Formation Maneuver Based On Passive And Periodic Relative Orbit:Linear Programming Approach

Along with the rapid development of small satellites technology,satellite formation flying is increasingly active,and has became a research focus of domestic and foreign scholars.Among them,the satellite formation control is a key technology of formation flying,has been extensively researched and achieved fruitful results.The problem of satellite formation control is mainly considered from two aspects:formation reconfiguration and formation-keeping.Reasonable design of the controller can maintain long-term formation flight and complete the required space missions efficiently.This article mainly studies satellite formation fuel-optimal maneuver control problem.The linear relative motion dynamics equations of satellites which described by orbital elements deviations is inferred based on the Gaussian perturbation equations.Relative dynamics equations is discretized into difference equations by using approximate discrete method,the purpose is transforming the optimal control problem which constrained by differential relative motion equations into linear programming problem which constrained algebraic equations,so the fuel-optimal maneuver control problem algorithm of satellite formation based on linear programming is proposed.The feasible optimal control sequence can be got by solving the problem of standard linear programming,transferring the track and keeping the satellite formation from diverge by control law.Finally,numerical simulation is proceeded in the MATLAB environment.The designed control law is applied to this passive periodic relative orbit of satellite,completing the maneuver of satellite formation from the initial orbit to expect orbit and the tasks of minimal fuel consumption.Simulation results show the effectiveness and rapidity of the proposed control scheme.