self-calibrating bundle adjustment is the state of the art in photogrammetric
reconstruction techniques (e.g. Atkinson,
1996). Our implementation uses non-linear least squares
optimization to solve for jointly optimal estimates of the camera parameters
and target coordinates. Fig. 5
plots a reconstruction of the lower surface of the wing and of reference
points on the head and tail. The camber and spanwise twist of the wing are
clearly visible in the surface colour, which represents the local geometric
angle of attack. The photogrammetric data therefore provide a rich source of
information for identifying multiple-input multiple-output models of the
flight dynamics, complementary to the simpler kinematic data derived from the
onboard instrumentation. An animation of a short section of the perching
sequence shown in Fig. 5 is
provided in the supplementary material, in order to demonstrate that it is
possible to extract detailed wing and body kinematic measurements from
free-flying birds using natural features of the plumage alone.
4 Conclusions
The experimental techniques that we have described make it possible to
determine the functional link between the state of a flying animal (i.e. its
orientation, velocity, angular velocity, etc.) and the forces and moments it
produces. This in itself is sufficient to derive a model of the flight
dynamics (Taylor and Thomas,
2003; Taylor and
bikowski, 2005; Taylor
et al., 2006), but in either case it will leave us with the
measured input–output relationships as a black box. This can still yield
useful insight into the mechanics of flight, for example by providing
quantitative information on the trade-off between stability and
manoeuvrability, or on the performance of the animal as characterized by its
frequency response. However, the details of the underlying physiology remain
opaque, and a key challenge is to begin to fill in the details of the black
box to produce a grey-box model in which information on the underlying
structure of the neuromuscular system is included in the model. This is partly
achievable using the methods we have already described. For example, by
allowing us to vary stimuli in the different sensory modalities independently
or in concert, the virtual-reality flight simulator allows us to investigate
how different sensory pathways combine to modulate flight control (see also
Sherman and Dickinson,
2004).
Nevertheless, detailed neurophysiological information will always be
important in ensuring that the structure of the model we fit is grounded
firmly in physiological reality. For example, whether we need to use
integro-differential equations so as to model the effects of integral control
is an empirical question that can be answered if we know enough about the
animal's neurophysiology to tell whether integral control is a likely
possibility. It is well known that neurons have integrative properties, but is
there any neurophysiological evidence to suggest that the exaggerated
responses seen in tethered flight really reflect controller saturation as
suggested in section 2.1.1? Neurophysiological information might also help us
to determine whether linear (Taylor and
Thomas, 2003; Sun and Xiong,
2005; Taylor et al.,
2006) modelling is likely to be appropriate, or whether non-linear
modelling (Taylor and bikowski,
2005) is required. We know that individual neurons display highly
non-linear response properties, but is this also true of the controller they
combine to produce? In fact, there are good reasons to expect that it might
not be. For instance, concordant visual and haltere inputs seem to combine
linearly in flies (Sherman and Dickinson,
2004), and the antennal positioning reaction of locusts seems to
render the response of the antennae to airflow more nearly linear in airspeed
(Gewecke and Heinzel, 1980).
This suggests that a linearized model might capture the overall system
response well, even if it could not be expected to capture the response
properties of the system's piecewise components.
Integrating mechanical and physiological models of animal flight dynamics and control presents significant challenges. Nevertheless, with the aid of neurophysiological understanding to inform the structure of our models, and a consequent understanding of the parameters that must be fitted experimentally, it should be possible to make progress in developing systems-level models of animal flight control. With such models in hand, we will at last begin to understand the complex evolutionary interaction between physics and physiology, from which derives the richness of animal flight dynamics.
Acknowledgments
We thank Tony Price for building the flight simulator, and `Cossack' and
Louise Crandal – eagle and handler – for their involvement in the
bird flight experiments. We thank Rafa
bikowski, Holger Krapp
and Simon Laughlin for many helpful discussions, and Gregg Abate, Johnny Evers
and Michael Ol for their support. G.K.T. is a Royal Society University
Research Fellow and RCUK Academic Fellow. R.J.B. is a Postdoctoral Research
Fellow at St Anne's College, Oxford. A.C.C. is a Royal Commission for the
Exhibition of 1851 Brunel Research Fellow. The virtual-reality flight
simulator was designed and built by G.K.T. and R.J.B., sponsored by the BBSRC
under grant number BB/C518573/1 to G.K.T. A.C.C. undertook the eagle wing
kinematics analysis, sponsored by the Air Force Office of Scientific Research,
Air Force Material Command, USAF, under grant number FA8655-05-1-3077 to
G.K.T., M.B. and A.L.R.T. J.G. undertook the analysis of data from the onboard
measurement system under a Doctoral Training Grant from the BBSRC and EPSRC to
G.K.T. S.M.W. wrote the software used to analyse the eagle wing kinematics,
sponsored by the EPSRC under grant number GR/S23049/01 to A.L.R.T. The US
Government is authorized to reproduce and distribute reprints for Governmental
purpose notwithstanding any copyright notation thereon.
Footnotes
Supplementary material available online at http://jeb.biologists.org/cgi/content/full/211/2/258/DC1
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) is extracted from the angle of the
trailing edge, as shown by the construction lines on the image. Tail pitch
angle (
) is extracted by measuring the deviation of the trailing edge
from its average position perpendicular to the line AB at the point A, and
making use of the known distance of the camera to the base of the tail. Tail
spread angle is not shown, but can also be determined from these data, giving
3 measurable kinematic degrees of freedom for the tail.
