Dynamics of Escaping Flight Initiations of
Drosophila melanogaster
Francisco A. Zabala
§
, Gwyneth M. Card, Ebraheem I. Fontaine,
Richard M. Murray, and Michael H. Dickinson
Division of Engineering and Applied Science
California Institute of Technology
Pasadena, California 91125
§
Author for correspondence (e-mail: fzabala@cds.caltech.edu)
Abstract
— We present a reconstruction of the dynamics
of flight initiation from kinematic data extracted from
high-speed video recordings of the fruit fly
Drosophila
melanogaster
. The dichotomy observed in this insect’s flight
initiation sequences, generated by the presence or absence
of visual stimuli, clearly generates two contrasting sets of
dynamics once the flies become airborne. By calculating
reaction forces and moments using the unconstrained
motion formulation for a rigid body, we assess the fly’s
responses amidst these two dynamic patterns as a step
towards refining our understanding of insect flight control.
I. I
Di
ffi
culties inherent to the miniaturization of un-
manned aircraft have evoked studies of biological mech-
anisms for the development of innovative means of
perception, actuation, and control. Particular interest has
been put into characterizing insect flight, where these
three components seem to interact quite e
ff
ectively. This
reverse engineering feat has not been without challenges;
roughly, we can classify these challenges into three ma-
jor categories: 1) modeling sensors (particularly vision),
[1]–[3], and actuators (unsteady e
ff
ects of flapping), [4]–
[6]; 2) mapping variations of wing and body kinematics
to the production of aerodynamic forces and moments,
[7]–[11]; and 3) understanding mechano-sensorial con-
nections that trigger such kinematic variations, [12]–
[20]. Further di
ffi
culties are also faced at a higher
stratus of insect flight control, in particular, recognizing
patterns of behavior and understanding decision-making
processes [21]. Figure 1 illustrates the authors’ view
of the macroscopic components of insect flight control,
and the general approaches followed for its study, as
presented in literature [1]–[20].
While simplified aerodynamic models give us ac-
ceptable estimates of the insect’s production of forces
and moments, other simplifications and assumptions
limit a comprehensive understanding of insect flight
Sensors
Flight
Controller
Body
position
attitude
velocity
acceleration
kinematic
patterns
aerodynamic
forces &
moments
Muscles
Wings
1
2
3
[Fry,Taylor,Zbikowski,Hedrick]
[Dickinson,Sane,Lehmann]
[Reiser, Tammero,Bender,Epstein,Card,
Egelhaaf,Boeddeker]
Approaches
[Heisenberg, Götz, Borst]
1
Stimulus
Fig. 1. Macroscopic Components of Insect Flight Control.
1
©
,
2
©
, and
3
©
represent the areas where the study of flight control has focused.
Last names correspond to most representative references included in
this text.
control. In the past, empirical assessments of the relation
between wing and body kinematics, and the production
of aerodynamic forces and moments have been made
by studying two flight conditions, namely, hovering and
stable forward flight. Under these conditions, plausible
responses to small perturbations about the insect’s de-
sired operating point have been investigated [9]–[11].
Naturally, this leads to two important questions: What
occurs when the perturbations are not small? Does
the insect consistently produce the same forces and
moments to counteract these perturbations? Our current
framework is aimed at answering these questions, with
the underlying motivation of refining our current under-
standing of insect flight control.
A way of approaching the study of insect flight control
has been by triggering consistent behaviors, and charac-
terizing specific outcomes. In particular, this approach
has yielded interesting results in the study of visually
elicited saccadic turns in free-flight [15] and tethered
insects [16], [19], as well as in simulation environments
Proceedings of the 2nd Biennial IEEE/RAS-EMBS International
Conference on Biomedical Robotics and Biomechatronics
Scottsdale, AZ, USA, October 19-22, 2008
978-1-4244-2883-0/08/$25.00 ©2008 IEEE
1
[12], [14], [17], [18], [20], [22]. Another instance of
such consistent behaviors has been identified during the
flight initiation of the insect
Drosophila melanogaster
[13], [23]–[26]. In this case, the presence or absence of
a visual stimulus [23]–[26] yields clearly distinct flight
patterns [13].
