The probability of the rendezvous between a single spacecraft and three non-coplanar constellation satellites is studied,and the necessary and sufficient conditions of the rendezvous without orbital maneuver are deduc...The probability of the rendezvous between a single spacecraft and three non-coplanar constellation satellites is studied,and the necessary and sufficient conditions of the rendezvous without orbital maneuver are deduced.The rendezvous orbit design can be transformed into the patching of two spacecraft orbits,either of which can achieve the rendezvous with two satellites.Firstly,due to the precious quality of spherical geometry,the unique existence of the rendezvous orbit for two constellation satellites is proved.Then,according to the difference between equispaced and non-equispaced orbital planes of three satellites,the necessary and sufficient conditions are given respectively,and the calculating method of the spacecraft orbit is proposed.At last,the constraint conditions between two different rendezvous orbits is derived,while the relative position of two groups of objects are under specific distribution.The results can be applied to the rendezvous between a single spacecraft and multiple constellation satellites without orbital maneuver.展开更多
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 p...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 optimal results obtained by the primer vector theory are already very close to the actual optimal solution.展开更多
基金supported by the Pre-Research Foundation of General Armament Department of China (Grant No. 6140551)
文摘The probability of the rendezvous between a single spacecraft and three non-coplanar constellation satellites is studied,and the necessary and sufficient conditions of the rendezvous without orbital maneuver are deduced.The rendezvous orbit design can be transformed into the patching of two spacecraft orbits,either of which can achieve the rendezvous with two satellites.Firstly,due to the precious quality of spherical geometry,the unique existence of the rendezvous orbit for two constellation satellites is proved.Then,according to the difference between equispaced and non-equispaced orbital planes of three satellites,the necessary and sufficient conditions are given respectively,and the calculating method of the spacecraft orbit is proposed.At last,the constraint conditions between two different rendezvous orbits is derived,while the relative position of two groups of objects are under specific distribution.The results can be applied to the rendezvous between a single spacecraft and multiple constellation satellites without orbital maneuver.
基金supported by the National Natural Science Foundation of China(Grant Nos. 10832004 and 11072122)
文摘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 optimal results obtained by the primer vector theory are already very close to the actual optimal solution.
