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First published online March 31, 2005
Journal of Experimental Biology 208, 1563-1572 (2005)
Published by The Company of Biologists 2005
doi: 10.1242/jeb.01558

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A single control system for smooth and saccade-like pursuit in blowflies

Norbert Boeddeker^* and Martin Egelhaaf

Bielefeld University, Department of Neurobiology, PO Box 10 01 31, 33501 Bielefeld, Germany

View larger version (28K): [in a new window]   Fig. 2. Saccade-like and smooth tracking during chasing flights of male blowflies. (A) Top view of a flight trajectory of a fly (black markers) chasing a black sphere (diameter: 8.3 mm) moving at a speed of 1.25 m s–1 on a circular track in a horizontal plane (grey line). The position (circle) and body axis orientation (lines) of the fly are shown every 20 ms. The fly follows the target for 4 s. (B) Flight trajectory of a fly chasing another fly in top view, plotted as in A. To allow an easier comparison, i.e. to have the same direction of target motion, the trajectories in B were vertically flipped before further analysis. (C,D) Plots of the error angle, (E,F) yaw orientation and (G,H) angular velocity, vs time for the chase. In order to use the same time scale in all plots, only the first 740 ms of the chase displayed in A are shown in C, E and G. The rotational velocity of the dummy target (716 deg. s–1) is indicated by the dotted line in G. All traces are affected by noise, primarily due to tape jitter (Boeddeker et al., 2003). Despite this methodical limitation the yaw velocity peaks due to saccade-like body rotations are readily visible in H.

View larger version (26K): [in a new window]   Fig. 1. Signal processing performed by the virtual fly. We implemented two visual pathways in the virtual fly: one for target fixation (A) and one for speed control (B). A further module that receives input from both pathways determines the virtual fly's actual position in the next simulation step (C). In each simulation step the fixation controller, converts the error angle according to the characteristic curve shown in C, weighted by Gp, and the retinal velocity, weighted by Gv, into angular velocity of the pursuing virtual fly (tn+1). The output of the virtual fly's speed controller depends on retinal target size according to the characteristic curve shown in the box and determines the absolute value of the fly's speed vector for the next simulation step [s(tn+1)]. First-order low-pass temporal filters are applied to the outputs of both visual pathways, lumping together inertial effects, neuronal processing and muscular reaction time. The filtered outputs from each pathway form the `intended' vector of locomotion of the virtual fly. A third module determines the virtual fly's velocity in the next simulation step as the sum of the actual fly velocity and the `intended' velocity vector weighted by the movement coefficient M. Six of the free model parameters were taken from our preceding study (Boeddeker and Egelhaaf 2003): the two first-order low-pass filter time constants acting on fixation (f=15 ms) and speed control (v=80 ms), the movement coefficient (M=0.0455), and three parameters characterising the transfer function of the speed controller (Sg=0.8 m s–1, Sv=67, and *= 0.0865). The gain factor for yaw rotation, depending on retinal target position (Gp), was set to 0.1 and the gain factor for yaw rotation, depending on retinal target velocity (Gv).

View larger version (27K): [in a new window]   Fig. 3. Chasing a realistically moving target by the virtual blowfly. The gain factor for retinal velocity input relative to the fixation controller is varied. The data shown in A–D are from a virtual blowfly using the `position-only servo', i.e. the virtual blowfly steers its flight direction only by minimising the error angle. (A) Trajectory of the virtual fly chasing the target (plotted as in Fig. 2A). After sharp turns of the target, the virtual fly makes saccade-like turns, but tends to overshoot the target and then makes a correctional movement. This behaviour leads to a curved path and fluctuations of the error angle (B) and yaw velocity (D). The yaw orientation (C) of the virtual fly changes in a step-like manner similar way to that seen in real flies (Fig. 1A). If the virtual blowfly uses a `position-plus-velocity servo', i.e. it uses both position and velocity information, (Gv=0.0015), flight performance is stabilised by reducing the overshooting of the target (E–H). Saccade-like turns are characterised by brief yaw velocity peaks (arrows in D,H). Increasing the gain of the velocity signal to higher values (Gv=0.025) leads to rather smooth flight trajectories and an elimination of saccade-like turns. This chasing performance differs greatly from the flight trajectories of real flies (I–L).