Control-Oriented Reduced Order Modeling of Dipteran Flapping Flight

Flying insects achieve flight stabilization and control in a manner that requires only small, specialized neural structures to perform the essential components of sensing and feedback, achieving unparalleled levels of robust aerobatic flight on limited computational resources. An engineering mechanism to replicate these control strategies could provide a dramatic increase in the mobility of small scale aerial robotics, but a formal investigation has not yet yielded tools that both quantitatively and intuitively explain flapping wing flight as an "input-output" relationship. This work uses experimental and simulated measurements of insect flight to create reduced order flight dynamics models. The framework presented here creates models that are relevant for the study of control properties. The work begins with automated measurement of insect wing motions in free flight, which are then used to calculate flight forces via an empirically-derived aerodynamics model. When paired with rigid body dynamics and experimentally measured state feedback, both the bare airframe and closed loop systems may be analyzed using frequency domain system identification. Flight dynamics models describing maneuvering about hover and cruise conditions are presented for example fruit flies (Drosophila melanogaster) and blowflies (Calliphorids). The results show that biologically measured feedback paths are appropriate for flight stabilization and sexual dimorphism is only a minor factor in flight dynamics. A method of ranking kinematic control inputs to maximize maneuverability is also presented, showing that the volume of reachable configurations in state space can be dramatically increased due to appropriate choice of kinematic inputs

Dynamic mode decomposition of the metachronal paddling wake

Metachronal paddling is a drag-based propulsion strategy observed in many aquatic arthropods in which a series of paddling appendages are stroked sequentially to form a traveling wave in the same direction as animal motion. Metachronal paddling’s relatively high force production makes these organisms highly agile, an attractive potential for bio-inspired autonomous underwater vehicles that is complicated by the lack of reduced order flow structure and dynamics models applicable to vehicle actuation and control design. This study uses particle image velocimetry to quantify the wake of a robot performing metachronal paddling. Then, dynamic mode decomposition is used to identify the frequency modes of the wake, which are used to reconstruct a reduced order model at Reynolds numbers of 32, 160, and 516. The results show that the kinetic energy in the metachronal paddling wake is well modeled using a superposition of the first 5 dynamic modes, and that there is typically little change in the reconstruction error when the reconstruction is performed with a higher number of dynamic modes. The low order paddling models identified using this method can be used to identify the physical mechanisms that differentiate metachronal paddling from synchronous paddling, and to develop control strategies to modulate these motions in bio-inspired autonomous underwater vehicles.Mechanical and Aerospace Engineerin

Tunnel setup attached to a beehive with camera setup to film the intersection.

Tunnel setup attached to a beehive with camera setup to film the intersection.</p

Ethanol exposed flight digitization.

A sample video footage where a 0% bee and 1% bee are flying together. Their reconstructions and planar wing motion are shown. (MP4)</p

Behavioral repertoire distribution by ethanol concentration.

Behavioural diversity was estimated via proportional analysis on manual labels. The results indicate a dominance of turning flight, where behaviors were consistent across concentrations, and that 1% and 5% trials had higher incidences of descending and ascending flight, respectively.</p

Characterizing body <i>B</i> and wing <i>W</i> variables in flight sequence.

Characterizing body B and wing W variables in flight sequence.</p

Wing kinematics: Bulk (left column) and trial-wise (right column).

Stroke vs deviation angle of each concentration’s mean wingstroke pattern (top row) shows the increasingly planar strokes with concentration in bulk analysis, while the individual analysis shows deviation from the trend in 5% concentration. Wing stroke and deviation angle stroke histories (bottom 2 rows, τ denotes non-dimensional time) are shown as for each concentration’s mean stroke μ ± its standard deviation σ. Stroke histories illustrate how the ethanol-related changes exceed standard deviations.</p

Definition of wing variables.

Stroke plane angle β and dorsal bias δ are determined relative to planar wingtip motion.</p

Mean <i>μ</i>_<i>i</i> and standard deviation <i>σ</i>_<i>i</i> of <i>i</i> = [0%, 1%, 2.5%, 5%] concentration datasets.

Asterisks indicate significant p-values (***<0.001, **<0.01, * < 0.05).</p

Mean <i>μ</i>_<i>i</i> and standard deviation <i>σ</i>_<i>i</i> of <i>i</i> = [0%, 1%, 2.5%, 5%] concentration datasets for wing variables for trial-wise and bulk wingstrokewise analysis.

Asterisks indicate significant p-values (***<0.001, **<0.01, * < 0.05).</p