Research On Trajectory Design And Guidance Algorithms For Mars Entry

With the development of Mars exploration research, the Mars Sample Return(MSR) and Crewed Mars mission have been put on the schedule for the new stage of Mars exploration. Landing accuracy of Mars Landers becomes a key factor which determines the success of above missions in the Mars exploration. To improve landing accuracy, efficient guidance and control during Mars atmosphere entry phase are crucial and essential. Therefore, researching the techniques and theory on Mars atmosphere enry phase, and designing reasonable trajectory plan and high-precision guidance system have been the vital and challenging topics in current Mars research. With the supports of the 973 Program “Research on GNC for Precise Landing on Planets” and the National Natural Science Foundation of China “Research on Autonomous Navigation Theory and Method for landing on Planets”, with the objective of improving the precision of parachute deployment point, this dissertation systematically and deeply studies trajectory optimization and guidance technologies during Mars entry phase. The main results achieved in this dissertation are summarized as follows.Firstly, trajectory optimization for Mars entry at atmosphere phase is studied. Based on the Mars entry dynamic model, the error sources which affect state dispersions at parachute deployment point are analyzed through Monte Carlo method. The results indicate that the uncertainties on atmospheric density and aerodynamic coefficients significantly influence parachute deployment precision. In order to decrease the impact of those uncertainties, the uncertainties on atmospheric density and aerodynamic coefficients are added as an additional state and propagated using first order homogeneous ordinary differential equations. The new robust performance metric is built when considering the characteristics of Mars Explorer in atmospheric entry phase. Finally, a state sensitivity-based robust trajectory design method is proposed, and the simulation results show that the new method can generate with less impact from prevalent uncertainties and perturbations in the design process.Then, the impacts of various error sources on parachute deployment point dispersions in atmospheric entry phase are analyzed quantitatively by linear covariance method and a covariance-based robust trajectory design method is proposed. Untilizing the equation of propagation and symmetry of covariance matrix, the method puts the covariance of parachute deployment point state into the original objective function. Meanwhile, it also takes the uncertainties on atmospheric density and aerodynamic coefficients, and Multi-scale constraints including dynamic constraints, control constraints, and state constraints into consideration. The trajectory generated by such designed method can effectively improve the precision of parachute deployment. Moreover, from the point of computational complexity and trajectory robust performance, the sensitivity-based optimal trajectory design algorithm and the covariance-based optimal trajectory design algorithm are compared under the same Mars entry scenario.Further, the method of trajectory tracking and control for Mars entry is investigated. Under the requirement of real-time and precision, considering the impacts of the initial entry deviation, the uncertainties of atmospheric density and aerodynamic coefficients, a novel trajectory tracking method is proposed based on model predictive static programming. By combining nonlinear model predictive control and approximate dynamic programming theory, the proposed method only requires solving static programming problems online, which results in simplied structure and explicit solutions. In addition, to satisfy the real time requirement, the method saves the computational time by computing sensitivity matrices recursively. The simulation shows that the difference between the actual flight trajectory and the nominal trajectory can be effectively reduced. As a result, the precision of parachute deployment is significantly increased.Finally, the key technologies in the predictive tracking guidance for Mars entry vehicle are explored. First, Mars entry trajectory is divided into three parts by the equilibrium glide condition: initial descent phase, equilibrium glide phase, and final descent phase. Based on the requirement of constant flightpath angle in equilibrium glide phase, a constant flight path angle-based analytical predictive tracking guidance method is proposed by using linear quadratic regulator control theory. This method takes the advantages of simple formulation, rapid computational speed, and good robustness, but is lack of the ability to adapt large uncertainty of aerodynamic coefficients. Therefore, the numerical predictive tracking guidance method is proposed. With this method, the Mars entry trajectory is divided into Pre-bank phase, range control phase, and heading alignment phase. Newton-Raphson method is used to determine the constant flight path angle in range control phase and the feedback linearization method is adopted to design trajectory tracking control law. The simulation shows that the method is able to ensure high landing precision at the price of low computing speed. The comparisons between the two predictive tracking guidance methods are executed and the robustness and adaptability of the two methods are discussed.