Trajectory Planning And Control Technology For Spacecraft Orbital Pursuit-Evasion Game

To protect the spacecraft from being rendezvoused with unknown objects in space like debris and improve the spacecraft’s survivability,this dissertation studies the orbital pursuit-evasion problem between two spacecraft via the theory of differential games.First,the methods for solving saddle-point solutions of the three-dimensional orbit pursuit-evasion game with complete information are proposed.Then,the optimal control laws for online pursuit-evasion game with incomplete information are designed.Finally,the semi-physical simulation experiment on the ground is conducted to testify the efficacy of the proposed guidance methods.The main contributions of this dissertation are summarized as follows.The methods for solving saddle-point solutions of the three-dimensional orbit pursuit-evasion game with complete information are proposed.1)To solve the two-point boundary value problem(TPBVP)in free-time differential game with linear dynamics,a dimension-reduction method is proposed.This method reduces the dimensionality of the problem from 12 to 4,and thus can compute the saddle-point solution efficiently.2)To solve the TPBVP in free-time differential game with nonlinear and perturbed dynamics,a new method,called combined shooting and collocation method method is presented.By decomposing the original problem into two layers,a sub-TPBVP in inner layer and nonlinear equations in outer layer,this method can acquire the saddle-point solution robustly.The optimal control laws for online pursuit-evasion game with incomplete information are designed.1)Taking the evader’s observation noises into consideration,this paper derives the saddle-point solution in the imperfect-information game with measurement errors.Compared with the solution in the perfect-information game,the new optimal control laws require the pursuer to utilize a part of controls to increase the evader’s observation errors,while the optimal controls of the evader are unchanged.2)Taking the evader’s observation time into consideration,this paper derives the saddle-point solution in the imperfect-information game with time-delay.The new solution have the same form with the solution without time-delay.However,the input of the state in evader’s solution is a virtual state,which is deduced from the state in the past.3)Considering that the payoff function is generally unknown in a realistic game,this paper designs an evading strategy via online parameter identification method,which identifies the weighting matrices in payoff function by strong tracking unscented Kalman filtering algorithm(STUKF).Simulation results show that the method can estimate the weighting matrices correctly.The semi-physical simulation on the ground for pursuit-evasion game is conducted.1)Based on the semi-physical experiment systems in the laboratory,the scheme of the pursuit-evasion experiment is designed.With the hardware for measurement and movement in the loop and the on-board computer equipped,the relative navigation,trajectory-planning and controls for motion are combined to form a close-loop simulation system for the pursuit-evasion game.2)By the principle of similarity,the pursuit-evasion on the ground is designed as a scaled model of that in space.Experiment results show that the proposed guidance laws via differential games are effective.Due to the time delay and the observation error,the actual trajectories deviate away from the optimal trajectories a little.Furthermore,the error in velocity is more obvious than that in position.In a word,the proposed trajectory-planning methods and optimal control strategies for orbital pursuit-evasion games extend the classical orbital differential game theory and help to develop the technology for space defense,which has much of value in improving the survivability of the satellite.