A Parallelizable Reachable Set Method for Pursuit-Evasion Games Using Interior-Point Methods

Jansson, Olli; Harris, Matt; Geller, David

doi:10.1109/aero50100.2021.9438323

Cited by 2 publications

(1 citation statement)

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“…For problems with linear dynamics and integral-constrained (rather than pointwise-constrained) controls, analytical solutions can be derived for the termination time and optimal trajectories. Motivated by this work, reachable set analyses have been used in dynamic flowfields [23], coordinate control [24], missile/sensor trade studies [25], and other game scenarios [26][27][28].…”

Section: Introductionmentioning

confidence: 99%

A Geometrical, Reachable Set Approach for Constrained Pursuit–Evasion Games with Multiple Pursuers and Evaders

Jansson

Harris

2023

Aerospace

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This paper presents a solution strategy for deterministic time-optimal pursuit–evasion games with linear state constraints, convex control constraints, and linear dynamics that is consistent with linearized relative orbital motion models such as the Clohessy–Wiltshire equations and relative orbital elements. The strategy first generates polytopic inner approximations of the players’ reachable sets by solving a sequence of convex programs. A bisection method then computes the optimal termination time, which is the least time at which a set containment condition is satisfied. The pursuit–evasion games considered are games with (1) a single pursuer and single evader, (2) multiple pursuers and a single evader, and (3) a single pursuer and multiple evaders. Compared to variational methods, this reachable set strategy leads to a tractable formulation even when there are state and control constraints. The efficacy of the strategy is demonstrated in three numerical simulations for a constellation of satellites in close proximity in low earth orbit.

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