Spacecraft Rendezvous and Pursuit/Evasion Analysis Using Reachable Sets

Venigalla, Chandrakanth; Scheeres, Daniel J.

doi:10.2514/6.2018-0219

Cited by 9 publications

(2 citation statements)

References 3 publications

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“…Besides, many other researchers also investigated a variety of relevant numerical methods. [13][14][15][16] Most of the numerical methods mentioned above demand a good initial guess for algorithm initialization. Reference 8 generated an initial value for SM by homotopy algorithms; In Reference.…”

Section: Introductionmentioning

confidence: 99%

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

Liao

Xin-long

et al. 2023

Proceedings of the Institution of Mechanical Engineers, Part G:

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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.

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Section: Introductionmentioning

confidence: 99%

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

Liao

Xin-long

et al. 2023

Proceedings of the Institution of Mechanical Engineers, Part G:

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“…two-sided optimal control method and it was first introduced by Isaacs [7,8] to deal with the missile interception problem. It had been applied in many research fields, including aircraft combat [9,10], homicidal chauffeur game [11], robot tracing [12], multi-objective cooperative control [13][14][15] and the SPE game [16][17][18]. According to whether there is a payoff function, differential game can be divided into quantitative differential game and qualitative differential game [19], and the two-player zero-sum differential game included in the former had been widely used for solving the SPE game problem [20].…”

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confidence: 99%

A Dimension-reduction method for the finite-horizon spacecraft pursuit-evasion game

Wang¹,

Li²,

Lei³

et al. 2023

JIMO

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<p style='text-indent:20px;'>The finite-horizon two-person zero-sum differential game is a significant technology to solve the finite-horizon spacecraft pursuit-evasion game (SPE game). Considering that the saddle point solution of the differential game usually results in solving a high-dimensional (24 dimensional in this paper) two-point boundary value problem (TPBVP) that is challengeable, a dimension-reduction method is proposed in this paper to simplify the solution of the 24-dimensional TPBVP related to the finite-horizon SPE game and to improve the efficiency of the saddle point solution. In this method, firstly, the 24-dimensional TPBVP can be simplified to a 12-dimensional TPBVP by using the linearization of the spacecraft dynamics; then the adjoint variables associated with the relative state variables between the pursuer and evader can be expressed in the form of state transition; after that, based on the necessary conditions for the saddle point solution and the adjoint variables in the form of state transition, the 12-dimensional TPBVP can be transformed into the solving of 6-dimensional nonlinear equations; finally, a hybrid numerical algorithm is developed to solve the nonlinear equations so as to obtain the saddle point solution. The simulation results show that the proposed method can effectively obtain the saddle point solution and is robust to the interception time, the orbital altitude and the initial relative states between the pursuer and evader.</p>

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