Research On Trajectory Planning Of Relative Motion Under Constant Thrust

Recent years has witnessed the rapid development of formation flying,and one of its key technologies is formation reconfiguation.In this paper,the problem of energy-optimal formation reconfiguration is studied.The main research contents are as follows.First,based on theory of spiral motion,the coupled ralative kinematices model of attitude and orbit is constructed using dual quaterions,in the presence of J2 perturbing acceleration and gravity-gradient torque.The reasons of coupling are analyzed,and the effects of coupling are shown through simulation.Then,the shape-based method is introduced to solve the problem of energyoptimal satellite formation reconfiguration with constant thrust acceleration.The closed-form solution of trajectory is obtained by finite fourier series method.The result is valiated in contrast with Gaussian Pseudo-Spectral method,and the proposed design method is computationally efficient and effective.Next,the problem of formation reconfiguration with only one constant thruster is studied.The target configuration is achieved by attitude maneuver to adjust thrust direction.The result of shape-based method is used to generate the initial estimation of the desired attitude.And the problem is solved using Legendre pseudo-spectral method.Finally,the indirect method is applied to solve the problem of energy-optimal satellite formation reconfiguration with constant thrust.The closed-form of optimal control input is derived using maximum principle.The fundamental matrixs of the state equation and costate equation are obtained in a closed form.The initial value of costate is proved to satisfy the normalization condition.Since Hamilton function of the system is constant,linear equations about costate variables are constructed.The initial estimation of costate is obtained using the result of shape-based methrod.An optimization algorithm is used to calculate the accurate value of initial costate and the problem is solved successfully.Finally,the results are extented to arbitrary elliptic orbit through homotopy method.