Our approach for this study consists of using ex-
tracted kinematic data (i.e., rotational and translational
positions, velocities and accelerations) from high-speed
video recordings of flight initiations of the fruit fly
Drosophila melanogaster
[13] to derive the flight dy-
namics of each insect. In particular, we use the responses
in the absence of stimuli as our nominal flight initiation
model, and investigate the perturbations in the dynamics
introduced by the presence of such stimuli.
The paper is divided into four sections; Section II
gives an overview of the flight initiation phenomenon in
Drosophila melanogaster
, and outlines the conclusions
presented in the founding work that led to this study
[13]. In Section III we present our reconstruction of
the dynamics of flight initiation, which is followed by
a discussion of the modulation of aerodynamic forces
and moments during takeo
ff
; we conclude in Section
IV summarizing the work and discussing our intents for
future directions.
II. K
A
F
I
Drosophila
A. Coordinate Frames, Transformations and Notation
The following figure summarizes the coordinate
frames used throughout this paper:
Fig. 2.
The two coordinate frames used in the paper.
We employ standard aerodynamic coordinate frames
to describe the motion of the insect in 3D space. We
use a (lab-) earth-fixed coordinate frame (
x
f
,
y
f
,
z
f
) and
a body-centered one (
x
b
,
y
b
,
z
b
)—alternatively denoted
as roll, pitch, and yaw—as presented traditionally in
aerodynamics literature [27].
B. Flight initiation of
Drosophila melanogaster
During flight initiation, insects must transition be-
tween walking (usually at zero velocity, i.e., standing
still) and flying in a way that allows them to propel
o
ff
the ground without damaging their wings [23]. For
the fruit fly, taking o
ff
is a process that comprises a
quick extension of the legs, in tandem with the first few
wing strokes. The main thrust for this study comes from
the identification of two modes of flight initiation in
Drosophila
[23]–[26], one of which results in tumbling
flights where the insect translates faster, but also rotates
rapidly around its three body-centered axes [13]. Figures
3 and 4 illustrate this phenomenon.
Fig. 3. Voluntary Flight Initiation. Prior wing elevation (-24.2ms – -
12.7ms), and simultaneous leg-extension and wing depression (-2.3ms
– 0ms) lead to a steady controlled flight initiation (0.8ms – 8.5ms).
Fig. 4.
Escape Flight Initiation. Leg extension begins prior to
wing elevation (-3.0ms – 0ms), this leads to flight initiation without
coordinated leg-extension and wing-depression (0ms), which in turn
results in tumbling flight (7.3ms – 18.0ms
+
).
These tumbling flights, which exhibit large, tran-
sient instabilities in comparison with nominal (i.e., non-
escaping) flight initiation trajectories, promote a new
interpretation of the insect’s flight control mechanisms
beyond typical
a priori
assumptions of small deviations
around an operating point. Moreover, the contrasting
nature of the two modes of flight initiation motivates an
explicit comparison between them using control theory
criteria (e.g., stability, performance, robustness, etc.).
2
A
!
1
!
0.5
0
0.5
1
x 10
4
p
[deg.s
−
1
]
!
1
!
0.5
0
0.5
1
x 10
4
q
[deg.s
−
1
]
!
1
!
0.5
0
0.5
1
x 10
4
r
[deg.s
−
1
]
0
10
20
30
!
1.3
!
0.6
0
0.6
1.3
x 10
7
time [ms]
p
!
[deg.s
−
2
]
0
10
20
30
!
1.3
!
0.6
0
0.6
1.3
x 10
7
time [ms]
q
!
[deg.s
−
2
]
0
10
20
30
!
1.3
!
0.6
0
0.6
1.3
x 10
7
time [ms]
r
!
[deg.s
−
2
]
B
!
0.6
!
0.3
0
0.3
0.6
u
[m.s
−
1
]
!
0.6
!
0.3
0
0.3
0.6
v
[m.s
−
1
]
!
0.6
!
0.3
0
0.3
0.6
w
[m.s
−
1
]
0
10
20
30
!
180
!
90
0
90
180
time [ms]
u
!
[m.s
−
2
]
0
10
20
30
!
180
!
90
0
90
180
time [ms]
v
!
[m.s
−
2
]
0
10
20
30
!
