Fuel Optimal Orbit Transfer Problem With Constraints

With the development of space technology, the complexity of the tasks of spacecrafts increases rapidly. As a result, the research of constrained optimal orbit transfer is of great significance and many researchers put their attention on orbits maneuvers with constraints. This thesis mainly discusses the study of path constrained problem and focuses on the design of fuel optimal orbit transfer with path constraints; the main content of this thesis is summarized as follows.Firstly, a new algorithm for fuel optimal Lambert problem is proposed. The transfer orbit and increment of velocities are parameterized with transverse eccentricity and the necessary and sufficient conditions for the minimum-fuel transfer are derived. The proposed method accommodates for both circular orbits and elliptic orbits; it can be applied to transfers between noncoplanar orbits as well as transfers between coplanar orbits; the orbit transfer with 180°transfer angle is also well treated. Simulation examples are provided to verify the effectiveness of the proposed method.Secondly, evasive maneuver problem is introduced and the application of primer vector theory in this field is discussed. The necessary conditions of primer on an optimal trajectory with path constraints are presented. The primer vector for two-impulse transfer, three-impulse transfer and multiple impulse transfer is derived. Utilizing the BFGS (Broydon-Fletcher-Goldfarb-Shanno) numerical algorithm, the evasive maneuver problem is optimized. The results show that the primer vector theory is instructive and the convergence speed is fast, but it has a large dependence on the initial guess and may converge to a local optimal solution.Finally, combining the advantages of primer vector theory and direct optimization method, a hybrid trajectory optimization algorithm is proposed. The number of the impulses is firstly fixed, and then the trajectory is optimized utilizing a direct numerical method that combines genetic algorithms and nonlinear programming. The results obtained are analyzed using primer vector theory and a further optimization plan is provided. The optimization is repeated until it satisfies the requirements. A simulation example proves that four-impulse maneuver usually gives the satisfied results for evasive maneuver problem.