Numerical solution of spacecraft pursuit-Evasion-Capture game based on progressive shooting method

Abstract

The time optimal pursuit-evasion-capture (PEC) game problem for two spacecraft with continuous constant thrust is studied, which is a typical and considerable game scenario in practice. Progressive Shooting Method (PSM) is proposed to solve the PEC game in this paper. The method solves the problem in two stages. First-shooting settles a simplified problem by substituting CW dynamics to simple dynamics, while second-shooting settles the original problem with the results of first-shooting. For first-shooting, an analytic initial guess construction method based on prior information is proposed, in which vague adjoint variables are expressed by quantities with clear physical meanings. Through qualitative analysis for the optimal trajectory, the quantities are approximately estimated and then analytic expressions of an initial guess are constructed. The proposed method provides an instructive way to deal with the difficulty that an initial guess is hard to provide for an optimal control problem based on indirect-method. Numerical results show that a PEC game can be solved by the proposed method with well convergence and high computational efficiency.

Keywords

pursuit-evasion-capture game optimal control initial guess construction shooting method homotopy algorithms

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References

Isaacs

. Differential games. New York: Wiley, 1965.

Horie

Conway

. Optimal fighter pursuit-Evasion maneuvers found via two-sided optimization. Journal of guidance, control, and dynamics 2006; 29(1): 105–112. DOI: 10.2514/1.3960

Conway

. A survey of methods available for the numerical optimization of continuous dynamic systems. J Optim Theory Appl 2012; 152(2): 271–306. DOI: 10.1007/s10957-011-9918-z

Horie

Conway

. Genetic algorithm preprocessing for numerical solution of differential games problems. Journal of guidance, control, and dynamics 2004; 27(6): 1075–1078. DOI: 10.2514/1.3361

Stupik

Pontani

Conway

. Optimal pursuit/evasion spacecraft trajectories in the hill reference frame. In: AIAA/AAS astrodynamics specialist conference. 2012: 4882, doi: 10.2514/6.2012-4882

Pontani

Conway

. Particle swarm optimization applied to space trajectories. Journal of Guidance, Control, and Dynamics 2010; 33(5): 1429–1441. DOI: 10.2514/1.48475

Shan

Ren

. Low-thrust trajectory design with constrained particle swarm optimization. Aerosp Sci Technol 2014; 36: 114–124. DOI: 10.1016/j.ast.2014.04.004

Hafer

Reed

Turner

, et al. Sensitivity methods applied to orbital pursuit evasion. Journal of Guidance, Control, and Dynamics 2015; 38(6): 1118–1126. DOI: 10.2514/1.G000832

Shi

Sun

. Satellite proximate pursuit-evasion game with different thrust configurations. Aerospace Science and Technology 2020; 99: 105715. DOI: 10.1016/j.ast.2020.105715

10.

Sun

Zhang

Loxton

, et al. Numerical solution of a pursuit-evasion differential game involving two spacecraft in low earth orbit. Journal of Industrial and Management Optimization (JIMO) 2015; 11(4): 1127–1147. DOI: 10.3934/jimo.2015.11.1127

11.

Zhu

Yang

, et al. Saddle point of orbital pursuit-evasion game under j2-perturbed dynamics. Journal of Guidance, Control, and Dynamics 2020; 43(9): 1733–1739. DOI: 10.2514/1.G004459

12.

Zhu

Yang

, et al. A dimension-reduction solution of free-time differential games for spacecraft pursuit-evasion. Acta Astronautica 2019; 163: 201–210. DOI: 10.1016/j.actaastro.2019.01.011

13.

Yazdaniyan

Shamsi

Foroozandeh

, et al. A numerical method based on the complementarity and optimal control formulations for solving a family of zero-sum pursuit-evasion differential games. Journal of Computational and Applied Mathematics 2020; 368: 112535. DOI: 10.1016/j.cam.2019.112535

14.

Jagat

Sinclair

. Optimization of spacecraft pursuit-evasion game trajectories in the euler-hill reference frame. In: AIAA/AAS astrodynamics specialist conference. 2014: 4131, doi: 10.2514/6.2014-4131

15.

Venigalla

Scheeres

. Spacecraft rendezvous and pursuit/evasion analysis using reachable sets. In: Space flight mechanics meeting, 2018. DOI: 10.2514/6.2018-0219

16.

Yuan

Zhang

, et al. Model predictive control for autonomous rendezvous and docking with a tumbling target. Aerospace Science and Technology 2017; 69: 700–711. DOI: 10.1016/j.ast.2017.07.022