180
!
90
0
90
180
time [ms]
w
!
[m.s
−
2
]
Fig. 5. Entire sequence for kinematics ([A] rotational, [B] translational) during flight initiation of a couple of fruit flies. Black (dark gray) trace
shows a voluntary take-o
ff
while magenta (light gray) corresponds to an escape response. Rotational kinematics
{
(
p
,
q
,
r
,
̇
p
,
̇
q
,
̇
r
)
}
are measured in
the body-fixed frame, while the translational are given relative to the lab-fixed frame
{
(
u
,
v
,
w
,
̇
u
,
̇
v
,
̇
w
)
}
. Note that the symbol (
′
) in the subplots
is meant to indicate ( ̇).
C. Body Kinematics
In [13], the kinematics of flight initiation for a set
of fruit flies were analyzed, and insightful results were
obtained. We present in Figure 5 a motivating example
where two (di
ff
erent) flies remain in the field of view
of the cameras for similar periods of time, in separate
ocassions. The black (darker grey) trace corresponds
to a fly performing a voluntary take-o
ff
, while the
magenta (lighter grey) corresponds to one executing an
escape response. These data include rotational as well
as translational rates
{
(
p
,
q
,
r
),(
u
,
v
,
w
)
}
and accelerations
{
( ̇
p
,
̇
q
,
̇
r
),( ̇
u
,
̇
v
,
̇
w
)
}
relative to the body- (
x
b
,
y
b
,
z
b
) and
lab-fixed (
x
f
,
y
f
,
z
f
) coordinate reference frames, respec-
tively (e.g., ̇
v
indicates the translational acceleration of
the fruit fly with respect to the lab-fixed
y
f
axis).
We observe that besides a noticeable di
ff
erence in
amplitude, the two sets of responses have very similar
patterns. This consistency was found in several pairs of
flies (one voluntary, and one escape), and it served as ad-
ditional motivation for investigating the di
ff
erences and
similarities under these two ‘conditions’ for initiating
flight. Notice that in the example illustrated in Figure
5 the major di
ff
erence between voluntary and escape
data is observed in the rotational kinematics about the
longitudinal axis of the fly (
p
,
̇
p
)—this di
ff
erence is
representative of the entire data, see [13] for details. In
Section III we analyze the dynamics of rotation in escape
and voluntary flight initiations, and we rationalize this
striking behavior.
Studying the dynamic responses during take-o
ff
also
required us to align the kinematic data at the instant
in time where each flight initiation occurred, for this
purpose we utilized the acceleration spike in the vertical
direction (clearly seen in the bottom-rightmost subplot
of Figure 5 where the data has not been aligned yet).
III. A
F
I
D
In this section, we use the kinematic data described
above to derive forces and moments acting on the body
in order to investigate the dynamics of voluntary and
escape flight initiations.
A. Mechanics of Unconstrained Motion
Applying Newton’s second law, the system of equa-
tions
F
T
(
t
)
=
m
̇
V
(
t
)
+
ω
(
t
)
×
(
m
V
(
t
))
(1)
M
T
(
t
)
=
[
I
]
̇
ω
(
t
)
+
ω
(
t
)
×
(
[
I
]
ω
(
t
)
)
,
describes the forces and moments about the 6DOF in
which an object can move in 3D space [27]. Boldface
notation is used to indicate vectorial quantities, and the
overdot ( ̇) is used to denote derivatives with respect to
time. Additionally,
F
T
denotes the total force, which
lumps insect’s weight, air resistance, leg forces, and
wing forces;
M
T
denotes the net moment about the
origin (located at the estimated center of mass)—another
lumped quantity;
m
denotes the mass of the fly (
m
=
1 [mg]);
V
and
ω
denote the translational and rotational
velocity vectors, respectively; and [
I
] denotes the inertia
tensor.
These reaction forces and moments are illustrated
in Figure 6 during voluntary (A,B,E,F) and escape
(C,D,G,H) takeo
ff
s. Traces for all flies are included,
and a particular pair of them—one voluntary, and one
escape—have been selected (black traces) to represent
the overall dynamic behavior. For the force data (A,C),
the top traces represent the
x
-
y
-
z
components of
F
1
=
m
̇
V
, where the superscript is used for indicating the first
(or second) right-hand side term in the corresponding
equation in (1). The middle traces correspond to
F
2
=
3
A
!
