This paper presents a novel approach to missile guidance using the differential geometry of curves and not relying on the line of sight information. The target's trajectory is treated as a smooth curve of known cu...
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This paper presents a novel approach to missile guidance using the differential geometry of curves and not relying on the line of sight information. The target's trajectory is treated as a smooth curve of known curvature and the new algorithm is based on the involute of the target's curve. The missile's trajectory uses the concept of virtual target to generate the correct involute trace. It is shown that the missile is either on the trace immediately or may be able to, reach it through an alignment procedure. In general, following the trace requires a three-dimensional maneuver in which the missile flies above the target's tangent plane. The projection of the three-dimensional trajectory onto the tangent plane coincides with the involute trace, but is traversed in the time-to-go, thus resulting in the intercept. Two air-to-air scenarios of point masses are considered for a maneuvering target of the F-16 fighter class: 1) a two-dimensional engagement with target executing a constant g turn;2) a three-dimensional engagement with target executing a barrel-roll maneuver. Perfect target information is assumed in simulations. In the first case, intercepts occur both for the involute law and proportional-navigation (PN) guidance;PN based intercepts occur quicker, but the involute-based trajectories are more difficult to evade and always result in a side impact. In the second case, PN fails to intercept the target, while the involute law is successful.
The design of optimal controllers for air-to-air missiles has been of much recent interest. Many control laws require a good estimate of the time-to-go (tgo) before intercept. This paper presents an algorithm for esti...
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The analytic expressions for a generic event trigger for a linear covariance analysis are developed. The event triggers are applied to the analysis of a common orbital rendezvous problem. Some unexpected results are o...
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The analytic expressions for a generic event trigger for a linear covariance analysis are developed. The event triggers are applied to the analysis of a common orbital rendezvous problem. Some unexpected results are observed and a flaw in an equation that is commonly used in standard linear covariance analysis applications is uncovered and remedied. A quantitative analysis of the effect of elevation-angle triggers for various rendezvous scenarios is presented.
Linear covariance analysis can serve as a viable technique in determining both navigation errors and trajectory dispersions for spacecraft rendezvous analysis and design. This work addresses issues that arise when mul...
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Linear covariance analysis can serve as a viable technique in determining both navigation errors and trajectory dispersions for spacecraft rendezvous analysis and design. This work addresses issues that arise when multiple events are triggered on state conditions in linear covariance analysis. To demonstrate the validity of the proposed solutions, performance metrics such as trajectory dispersions, navigation errors, delta-v dispersions, and event time dispersions are carefully analyzed and confirmed with Monte Carlo simulation results.
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