Research On Two-satellite Formation Control Based On Lyapunov Function

Micro-satellite formation flight technology and related research is increasingly mature.Satellite formation can achieve the same or even batter application effects compare to large satellite.Focusing on the micro-satellite formation and with two-star formation as the research object,This paper mainly researched two aspects of pivotal technique: relative navigation and formation control.Main content includes satellite formation relative motion dynamics model and orbit,the relative navigation scheme,control algorithm of formation maintain,etc.Details are as follows.Based on two-body hypothesis,the satellite formation mechanism was studied using dynamic method.Assuming that the orbit shape of the formation is a circle or a similar circle,set up and simplify the relative motion dynamics model,then get the Hill equations.By derivation the Hill equations,get the orbit equations and conditions in the form of dynamic.Through a mathematical simulation case to show that orbit is a space-plane ellipse,and the center of the ellipse is the reference satellite.At last,through a further study of the formation structure,discusses the relationship between phase parameter in the z direction and the space shape of the orbit.A measurement and observation method which using laser range finder is proposed in this paper.Then approached estimation values of relative distance and velocity by using Extend Kalman Filter.Using a mathematical simulation case to test and verify the convergence and the accuracy of the Extend Kalman Filter.Known as key technique of formation flying,satellite formation control and keeping is investigated deeply here.Focusing on the satellite formation system,which the reference satellite is close to the surround satellite,the perturbation is omitted,and the orbit of the reference satellite is round,two control method based on PD control theory and Lyapunov function algorithm was designed,and their stability was proved by Lyapunov stabilization theorem.In the process of designing control laws,the key is the construction of Lyapunov function.A logarithmic function which differs from the usual quadratic function is constructed as the Lyapunov function.Then,by comparing the logarithmic function with the usual quadratic function theoretically,proved that the constructed logarithmic function has higher numerical accuracy and faster convergence speed than the usual quadratic function.Numerical simulation results have shown the improved performance of the presented schemes.And through the contrast experiment,compared and analyzed the influence of control parameters of the control law based on Lyapunov function.