2
!
1
0
1
2
x 10
!
4
F
x
1
[N]
!
2
!
1
0
1
2
x 10
!
4
F
x
2
[N]
0
5
10
15
20
25
30
35
40
!
2
!
1
0
1
2
x 10
!
4
time [ms]
F
x
T
[N]
!
2
!
1
0
1
2
x 10
!
4
F
y
1
[N]
!
2
!
1
0
1
2
x 10
!
4
F
y
2
[N]
0
5
10
15
20
25
30
35
40
!
2
!
1
0
1
2
x 10
!
4
time [ms]
F
y
T
[N]
!
2
!
1
0
1
2
x 10
!
4
F
z
1
[N]
!
2
!
1
0
1
2
x 10
!
4
F
z
2
[N]
0
5
10
15
20
25
30
35
40
!
2
!
1
0
1
2
x 10
!
4
time [ms]
F
z
T
[N]
B
0
5
10
15
20
25
30
35
40
0
1
2
3
x 10
!
4
time [ms]
F
total
[N]
C
!
2
!
1
0
1
2
x 10
!
4
F
x
1
[N]
!
2
!
1
0
1
2
x 10
!
4
F
x
2
[N]
0
5
10
15
20
25
30
35
40
!
2
!
1
0
1
2
x 10
!
4
time [ms]
F
x
T
[N]
!
2
!
1
0
1
2
x 10
!
4
F
y
1
[N]
!
2
!
1
0
1
2
x 10
!
4
F
y
2
[N]
0
5
10
15
20
25
30
35
40
!
2
!
1
0
1
2
x 10
!
4
time [ms]
F
y
T
[N]
!
2
!
1
0
1
2
x 10
!
4
F
z
1
[N]
!
2
!
1
0
1
2
x 10
!
4
F
z
2
[N]
0
5
10
15
20
25
30
35
40
!
2
!
1
0
1
2
x 10
!
4
time [ms]
F
z
T
[N]
D
0
5
10
15
20
25
30
35
40
0
1
2
3
x 10
!
4
time [ms]
F
total
[N]
E
!
8
0
8
x 10
!
9
M
x
1
[N.m]
!
8
0
8
x 10
!
9
M
x
2
[N.m]
0
5
10
15
20
25
30
35
40
!
8
0
8
x 10
!
9
time [ms]
M
x
T
[N.m]
!
8
0
8
x 10
!
9
M
y
1
[N.m]
!
8
0
8
x 10
!
9
M
y
2
[N.m]
0
5
10
15
20
25
30
35
40
!
8
0
8
x 10
!
9
time [ms]
M
y
T
[N.m]
!
8
0
8
x 10
!
9
M
z
1
[N.m]
!
8
0
8
x 10
!
9
M
z
2
[N.m]
0
5
10
15
20
25
30
35
40
!
8
0
8
x 10
!
9
time [ms]
M
z
T
[N.m]
F
0
5
10
15
20
25
30
35
40
0
0.2
0.4
0.6
0.8
1
x 10
!
8
time [ms]
M
total
[N.m]
G
!
8
0
8
x 10
!
9
M
x
1
[N.m]
!
8
0
8
x 10
!
9
M
x
2
[N.m]
0
5
10
15
20
25
30
35
40
!
8
0
8
x 10
!
9
time [ms]
M
x
T
[N.m]
!
8
0
8
x 10
!
9
M
y
1
[N.m]
!
8
0
8
x 10
!
9
M
y
2
[N.m]
0
5
10
15
20
25
30
35
40
!
8
0
8
x 10
!
9
time [ms]
M
y
T
[N.m]
!
8
0
8
x 10
!
9
M
z
1
[N.m]
!
8
0
8
x 10
!
9
M
z
2
[N.m]
0
5
10
15
20
25
30
35
40
!
8
0
8
x 10
!
9
time [ms]
M
z
T
[N.m]
H
0
5
10
15
20
25
30
35
40
0
0.2
0.4
0.6
0.8
1
x 10
!
8
time [ms]
M
total
[N.m]
Fig. 6.
