Optimal four-impulse rendezvous between coplanar elliptical orbits  

作　　者：WANG JianXia BAOYIN HeXi LI JunFeng SUN FuChun 

机构地区：[1]School of Aerospace, Tsinghua University, Beijing 100084, China [2]Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China

出　　处：《Science China(Physics,Mechanics & Astronomy)》2011年第4期792-802,共11页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos. 10832004 and 11072122)

摘　　要：Rendezvous in circular or near circular orbits has been investigated in great detail, while rendezvous in arbitrary eccentricity elliptical orbits is not sufficiently explored. Among the various optimization methods proposed for fuel optimal orbital rendezvous, Lawden＇s primer vector theory is favored by many researchers with its clear physical concept and simplicity in solu- tion. Prussing has applied the primer vector optimization theory to minimum-fuel, multiple-impulse, time-fixed orbital ren- dezvous in a near circular orbit and achieved great success. Extending Prussing＇s work, this paper will employ the primer vec- tor theory to study trajectory optimization problems of arbitrary eccentricity elliptical orbit rendezvous. Based on linearized equations of relative motion on elliptical reference orbit （referred to as T-H equations）, the primer vector theory is used to deal with time-fixed multiple-impulse optimal rendezvous between two coplanar, coaxial elliptical orbits with arbitrary large ec- centricity. A parameter adjustment method is developed for the prime vector to satisfy the Lawden＇s necessary condition for the optimal solution. Finally, the optimal multiple-impulse rendezvous solution including the time, direction and magnitudes of the impulse is obtained by solving the two-point boundary value problem. The rendezvous error of the linearized equation is also analyzed. The simulation results confirmed the analyzed results that the rendezvous error is small for the small eccentric- ity case and is large for the higher eccentricity. For better rendezvous accuracy of high eccentricity orbits, a combined method of multiplier penalty function with the simplex search method is used for local optimization. The simplex search method is sensitive to the initial values of optimization variables, but the simulation results show that initial values with the primer vector theory, and the local optimization algorithm can improve the rendezvous accuracy effectively with fast convergence, because the optiRendezvous in circular or near circular orbits has been investigated in great detail,while rendezvous in arbitrary eccentricity elliptical orbits is not sufficiently explored.Among the various optimization methods proposed for fuel optimal orbital rendezvous,Lawden's primer vector theory is favored by many researchers with its clear physical concept and simplicity in solution.Prussing has applied the primer vector optimization theory to minimum-fuel,multiple-impulse,time-fixed orbital rendezvous in a near circular orbit and achieved great success.Extending Prussing's work,this paper will employ the primer vector theory to study trajectory optimization problems of arbitrary eccentricity elliptical orbit rendezvous.Based on linearized equations of relative motion on elliptical reference orbit (referred to as T-H equations),the primer vector theory is used to deal with time-fixed multiple-impulse optimal rendezvous between two coplanar,coaxial elliptical orbits with arbitrary large eccentricity.A parameter adjustment method is developed for the prime vector to satisfy the Lawden's necessary condition for the optimal solution.Finally,the optimal multiple-impulse rendezvous solution including the time,direction and magnitudes of the impulse is obtained by solving the two-point boundary value problem.The rendezvous error of the linearized equation is also analyzed.The simulation results confirmed the analyzed results that the rendezvous error is small for the small eccentricity case and is large for the higher eccentricity.For better rendezvous accuracy of high eccentricity orbits,a combined method of multiplier penalty function with the simplex search method is used for local optimization.The simplex search method is sensitive to the initial values of optimization variables,but the simulation results show that initial values with the primer vector theory,and the local optimization algorithm can improve the rendezvous accuracy effectively with fast convergence,because the optimal results obtained by the primer vector t

关 键 词：If the initial values are taken randomly it is difficult to converge to the optimal solution. elliptical orbit rendezvous primer vector fuel optimal 

分 类 号：O562.1[理学—原子与分子物理] P144[理学—物理]