May_EDFA_Digital

edfas.org ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 22 NO. 2 18 equal, ν → pl = ν → tl ). Because the prey does not change direc- tion or speed during the engagements considered here, proportional navigation produces straight-line trajecto- ries that do not require additional dragonfly maneuvers before successful interception. Of particular interest is understanding how proportional navigation might be implemented using visual input, specifically prey-image drift away from the fovea. PURSUIT IN THE DRAGONFLY MODEL Figure 3 shows hunting trajectories resulting from foveating prey while the fovea is located in the center of the eye-screen. Themodel dragonfly heads directly at the prey at all times, a strategy known as “classical pursuit.” [1-2] The two prey trajectories in Fig. 3 are identical to those in Fig. 2, with the location of the prey at each time step indicated by the red stars (with the initial location of the prey indicated by the open red circle). The position of the dragonfly at each time step is indicatedby theblack circles. Generally, pursuit behavior is characterizedby a curved trajectory towards the prey, requiring the pursuer to travel a greater distance (relative to the prey) for a successful capture. While classical pursuit is a viable strategy for prey-capture used by many species of animals includ- ing houseflies and honeybees, [1] it is known to require a speed overmatch to be generally successful. For example, in Fig. 3b, the dragonfly falls directly behind the prey and (becausedragonfly andprey aremoving at the same speed in these simulations) is unable to catch up. Fig. 2 Example prey trajectories. In both panels, the dragonfly’s initial position is the origin (open black circle) and the prey’s initial position (open red circle) is (10,2,0). The prey’s position at each time step is indicated by a red star. The green line indicates the geometrically shortest path to interception, as calculated using proportional navigation guidance. (a) Preymoves towards the dragonfly, but only along the x-axis. (b) Prey moves towards the dragonfly along the x-axis, but at the same time away from the dragonfly in the y-direction. (b) (a) Fig. 3 Classical pursuit in the dragonflymodel. Twohunting scenarios for which the model dragonfly maneuvers to maintain the prey’s image on the fovea at the center of thedragonfly’s eye-screen. Prey trajectories are identical to those in Fig. 2a and b. Prey positions and model dragonfly positions at each time step are indicated by the red stars and open black circles, re- spectively. Larger red andblack circles indicate start- ing positions of the prey and the model dragonfly. (b) (a)