Reaction forces and moments during voluntary (A,B,E,F) and escape (C,D,G,H) take-o
ff
s. The black traces correspond to individual
flies (one for escape data, another for voluntary) selected to represent the overall dynamic behavior. For the force data (A and C), the top
traces represent the
x
-
y
-
z
components of the first term on the right-hand side of (1), while the middle traces correspond to the second term. The
bottom traces show the total force, and its magnitude is depicted in B and D. The presentation of the moment data (E,F,G,H) is analogous. The
solid, horizontal trace, and the data point at 0 [ms] in B and D correspond to comparable results reported in literature: the data point (274 [
μ
N])
corresponds to the force produced by the legs of flies in response to a visual stimulus [28] (comparable to our escape data); meanwhile, the
horizontal trace (20
.
1 [
μ
N]) represents the average force produced by the wings during forward flight [29] (comparable to both sets of data).
Results in literature describing moment data are not suitable for comparison with ours.
4
ω
×
(
m
V
). Finally, the bottom traces show the total force,
F
T
, while its total magnitude is depicted in the right
half of the figure (B,D). The moment data (E,F,G,H) is
presented in an analogous manner.
B. Discussion
We observe that the initial forces (at 0 [ms]) generated
during escaping takeo
ff
s exceed those corresponding to
voluntary ones (net forces almost double). Although,
given that a considerable subset of escaping takeo
ff
s take
place without wing depression (i.e., the first wingbeat
occurs
after
losing contact with the substrate), and their
dynamics are similar to those that do include an initial
wingbeat (in terms of magnitude), we can assess that
the main di
ff
erence between forces generated in the two
types of flight initiation relates to the jump (a more
detailed justification is given in [13]). Moreover, given
the kinematic behavior of escaping responses [13], we
understand that 1) leg forces play a crucial role in the
steadiness of flight initiations, and 2) wing forces are
not su
ffi
cient to guarantee a steady takeo
ff
in visually
elicited responses.
The moments produced during flight initiations (Fig-
ure 6) are based on an approximation of the shape of the
fly by a cylinder. Recall that the moment of inertia tensor
for a cylinder comprises three principal components
I
xx
=
1
2
(
mR
2
)
,
I
yy
=
I
zz
=
1
12
(
mL
2
)
+
1
4
(
mR
2
)
,
and six
o
ff
-diagonal terms
I
xy
=
I
yx
=
I
xz
=
I
zx
=
I
yz
=
I
zy
=
0
.
Solving for
M
x
in (1):
M
x
=
I
xx
̇
p
+
(
I
zz
−
I
yy
)
qr
, where (
I
zz
−
I
yy
)
=
0
,
(2)
which implies that the insect’s moment about the
x
b
-
axis is approximately proportional to the rotational ac-
celeration about this axis irrespective of coupling (the
approximation would be exact if the fly’s shape would
actually be a cylinder). According to the kinematic
data [13], the most significant dissimilarity between
voluntary and escape flight initiations corresponds to
the rotational rate and acceleration about this axis.
Based on our earlier assessment about the di
ff
erence in
forces generated during voluntary and escape takeo
ff
s,
we center our attention at time
t
=
0 [ms]. However,
we are limited in this set of experiments by the fact
that forces and moments were not measured directly (as
produced by the insect), and thus, we carefully interpret
the results.
Typical values for longitudinal and radial lengths of
Drosophila
are
L
=
2
.
5 [mm], and
R
=
0
.
7 [mm] [7]. If
we use these values to calculate our simplified moment
of inertia tensor, we have
I
yy
=
I
zz
=
386
147
I
xx
≈
2
.
6
I
xx
.
(3)
And so, given that peak rotational rates with respect
to the
x
b
-axis during escape responses were more than
three times those observed during voluntary ones, while
the peak rotational rates about the other two axes,
y
b
and
z
b
, were roughly twice as large [13]. Then, the
lower moment of inertia about the
x
b
-axis—in compar-
ison with the other two body axes (3)—could partially
account for the di
ff
erence in rotational rates about the
three body axes, depending on the torques generated by
the fly during takeo
ff
.
