Comparison of Two Optimal Guidance Methods for the Long-Distance Orbital Pursuit-Evasion Game

Zeng, Xuanke; Lee, Yang; Zhu, Yanbo; Yang, Fuyunxiang

doi:10.1109/taes.2020.3024423

Cited by 23 publications

(11 citation statements)

References 14 publications

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“…When the e = 0, the state equations of the game will be linear and time-invariant, which means fewer variables are necessary to determine a problem and lower requirements for DNNs to approximate the mapping. Table 1 shows the necessary inputs and outputs of the DNNs for both models, where R c is the radius of the virtual reference orbit and e and M are as mentioned before in equations ( 5)- (7). From the table, generating samples based on OPEG is more simple where the inputs are timeinvariant and the number of inputs is fewer.…”

Section: Samples Generatingmentioning

confidence: 99%

“…[2][3][4][5] The motion of spacecraft depends on the relative distance and reveals the derivatives of states. Different from Pontani and Conway 6 and Zeng et al, 7 where the initial separation of two players is long and the motion is described in the earth-centered inertial frame, this work focuses on the problem where the spacecraft separation is far smaller than the imaginary reference orbital radius and the motion of spacecraft is described in the rotating coordinate frame. In most previous studies, [8][9][10][11][12][13][14][15][16] the model for such problem was always based on the Hill-Clohessey-Wiltshire equation (HCW) 17 which is only appropriate for nearcircular orbits.…”

Section: Introductionmentioning

confidence: 99%

“…Shen and Casalino 23 studied the problem with time-varying mass and introduced the solution to the rendezvous problem with nonmaneuvering evader as the tentative guess for the original problem. Zeng et al 7 constructed the long-distance game problem in two frames and compared the accuracy and efficiency by introducing the weight coefficient vector in the objective function In these publications, the TPBVP is always high-dimensional and extremely sensitive to the initial value. In addition, the introduced costates are physically unintuitive and have no boundary limits.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Numerical solution for elliptical orbit pursuit-evasion game via deep neural networks and pseudospectral method

Zhang

Zhu

Lee

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part G:

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This paper presents an efficient and stable DNNs-based Radau pseudospectral method for the free-time elliptical orbit pursuit-evasion game based on the equivalent reconstruction of the game model. Firstly, the relative dynamics equations are established by adding the nonlinear terms caused by the eccentricity to the Hill–Clohessy–Wilshire equations. Then the original pursuit-evasion problem is deduced to a 4-dimensional one-sided optimal control problem (OCP) based on the equivalent reconstruction. Secondly, in order to apply the deep neural networks (DNNs) to map the relationship between the OCP and the solution, the normalization of costates is introduced to eliminate the non-uniqueness of solutions when generating samples for training DNNs. Thirdly, the DNNs-based Radau pseudospectral method is proposed where the DNNs output the guesses of solutions to the derived OCP and the Radau pseudospectral method optimizes the histories of controls obtained by the guesses to the convergence. The simulation results demonstrate that the proposed method converges more stably and decreases the calculation time greatly compared with the traditional indirect method.

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Section: Samples Generatingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical solution for elliptical orbit pursuit-evasion game via deep neural networks and pseudospectral method

Zhang

Zhu

Lee

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part G:

Self Cite

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“…Moreover, the nonlinear control for OPE game was realized using the state-dependent Riccati equation method in [12]. Two optimal guidance methods, namely, the Cartesian model and the spherical model, for the long-distance OPE game were proposed in [13]. The PE differential game for satellites with continuous thrust was investigated from the viewpoint of reachable domain in [14].…”

Section: Introductionmentioning

confidence: 99%

Escape-Zone-Based Optimal Evasion Guidance Against Multiple Orbital Pursuers

Zhang

Shi³

et al. 2023

IEEE Trans. Aerosp. Electron. Syst.

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The orbital evasion problem is getting increasing attention because of the increase of space maneuvering objects. In this paper, an escape-zone-based optimal orbital evasion guidance law for an evading spacecraft on near circular reference orbit is proposed against multiple pursuing spacecraft with impulsive thrust. The relative reachable domain is introduced first and approximated as an ellipsoid propagating along the nominal trajectory under the short-term assumption. The escape zone for the impulsive evasion problem is presented herein as a geometric description of the set of terminal positions for all the impulsive evasion trajectories that are not threatened by the maneuvers of pursuers at the maneuver moment. A general method is developed next to calculate the defined escape zone through finding the intersection of two relative reachable domain approximate ellipsoids at arbitrary intersection moment. Then, the two-sided optimal strategies for the orbital evasion problem are analyzed according to whether the escape zone exists, based on which the escape value is defined and used as the basis of the proposed orbital evasion guidance scheme. Finally, numerical examples demonstrate the usefulness of the presented method for calculating escape zone and the effectiveness of the proposed evasion guidance scheme against multiple pursuing spacecraft. 1

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“…As an important part of modern control theory, optimal control has been widely applied in many practical engineering fields such as aerospace, 1–3 robotics, 4 and transportation 5 . Taking the aerospace field as an example, the soft landing of the detector on the planet, the re‐entry guidance of the vehicle, the orbit transfer of the spacecraft and so on can be regarded as the optimal control problems (OCPs).…”

Section: Introductionmentioning

confidence: 99%

Successive Chebyshev pseudospectral convex optimization method for nonlinear optimal control problems

Chen

Yang

2021

Intl J Robust & Nonlinear

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This article aims at proposing a successive Chebyshev pseudospectral convex optimization method for solving general nonlinear optimal control problems (OCPs). First, Chebyshev pseudospectral discrete scheme is used to discretize a general nonlinear OCP. At the same time, a convex subproblem is formulated by using the first‐order Taylor expansion to convexify the discretized nonlinear dynamic constraints. Second, a trust‐region penalty term is added to the performance index of the subproblem, and a successive convex optimization algorithm is proposed to solve the subproblem iteratively. Noted that the trust‐region penalty parameters can be adjusted according to the linearization error in iterative process, which improves convergence rate. Third, the Karush–Kuhn–Tucker conditions of the subproblem are derived, and furthermore, a proof is given to show that the algorithm will iteratively converge to the subproblem. Additionally, the global convergence of the algorithm is analyzed and proved, which is based on three key lemmas. Finally, the orbit transfer problem of spacecraft is used to test the performance of the proposed method. The simulation results demonstrate the optimal control is bang‐bang form, which is consistent with the result of theoretical proof. Also, the algorithm is of efficiency, fast convergence rate, and high accuracy. Therefore, the proposed method provides a new approach for solving nonlinear OCPs online and has great potential in engineering practice.

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Comparison of Two Optimal Guidance Methods for the Long-Distance Orbital Pursuit-Evasion Game

Cited by 23 publications

References 14 publications

Numerical solution for elliptical orbit pursuit-evasion game via deep neural networks and pseudospectral method

Numerical solution for elliptical orbit pursuit-evasion game via deep neural networks and pseudospectral method

Escape-Zone-Based Optimal Evasion Guidance Against Multiple Orbital Pursuers

Successive Chebyshev pseudospectral convex optimization method for nonlinear optimal control problems

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