For several
decades the visuo-motor control system of flies has been extensively
studied. However, recent results have cast new light on many long standing
assumptions about the operation of the flight control system. In this
project we seek to demonstrate that through a faithful model of the
fly's behavior, it is possible to provide some context within which
controlled behavioral assays can be interpreted.
An early model of visuomotor control in flies was the optomotor equilibrium
reflex. A fly presented with a visually rotating environment will turn
in the direction of the rotation (Götz 1968). This response is
thought to minimize image rotation during flight and stabilize the course
of the fly. Recent work in the Dickinson lab shows the optomotor response
to be an artifact, explained by the linear sum of a system which responds
to lateral rotatory stimuli (Tammero 2003). In a tethered flight arena,
flies exhibit a robust tendency to orient towards a visual pole of contraction.
This behavior suggests that perhaps such a system could be used to detect
the direction of wind. In this project we investigated the use of the
fly's vision system as the sole sensory modality to counteract the effect
of wind disturbances during upwind flight. Our goal is to understand
the physical mechanisms involved and circumstances under which a fly
can track a given wind direction, given only the sensory information
available from the vision system. The initial portion of the project
was spent understanding and modeling the appropriate physics of the
body dynamics and aerodynamics, vision system, wing aerodynamics, and
sensory-motor processing. The latter portion of the project was spent
understanding the closed loop system in terms of performance to step
changes in wind direction and robustness to changes of environmental
conditions such as contrast.
The modeling effort focused on each of the blocks in the closed loop
simulation, including body dynamics, body and wing aerodynamics, vision
and the sensory-motor system (Figure 3). An effort was made to understand
and include detailed and relevant physics, especially in the aerodynamics
and vision blocks, which were carefully designed to include recent results
in the literature.
We performed a simple experiment using the dynamically-scaled robotic
fly (Robofly) to generate data for the aerodynamic drag on the fly’s
body. A dynamic model was created which coupled the planar body aerodynamics
to recent results (Fry, et al. 2003), which concluded that the yaw axis
rotational dynamics were dominated by inertia, rather than by viscous
effects, as was previously thought. Throughout the model the system
was simplified to planar dynamics with one axis (yaw) of rotation. In
modeling the aerodynamics of the wings, we chose to use real wing kinematics
coupled to a quasi-steady model for the force production that has been
developed in the Dickinson lab (Sane and Dickinson 2002).
The visual system was modeled as an array of Elementary Motion Detectors
(EMDs) coupled with a matched filter logic that feeds back an estimate
of the location of the visual pole of contraction. The sensory-motor
system essentially acts as a proportional controller on this visual
pole location, which interpolates between pre-determined sets of wing
kinematics known (via Robofly) to generate the correct types of forces
and torques required for realistic motion.
Figure 5. Closed loop upwind flight model with disturbances
Closed Loop Performance
From the step response and frequency response data (Figure 4) it is
clear that the closed loop system is stable. Stability of this system
corresponds to orientation upwind, evidenced by the approximately zero
steady state error in the step response plots. Cast as a tracking problem,
the tracking error is the amount of sideslip the fly experiences, which
is the difference between the inertial velocity orientation and the
orientation of the fly's body (these are the two step responses plotted
in Figure 4, at steady state these converge, so the tracking error is
zero). From the frequency response data, we can see the system is robust
to low frequency fluctuations, which are certainly on the order of the
wind disturbance a fly should encounter.
We also examined the effect of the contrast levels in the environment
on the closed loop frequency response. It turns out that contrast levels
have no effect on performance in our model in the non-noisy environment
we have simulated. The Reichardt-Hassenstein model predicts a quadratic
dependence on contrast—that is in an environment with half the
contrast the response is reduced to 25%. When we include this magnitude
reduction in our model, it changes nothing, because the controller uses
the phase of the EMD response, and is independent of its magnitude,
unless the signal to noise ratio becomes intolerable.
Conclusions
This project has shown that a realistic simulator of closed loop behavior
can be a significant tool for future research in insect flight control.
However, the model must be extended to a full 3-dimensional simulation
to be truly useful. Our simplified planar world forced us to use a 1-dimensional
visual array. Certainly a globally sensitive visual system presents
more complexity to the controller, but also more information about the
world. There is evidence that optimal visually-guided behavior requires
global optic flow (Dahmen, et al. 2001). Our results with contrast levels
suggest that feeding back the phase of the EMD response is a more robust
control strategy than anything dependent on the optic flow magnitude.
This warrants further analysis, with a proper noise model of real-world
image statistics. Our method for generating wing kinematics was a convenient
way to achieve realistic forces in simulation, however it is unlikely
that smoothly interpolating between ‘endpoint’ kinematics
is analogous to insect-like control over the wing kinematics. Clearly
much of the changes in the kinematics are highly correlated, though
it is not clear what parameterization would best reveal these correlations.
Furthermore, our method assumes that the fly has amazingly precise control
over the kinematics; is this valid or is there a slightly different
way that flies control flight forces? This project has demonstrated
the feasibility of visually-guided orientation upwind, however we did
not address the associated velocity control problem, that is, once oriented
upwind how does a fly transition from backwards to forward flight in
the upwind direction. For this to occur the fly must be able to pass
from orienting to a frontal contracting pole to a frontal expanding
pole. It seems unlikely that a smooth control law can operate with such
discontinuities.
References
Dahmen, H.-J., Franz, M. O., and Krapp, H. G. (2001). Extracting egomotion
from optic flow: limits of accuracy and neural matched filters. In Zanker,
J. and Zeil, J., editors, Motion vision: computational, neural and ecological
constraints, pages 143–168. Springer Verlag, Berlin.
Fry, S., Sayaman, R., and Dickinson, M. (2003). The aerodynamics of
free-flight maneuvers in drosophila. Science, 300(5618):495–498.
Götz, K. G. (1968). Flight control in Drosophila by visual perception
of motion. Kybernetik, 9:159–182.
Sane, S. and Dickinson, M. (2002). The aerodynamic effects of wing rotation
and a revised quasisteady model of flapping flight. J. Exp. Biol., 205(8):1087–1096.
Tammero, L. F., Frye, M. A., and Dickinson, M. H. (2003). Spatial organization
of visuomotor reflexes in Drosophila. Sumbitted to J. Exp. Biol.