We can also consider ‘lateral’ and ‘longitudinal’,
F
lat
B
√
(
F
T
z
)
2
+
(
F
T
y
)
2
,
and
F
lon
B
√
(
F
T
z
)
2
+
(
F
T
x
)
2
,
components of the initial forces; a significant di
ff
erence
between them (e.g.,
F
lat
[
t
=
0]
>>
F
lon
[
t
=
0]) could
also account for an increase in the rotation about
x
- or
y
-axis during escaping takeo
ff
s.
A third possibility could be an asymmetry in the
forces generated by each leg, which would result if
the insect actually produced di
ff
erent forces with its
muscles, or if the legs lost contact with the ground at
di
ff
erent times. Given that the data do not o
ff
er details
about leg-specific kinematics, we are unable to assess
this hypothesis concretely. We can, however, expand the
left hand side of (1) by decomposing the total force as,
F
T
(
t
)
=
F
A
(
t
)
+
F
L
(
t
)
+
U
(
t
)
+
W
,
where
(4)
F
A
(
t
)
=
f
(
α
(
t
)
,φ
(
t
)
,...
)
,
and
F
L
(
t
)
=
g
(
ξ
(
t
)
,ψ
(
t
)
,...
)
.
Using
W
to denote the insect’s weight vector,
U
(
t
) to
denote air resistance,
F
A
(
t
) to denote the aerodynamic
force produced by the insect’s wings;
f
:
S
→
R
3
to
indicate the mapping of the
n
-dimensional space
S
=
{
α
(
t
)
,φ
(
t
)
,...
}
(of
n
di
ff
erent wing kinematic parameters)
to wing forces;
F
L
(
t
) to denote the force produced by
the legs; and
g
:
Q
→
R
3
to indicate the mapping of the
j
-dimensional space
Q
=
{
ξ
(
t
)
,ψ
(
t
)
,...
}
(of
j
di
ff
erent
leg kinematic parameters) to leg forces.
This expansion (4) allows us to establish at least two
comparisons between our results and those in literature.
Since leg forces are only active for as long as there is
contact with the substrate, first, we consider our initial
forces (
t
=
0 [ms]), which averaged to 97
.
3
±
5
.
1 [
μ
N] for
voluntary, and 173
.
1
±
20
.
1 [
μ
N] for escaping takeo
ff
s;
mean
±
s.d.;
n
=
12
,
23 respectively. And, we compare
them to those reported by Zumstein
et al
, which were
measured during visually elicited takeo
ff
s and peaked
at 274 [
μ
N] [28]. These measurements were made in
tethered flies and the results were highly dependent
on ‘leg angles’, which could partially account for our
underestimates. Secondly, since the unsteady dynamics
induced by the jump become negligible after a certain
5
period of time (particular to each individual fly), the
‘tail’ of our dynamic data approximate the sum of
aerodynamic forces produced by the insect’s wings, the
e
ff
ect of gravity, and the air resistance. Neglecting the
e
ff
ects of air resistance, these estimates are similar to
those in literature where it is found that the maximum
average force produced throughout a wingstroke (for
Drosophila melanogaster
) is around 200% of body
weight (approximately 20
.
1
μ
N) [29].
IV. C
F
W
In this paper we presented a framework for studying
the dynamics of flight initiation in
Drosophila
. The
reconstruction of kinematic data of the fruit fly’s takeo
ff
allowed the derivation of the forces and moments experi-
enced by the animal. The importance of flight initiation
behavior in this particular study is that it allowed, in
a consistent manner, the observation of the insect’s
response while undergoing di
ff
erent dynamics. Thus, an
emergent direction from this study is characterizing such
response as a function of the insect’s wing kinematic
patterns (the wings constitute the only active actuation
mechanism after take-o
ff
). Understanding how aerody-
namic forces and moments are produced is essential to
fully assess the dynamic behavior of the fly.
Another emergent aspect from this study is the as-
sessment of some of the disturbances that must be han-
dled by the insect’s flight controller. We have observed
throughout this paper that this is a salient feature during
the escaping takeo
ff
s, where large rotation rates need
to be mitigated. Thus, a future direction that we shall
follow is to study the transient ‘impulsive’ disturbances
introduced by the fly’s jump in relation to the leg
kinematics; and subsequently, to assess the fly’s response
to them.
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