An optimal guidance method for free-time orbital pursuit-evasion game

With the development of space rendezvous and proximity operations(RPO)in recent years,the scenarios with noncooperative spacecraft are attracting the attention of more and more researchers.A method based on the costate normalization technique and deep neural networks is presented to generate the optimal guidance law for free-time orbital pursuit-evasion game.Firstly,the 24-dimensional problem given by differential game theory is transformed into a three-parameter optimization problem through the dimension-reduction method which guarantees the uniqueness of solution for the specific scenario.Secondly,a close-loop interactive mechanism involving feedback is introduced to deep neural networks for generating precise initial solution.Thus the optimal guidance law is obtained efficiently and stably with the application of optimization algorithm initialed by the deep neural networks.Finally,the results of the comparison with another two methods and Monte Carlo simulation demonstrate the efficiency and robustness of the proposed optimal guidance method.

An escape strategy in orbital pursuit-evasion games with incomplete information

The orbital pursuit-evasion game is typically formulated as a complete-information game,which assumes the payoff functions of the two players are common knowledge.However,realistic pursuit-evasion games typically have incomplete information,in which the lack of payoff information limits the player’s ability to play optimally.To address this problem,this paper proposes a currently optimal escape strategy based on estimation for the evader.In this strategy,the currently optimal evasive controls are first derived based on the evader’s guess of the pursuer’s payoff weightings.Then an online parameter estimation method based on a modified strong tracking unscented Kalman filter is employed to modify the guess and update the strategy during the game.As the estimation becomes accurate,the currently optimal strategy gets closer to the actually optimal strategy.Simulation results show the proposed strategy can achieve optimal evasive controls progressively and the evader’s payoff of the strategy is lower than that of the zero-sum escape strategy.Meanwhile,the proposed strategy is also effective in the case where the pursuer changes its payoff function halfway during the game.

Guidance strategy of motion camouflage for spacecraft pursuit-evasion game

This work is inspired by a stealth pursuit behavior called motion camouflage whereby a pursuer approaches an evader while the pursuer camouflages itself against a predetermined background.We formulate the spacecraft pursuit-evasion problem as a stealth pursuit strategy of motion camouflage,in which the pursuer tries to minimize a motion camouflage index defined in this paper.The Euler-Hill reference frame whose origin is set on the circular reference orbit is used to describe the dynamics.Based on the rule of motion camouflage,a guidance strategy in open-loop form to achieve motion camouflage index is derived in which the pursuer lies on the camouflage constraint line connecting the central spacecraft and evader.In order to dispose of the dependence on the evader acceleration in the open-loop guidance strategy,we further consider the motion camouflage pursuit problem within an infinite-horizon nonlinear quadratic differential game.The saddle point solution to the game is derived by using the state-dependent Riccati equation method,and the resulting closed-loop guidance strategy is effective in achieving motion camouflage.Simulations are performed to demonstrate the capabilities of the proposed guidance strategies for the pursuit–evasion game scenario.

Impulsive thrust strategy for orbital pursuit-evasion games based on impulse-like constraint

This paper proposes a novel impulsive thrust strategy guided by optimal continuous thrust strategy to address two-player orbital pursuit-evasion game under impulsive thrust control.The strategy seeks to enhance the interpretability of impulsive thrust strategy by integrating it within the framework of differential game in traditional continuous systems.First,this paper introduces an impulse-like constraint,with periodical changes in thrust amplitude,to characterize the impulsive thrust control.Then,the game with the impulse-like constraint is converted into the two-point boundary value problem,which is solved by the combined shooting and deep learning method proposed in this paper.Deep learning and numerical optimization are employed to obtain the guesses for unknown terminal adjoint variables and the game terminal time.Subsequently,the accurate values are solved by the shooting method to yield the optimal continuous thrust strategy with the impulse-like constraint.Finally,the shooting method is iteratively employed at each impulse decision moment to derive the impulsive thrust strategy guided by the optimal continuous thrust strategy.Numerical examples demonstrate the convergence of the combined shooting and deep learning method,even if the strongly nonlinear impulse-like constraint is introduced.The effect of the impulsive thrust strategy guided by the optimal continuous thrust strategy is also discussed.