Research On Spacecraft Autonomous Navigation And Control Based On Observability And Controllability Theory

The development of techniques for autonomous navigation and control has become an important topic in the domain of aerospace science. Because the spacecraft system and its mission are more and more complex, it raises higher demand for advanced navigation and control technology. On the other hand, the nonlinearity of the spacecraft system challenges the design and analysis of the navigation and control system. The present thesis studies the observable selction and performance analysis of spacecraft autonomous navigation, as well as the method of low-thrust orbit transfer from the control point of view by using nonlinear observability and controllability theory. The main contents of this dissertation are as follows:Firstly, the observability problem of autonomous navigation systems is studied. The robustness of observability is studied for linear systems under nonlinear perturbations in the state dynamics and the output channel, which demonstrates the validity of linearization for observability analysis of nonlinear systems, corresponding method is used to autonomous navigation system based on line-of-sight (LOS) vector measurement, and simulation of flyby autonomous navigation is given. Then, by using the theory of ordinary differential equation, the functional relationship between the output and the initial state is derived for nonlinear dynamic systems, and a observability criteria is formulated in the form of rank conditions based on inverse function theorem, which is used to analyse the observability of various combinations of measurements for spacecraft and reference point in a central gravitation field.Secondly, the measure of observability and performance analysis of autonomous navigation algorithm is studied. An analytical expression of observability index by using condition number for nonlinear determinant systems is presented, by using which the effects of selection of observables on analysis of dynamics for spacecraft in the restricted three body system are given. Then, the observability degree for stochastic nonlinear systems is defined by using the trace of FIM (Fisher Information Matrix), and autonomous navigation system based on LOS measurement is analysed. Further, according to the relationship between FIM and the accuracy of navigation filter, a methodology of performance analysis of autonomous navigation algorithm is presented, which can be used as a standard in design and analysis of practical navigation system.Thirdly, the method of low-thrust control for orbit transfer is studied based on controllability analysis. To give a practical controllability criterion for low-thrust spacecraft system, controllability of affine nonlinear systems is studied by using differential geometric theory, the controllability criterion based on weakly positively Poisson stability of drift vector field is developed, by using which the controllalbiltiy property of the low-thrust transfer between elliptic orbits is analysed. A damping feedback stabilizer is then designed to steer a spacecraft from initial elliptic orbit to a given elliptic orbit, and the performance of the proposed cotroller is lillustrated by simulating an orbital transfer between two elliptic orbits around the Earth.Lastly, semi-physical simulation system of autonomous navigation and control is built up based on optical navigation camera, lunar picture simulator and Matlab/Simulink/dSPACE integration simulation flatform. The line-of-sight vector from spacecraft to Moon's center is constructed by using optical navigation camera and laser altimeter, and the expanded Kalman filter is adopted to estimate the inertial position and velocity of the spacecraft.The output of autonomous navigation module is used as the feedback information of spacecraft for Lunar orbital transfer from higher orbit to lower orbit, simulation results demonstrate the feasibility of autonomous navigation based on LOS vector measurement and low-thrust control based on damping feedback.