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Pure Pursuit with an Effector

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Abstract

The study of pursuit curves is valuable in the context of air-to-air combat as pure pursuit guidance (heading directly at the target) is oftentimes implemented. The problems considered in this paper concern a Pursuer, implementing pure pursuit (i.e., line of sight guidance), chasing an Evader who holds course. Previous results are applicable to the case in which capture is defined as the two agents being coincident, i.e., point capture. The focus here is on obtaining results for the more realistic case where the pursuer is endowed with an effector whose range is finite. The scenario in which the Evader begins inside the Pursuer’s effector range is also considered (i.e., escape from persistent surveillance, among other potential applications). Questions herein addressed include: does the engagement end in head-on collision or tail chase, will the Evader be captured or escape, what is the minimum distance the Pursuer will attain, for two Pursuers, is simultaneous capture/escape optimal and, if so, what is the optimal heading for the Evader (max time to capture, or min time to escape), and the feasibility for a fast Evader to escape from many Pursuers. Where possible, closed-form, analytic results are obtained, otherwise attention is given to computability with an eye towards real-time, on-board implementation.

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Notes

  1. We utilize this convention in some portions of the text to match the work of [1].

  2. This had been left as an exercise to the reader in [1]. It can be shown, using (9) that the distance asymptotically approaches \(\tfrac{d_0 (\cos \psi _0 + 1)}{2}\).

  3. Unequal Pursuer speeds can also be handled by keeping track of, e.g., \(\mu _1\) and \(\mu _2\) throughout the derivation, and similarly for unequal effector ranges via \(l_1\) and \(l_2\).

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Acknowledgements

This paper is based on work performed at the Air Force Research Laboratory (AFRL) Control Science Center. Distribution Unlimited. 16 Feb 2022. Case #AFRL-2022-0728.

Funding

This work has been supported in part by AFOSR LRIR No. 21RQCOR084.

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Authors and Affiliations

  1. Control Science Center, Air Force Research Laboratory, Wright-Patterson Air Force Base, 2210 8th St., Dayton, OH, 45433, USA

    Alexander Von Moll

  2. Department of Electrical Engineering and Computing Systems, University of Cincinnati, 2600 Clifton Ave., Cincinnati, OH, 45221, USA

    Alexander Von Moll & Zachariah Fuchs

  3. Department of Electrical Engineering and Computing Systems, Air Force Institute of Technology, Wright-Patterson Air Force Base, 2950 Hobson Way, Dayton, OH, 45433, USA

    Meir Pachter

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  1. Alexander Von Moll
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Contributions

AVM prepared the manuscript, developed theoretical results, and produced the examples. MP developed the algorithm for computing finite-capture-radius capture time and aided in the analysis. ZF contributed to the analysis as well.

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Correspondence to Alexander Von Moll.

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Von Moll, A., Pachter, M. & Fuchs, Z. Pure Pursuit with an Effector. Dyn Games Appl 13, 961–979 (2023). https://doi.org/10.1007/s13235-022-00481-9

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