Numerical solution of a pursuit-evasion differential game  involving two spacecraft in         low earth orbit

Songtao Sun; Qiuhua Zhang; Ryan Loxton; Bin Li

doi:10.3934/jimo.2015.11.1127

Article Contents

2015, Volume 11, Issue 4: 1127-1147. Doi: 10.3934/jimo.2015.11.1127

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Numerical solution of a pursuit-evasion differential game involving two spacecraft in low earth orbit

1.
Department of Astronautical Science and Mechanics, Harbin Institute of Technology, Harbin
2.
Department of Mathematics and Statistics, Curtin University, Perth 6845
3.
Department of Mathematics and Statistics, Curtin University, Perth

Received: October 31, 2013

Revised: June 30, 2014

Published: September 2015

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Abstract

This paper considers a spacecraft pursuit-evasion problem taking place in low earth orbit. The problem is formulated as a zero-sum differential game in which there are two players, a pursuing spacecraft that attempts to minimize a payoff, and an evading spacecraft that attempts to maximize the same payoff. We introduce two associated optimal control problems and show that a saddle point for the differential game exists if and only if the two optimal control problems have the same optimal value. Then, on the basis of this result, we propose two computational methods for determining a saddle point solution: a semi-direct control parameterization method (SDCP method), which is based on a piecewise-constant control approximation scheme, and a hybrid method, which combines the new SDCP method with the multiple shooting method. Simulation results show that the proposed SDCP and hybrid methods are superior to the semi-direct collocation nonlinear programming method (SDCNLP method), which is widely used to solve pursuit-evasion problems in the aerospace field.

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Mathematics Subject Classification: Primary: 91A25; Secondary: 49M37, 49N90.

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