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edfas.org ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 22 NO. 2 20 Searching across approach trajectories is not feasible for thismodel because the dragonfly and preymove at the same speed. Instead, the process for the dragonflymodel (Fig. 4) is simplified by using prey-image drift on the eye- screen as an error signal not only for adjusting the model dragonfly’s trajectory, but also the location of its fovea. If, for a given simulation-time step, the dragonfly is required to adjust its pitch and yaw by ∆ϕ and ∆θ respectively, to maintain the prey-image on the fovea, the location of the fovea is then shiftedby ∆ƒ x in the horizontal direction (from the dragonfly’s perspective) and ∆ƒ y in the vertical direc- tion (also from the dragonfly’s perspective), such that: (Eq 2) (Eq 3) where ∈ is the distance from the dragonfly head to the center of the eye-screen and Q modulates the rate of error correction. For the simulations presented here, Q = 1 and the fovea is shifted by a quantity equal in magnitude but opposite in direction to prey-image translation ( ∆ƒ x = -∆ h x and ∆ƒ y = -∆ h y ) caused by the dragonfly rotation. The success of thismodel (with error correction based upon prey-image slippage) is demonstrated in Fig. 4a. As in Fig. 3, prey andmodel dragonfly locations at each time step are plotted as red stars or black circles, respectively. The prey trajectory and initial dragonfly fovea location and trajectory (as well as starting locations of both prey and dragonfly) are identical to that of Fig. 3b. While a classical pursuit strategywas unsuccessful in Fig. 3b, with error-correction based upon prey-image slippage, the model dragonfly adjusts course to something more akin to proportional navigation and successfully captures the prey. For reference, the parallel navigation trajectory (from Fig. 2b) is replotted for comparison. Although the model dragonfly intercepts the prey slightly later, the success- ful modification of what initially was a classical pursuit approach suggests that a similar model could be applied to a broader range of scenarios, including ones in which the prey is actively evading the dragonfly. The impact of the error-correction component on fovea location is demonstrated in Fig. 4b. Because this particular prey-trajectory required that the model dragonfly adjust its yaw angle (rotating to the left from the dragonfly’s perspective) but not its pitch, only the x-coordinate of the fovea on the eye-screen (horizontal from the dragonfly’s perspective) was corrected. Figure 4b is the x-coordinate of the fovea plotted as a function of time (on the y-axis). The initial x-coordinate of the fovea (indicatedby the open black circle) was at zero (the initial location of the fovea was in the center of themodel eye-screen). As the engage- ment continued, the foveamoved to the right (negative on the ordinate axis of the eye or to the dragonfly’s right). The final fovea position (indicated by the star) is x = - 0.0058 on the eye-ordinate axis, resulting in amuch sharper turn to the dragonfly’s left than would have resulted had the fovea’s position not been adjusted. Range-vector correlation is commonly used as a measure of proportional navigation. [1,5] The range vector ( r ) is defined as the vector representing the distance and direction of the prey from the model dragonfly. To calculate range vector correlation, first calculate ∆ r t = r t - r t - 1 , the vector representing the change in range vector fromtheprevious time step. The range-vector corre- lation is the dot product of the change in range vector with the range vector: ∆ r t ⋅ r t . For pure proportional navigation, the change in range vector is in the opposite direction of the range vector, resulting in a range vector correlation of - 1. Figure 4c is the range-vector correlation, plotted as a function of simulation time for the dragonflymodel (black circles) andproportional navigation trajectory (green line). As expected, the range-vector correlation of the pure pro- portional navigation trajectory (green) remains at - 1 for thedurationof the engagement. The range-vector correla- tion of the dragonfly goes to - 1 over time, indicating that with error-correction, the model dragonfly is capable of implementingproportional-navigation. It shouldbe noted that as the dragonfly approaches the prey, | r | becomes relatively small. As a result, during the last few time steps before capture, range-vector correlation can appear to approach infinity as | ∆ r t | becomes small. The upswings in range-vector correlation close to the maximum of the ordinate axis are artifacts and should be ignored. CONCLUSIONS Neural systems are a relatively untapped source of inspiration for engineering solutions. The focus here is on the dragonfly, taking advantage of the fact that its nervous system is highly evolved for hunting. The model presented here, inspired by dragonfly hunting, success- fully implements proportional navigation using prey- image drift on the model eye-screen as an input with knowledge of self-maneuvers to maintain prey-image position as an error signal for correcting its interception trajectory. This error signal could arise from an internally generated forward model of prey-image slippage re- sulting from model maneuvers. Future work will explore this mechanism, as well as the viability of implement- ing this interception model on a man-made intercep- tion system. → → → → → → → →