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edfas.org 1 7 ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 22 NO. 2 slower prey speed would have required additional con- straints describing the trade-off between expending addi- tional energy and reaching the target sooner. Moreover, given that a longer-term objective for this model is to eventually inform interception in a man-made system, it seemed reasonable to remove the biological dragonfly’s speed overmatch (relative to typical prey). One outcome of thismodificationwas that engagements took place over larger distances than realistic for biological dragonflies and their prey (tens of meters rather than one meter). The eyes of the dragonfly are simulated as a two- dimensional screen (referred to as the eye-screen, see Fig. 1). While dragonflies have two eyes and depth percep- tion, [15] the design of this model assumes that dragonflies do not rely upon depth perception for prey hunting. Figure 1 includes a schematic of the model dragonfly. The dragonfly head is indicated by the open black circle (located at the origin) and is also the reference point for calculating changes inpitch and yawangles as the dragon- flymaneuvers. For reference, the dragonfly body is drawn as a solid black line aligned to the dragonfly’s direction of movement. The eye-screen is delineated by dashed blue lines and blue diamonds (one at each corner). The red star is the prey, with the dashed red line indicating the line-of- sight from dragonfly head to prey (also referred to as the range-vector). The open red circle indicates the location of the prey-image (the prey projected onto the eye-screen). In this particular example, the prey-image falls directly in the center of the eye. In practice, the size of the eye is not restricted, but the scenarioswe considerednever required an area as large as that illustrated in the figure. Prey-image drift on the eye-screen is determined by how the prey moves relative to the dragonfly, and the model maneuvers to compensate for prey-image drift. Each time step (1/100s), the dragonfly adjusts pitch and yaw (for simplicity, roll was not included in this model) to re-center theprey-imageon the fovea. A successful capture is defined as any point in time in which the dragonfly distance from the prey is less than the distance that the dragonfly moves within one time step of the simulation. RESULTS The simulations for two different prey trajectories are shown inFig. 2. The startingpositionsof both thedragonfly (open black circle) and the prey (open red circle) are iden- tical in both panels. For Fig. 2a, the prey moves along the x-axis towards the dragonfly’s initial position. For Fig. 2b, the preymoves along the x-axis towards dragonfly’s initial position but at the same time moves away from the drag- onfly along the y-axis, a more difficult scenario. The green trajectories in Fig. 2 are the interception tra- jectories calculated using the parallel navigation rule. [10] Parallel navigation determines the geometrically short- est (and therefore time-optimal) interception trajectory and results from proportional navigation guidance. To calculate parallel navigation trajectories, the transverse component of prey velocity is found by first projecting prey velocity onto the line-of-sight between the dragonfly headand the prey (thus calculating the component of prey velocity along the line-of-sight, ν → tl ): (Eq 1) where ν → H is the prey velocity and l → pt is the line-of-sight between the dragonfly and the prey. The transverse component of prey velocity is ν → tt = ν → H -ν → tl . For parallel navigation, the dragonfly matches this component (the transverse component of dragonfly velocity is ν → pt = ν → tt ) and then devotes remaining resources to movement towards the prey along the range-vector (equivalent to the line-of-sight to the prey). The dragon- fly velocity component along the range-vector is then ν → pl = where | ν → D | is the speed of the dra- gonfly. (Because model dragonfly and prey speeds are Fig. 1 Example model dragonfly engagement with prey. The dragonfly’s eye-screen is drawn with dashed blue lines (blue diamonds indicate corners). The red star is the dragonfly’s prey. The dashed red line is the line-of-sight fromdragonfly head (black circle) to the prey. The prey’s image projected onto the eye is marked by the open red circle. The dragonfly’s body (solid black line) is provided solely as a reference (the body is aligned with the direction of flight). For clarity, the distance from the dragonfly head to the eye-screen and the size of the eye-screen are significantly increased in this figure.