Research Of Trajectory Optimization Design And Guidance Method For Landing On Asteroids

As an important branch in the field of the deep space exploration, the asteroids exploration activity has become the key planning area of the space activities of human beings. With the successful launch of the Rosetta comet detector by the European Space Agency(ESA) and the Deep Impact detector to impact a comet by the National Aeronautics and Space Administration(NASA), countries all around the world who master space exploration technology formulate plans and task on the asteroids exploration in succession. The wave of the competition for the deep space asteroids exploration has been constantly expanding, and the asteroids exploration activity is burgeoning. The technology of the asteroids exploration not only represents the strong ability of a nation, but also highlights the level of science and technology as well as the degree of social progress.On the background of the fixed-point landing on the irregular asteroids Eros433, this paper will focus on the research of establishing the gravity modeling of irregular asteroids, trajectory optimization design and nominal trajectory tracking guidance of the process of the detector landing asteroids.First of all, based on the method of the spheric harmonic function, we establish the gravity modeling of irregular asteroids. Then, taking into account the asteroid’s spin motion and neglecting the external disturbance such as gravitational perturbation of sun as well as solar radiation pressure, we establish the orbital dynamic equations of the detector in the asteroid fixed coordinate system.Moreover, we study the application of the pseudo-spectral method and the indirect method in the trajectory optimization design problem systematically. Then, we design the scheme of trajectory optimization design with the fuel-optimal control performance index using pseudo-spectral method and indirect method respectively, and introduce the homotopy technique into the traditional indirect method with the purpose of solving the sensitivity of two-point boundary value problems to the initial value of the control problem with the fuel-optimal control performance index under the indirect method. We analyze the optimal trajectory designed by both pseudo-spectral method and the indirect method, and compare the advantages and disadvantages of the two methods.Last but not the least, we introduce the disturbance observer(DOB) into the traditional dynamic surface control method. Considering the modeling error of the gravitational field of asteroids and the external disturbance of the detector, we design a control law for the nominal trajectory tracking guidance based on the disturbance observer and the dynamic surface control. Then, we analyze the stability of the closed-loop control system designed based on the Lyapunov stability theory. Taking the optimal trajectory designed by indirect respectively as the nominal trajectory, we verify the feasibility of the trajectory tracking guidance control law designed.