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First published online January 18, 2008
Journal of Experimental Biology 211, 423-432 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.011791

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Active control of free flight manoeuvres in a hawkmoth, Agrius convolvuli

Hao Wang^1,2,*, Noriyasu Ando¹ and Ryohei Kanzaki¹

¹ Research Center for Advanced Science and Technology, the University of Tokyo, Tokyo, Japan
² Japan Society for the Promotion of Science (JSPS), Tokyo, Japan

View larger version (20K): [in this window] [in a new window]   Fig. 1. Experimental setup used to record flight manoeuvres and EMG activity synchronously. Hawkmoths with a ventrally attached telemeter were released into an enclosed electromagnetically shielded flight arena and imaged with one high-speed camera associated with a fringe pattern projector (FPP) set at 1000 frames s–1.

View larger version (31K): [in this window] [in a new window]   Fig. 2. Three-dimensional reconstruction of optical fringes and body-fixed coordinate frame. (A) One example of a recording frame with the deformed fringes on the wings (back view, elevation=azimuth=0°). The brightest one was the reference fringe. (B) Surface topography of body and wings by three-dimensional reconstruction (rear lateral view, elevation=10°, azimuth=7°). Blue curves indicate the reconstructed laser fringes; green curves, lateral leading edges; red curves, 50% cross-section along wingspan. Green crosses indicate wing bases; red crosses, middle points of leading edges. Body-fixed coordinate frame (magenta vectors) deduced by three-dimensional reconstruction is also superimposed. Euler angles are indicated by the grey curved arrows, whose rotations have an ordered sequence of yaw (), pitch (β) and roll () according to the Fick coordinate system (Haslwanter, 1995; Schilstra and Hateren, 1998). Signs comply with the right-hand rule, and the reference orientation is coincident with the global coordinate frame (denoted by the coordinate grid) fixed on the flight arena.

View larger version (19K): [in this window] [in a new window]   Fig. 3. Definitions of wing kinematics and muscle activities. (A) Quantification of the wing position at the ventral stroke reversal. The body-fixed coordinate frame is shown in black. The leading edge of the right forewing is indicated by a green line located in the fifth quadrant. The red and blue lines indicate the projected leading edges on the coordinate plane of xoy and xoz, respectively. Flapping angle (, in red) and deviation angle (, in blue) are defined as the included angles between the leading edge and the corresponding projection planes (>0 if z<0, >0 if y>0, and vice versa). The corresponding bilateral differences, treating left side as the reference, were exhibited by and , respectively. (B) Definition of the EMG activities. Cycle length () is the interval between the first DLM spikes in the adjacent wingbeats, which can be understood as a half-closed–half-open interval, in which the anterior DLM reference spike was included while the posterior one was excluded. The activities of the DVM and 3AXM were expressed by the firing timing relative to the anterior DLM reference spike. DVM and 3AXM latencies (DV and 3AX) are their onset timing relative to the anterior DLM reference. DVM and 3AXM phases (DV and 3AX) are defined as the ratio of latencies to the cycle length, treating it as 360°. The corresponding bilateral differences in latency and phase, treating left side as the reference, were exhibited by and , respectively.

View larger version (19K): [in this window] [in a new window]   Fig. 4. Flight trajectory and body attitudes during obstacle avoidance manoeuvres (corresponding to the time course in Fig. 5A). Body attitude for every wingbeat of the captured sequence is indicated by the body-fixed frame, of which red, green and blue vectors represent the x-, y- and z-axis in Fig. 2B, respectively. The corresponding orthogonal projections are shown in black, with dots indicating the origins of local frames and lines the body axes (collinear with y-axis). The hawkmoth approached the target, performed an avoidance manoeuvre, and then accelerated away by backward flight. The grey arrow indicates the start of this recording.

View larger version (110K): [in this window] [in a new window]   Fig. 5. Time courses for synchronizing analyses on EMG and kinematics. The EMG firing spikes are indicated by the solid arrowheads (for DLM) and open arrowheads (for DVM or 3AXM). Data markers denote different timings by different shapes: open squares for DLM firing timing, open circles for DVM and 3AXM firing timing, solid circles for ventral stroke reversal timing, solid squares for dorsal stroke reversal timing. The alternating white–grey strips are employed to discriminate the time of ventral stroke reversal. The span of the strips does not represent the wingstroke cycle defined by the DLM intervals in Fig. 3B. (A) One case of bilateral DLM–DVM recordings and analysis. The black curves in wing position, as a comparison, denote the flapping and deviation angles (both in inverse values) at the dorsal stroke reversals; solid and dashed lines for right and left side, respectively. (B) One case of left-side DLM–DVM–3AXM recordings and analysis. (C) One case of bilateral 3AXM recordings and analysis. Because of the absence of the DLM reference, only the bilateral latency difference is shown. a.u., arbitrary units.

View larger version (73K): [in this window] [in a new window]   Fig. 6. Individual regressions for the left-side DLM–DVM–3AXM recordings (A,B,D,E,G–I), the bilateral DLM–DVM recordings (C) and the bilateral 3AXM recordings (F). Regression lines are shown by solid lines if the slope of the individual regression was significant and if the covariates (DV, DV, 3AX, 3AX, or ) attained overall significance in the corresponding pooled general linear model; otherwise, they are shown by dashed lines. The different colours distinguish data from the different individuals. For each individual, data from several flight sequences were pooled. See Figs 2 and 3 for definitions. (A,B) Graphs of flapping angle against DVM latency DV (A) and 3AXM latency 3AX (B); and (C) graph of bilateral difference in flapping angle against bilateral difference in DVM latency DV. (D,E) Graphs of deviation angle against 3AXM latency 3AX (D) and DVM latency DV (E); and (F) graph of bilateral difference in deviation angle against bilateral difference in 3AXM latency 3AX. (G–I) Graphs of pitch angle β against flapping angle (G), deviation angle (H) and 3AXM latency 3AX (I).

View larger version (25K): [in this window] [in a new window]   Fig. 7. The left wing tip trajectories projected on the yoz plane in the body-fixed coordinate frame. The data correspond to the time course in Fig. 5B. Assuming that the aerodynamic centre was located at a point 0.25 chord lengths behind the leading edge (Milne-Thomson, 1973; Usherwood and Ellington, 2002), the deviation angles are shifted about 18° along the local y-axis backwards to approximate the trajectories of force application point. The wing tips at the ventral stroke reversals are indicated by the colour-mapped circles to denote the 3AXM latency. The wing tips at the dorsal side are marked by the dark grey squares, and the wing base is marked by the black circle. The centre of gravity was estimated by the plumb bob method for body (telemeter attached ventrally) only, neglecting the influence of the relatively light wings.