Analytical Pursuit-Evasion Game Strategy in Arbitrary Keplerian Reference Orbits

TL;DR

This paper presents an analytical strategy for pursuit-evasion games in arbitrary Keplerian orbits, significantly reducing computation time and improving success rates over conventional methods, especially in high-eccentricity scenarios.

Contribution

It introduces an analytical solution to the differential Riccati equation for various orbit types, enabling efficient pursuit-evasion strategies in complex orbital environments.

Findings

Analytical solution reduces CPU time by over 99.8%.

Strategy achieves success in all tested scenarios, including high-eccentricity orbits.

Effective even with orbital disturbances.

Abstract

This paper develops an analytical strategy for solving the linear quadratic pursuit-evasion game in arbitrary Keplerian reference orbits. The motion of the pursuer and evader is described using the controlled Tschauner-Hempel equations, and the optimal game strategies of the pursuer and evader are presented by the solution of the differential Riccati equation.The analytical solution of the differential Riccati equation is presented for elliptic, parabolic, and hyperbolic reference orbits, thereby enabling an analytical pursuit-evasion game strategy. Then, the procedure to solve the pursuit-evasion game using this analytical strategy is proposed. Simulations of pursuit-evasion game in elliptic, parabolic, and hyperbolic reference orbits validate the effectiveness of the developed analytical strategy. Results indicates that the analytical strategy saves the CPU time by more than 99.8$\%$ compared to the numerical one, highlighting the efficiency of the developed strategy. The developed analytical strategy is also applicable to pursuit-evasion game scenarios considering orbital disturbances. Compared to the conventional strategy, which succeed in only two out of six test scenarios, the developed strategy achieves success in all six cases, particularly demonstrating its effectiveness in high-eccentricity cases.