In this paper,minimum-fuel rendezvous is investigated for the case in which the reference orbit is highly elliptic.To this end,the well-known Tschauner-Hempel equations are used to describe the relative motions betwee...In this paper,minimum-fuel rendezvous is investigated for the case in which the reference orbit is highly elliptic.To this end,the well-known Tschauner-Hempel equations are used to describe the relative motions between rendezvous spacecraft and the target.Lawden’s primer vector theory is then applied on this linear but time-varying system.The analytical solution of the required primer vector for this problem is then derived by using a recently developed method.For the existing non-optimal solutions which don’t satisfy the conditions,the methods are further designed to improve the performance by shifting impulses or adding a new one.Finally,two algorithms are developed for free-impulse time-fixed rendezvous problems.The first algorithm can determine the globally optimal trajectory with the optimal number of impulses.The second one enables for fast trajectory planning.The proposed algorithms have been successfully applied to coplanar and three-dimensional rendezvous problems in which the target is flying on highly elliptical orbits.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 opti展开更多
In this paper,the optimal interplanetary transfer including planetary escape and capture phases is investigated in the heliocentric frame.Based on primer vector theory,a modi ed cost function with variable coecients i...In this paper,the optimal interplanetary transfer including planetary escape and capture phases is investigated in the heliocentric frame.Based on primer vector theory,a modi ed cost function with variable coecients is developed to re ect the gravitational e ect more precisely.The necessary conditions as well as the transversality conditions of the new cost function are derived to search the optimal solution in xed-time.By introducing the initial and nal coasts,the optimal interplanetary transfer is extended to the time-free situation.Finally,the proposed method is applied to the Earth-Mars and Earth-Asteroid transfer.Comparisons with existing methods show that the proposed method can provide better transfer performances with high eciency.The proposed method extends the application of primer vector theory and provides a fast and accurate reference for preliminary mission design in spacecraft planetary exploration.展开更多
基金supported by National Natural Science Foundation of China(No.12172288)National Key Basic Research Program of China:Gravitational Wave Detection Project(Nos.2021YFC2202601 and 2021YFC2202603)General Program of Natural Science Foundation of Higher Education of Jiangsu Province(No.21KJB590001)。
文摘In this paper,minimum-fuel rendezvous is investigated for the case in which the reference orbit is highly elliptic.To this end,the well-known Tschauner-Hempel equations are used to describe the relative motions between rendezvous spacecraft and the target.Lawden’s primer vector theory is then applied on this linear but time-varying system.The analytical solution of the required primer vector for this problem is then derived by using a recently developed method.For the existing non-optimal solutions which don’t satisfy the conditions,the methods are further designed to improve the performance by shifting impulses or adding a new one.Finally,two algorithms are developed for free-impulse time-fixed rendezvous problems.The first algorithm can determine the globally optimal trajectory with the optimal number of impulses.The second one enables for fast trajectory planning.The proposed algorithms have been successfully applied to coplanar and three-dimensional rendezvous problems in which the target is flying on highly elliptical orbits.
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 opti
基金This work was supported by Chang Jiang Scholars Program,the National Natural Science Foundation of China(Grant No.11572038 and No.11772050)Graduate Technological Innovation Project of Beijing Institute of Technology.
文摘In this paper,the optimal interplanetary transfer including planetary escape and capture phases is investigated in the heliocentric frame.Based on primer vector theory,a modi ed cost function with variable coecients is developed to re ect the gravitational e ect more precisely.The necessary conditions as well as the transversality conditions of the new cost function are derived to search the optimal solution in xed-time.By introducing the initial and nal coasts,the optimal interplanetary transfer is extended to the time-free situation.Finally,the proposed method is applied to the Earth-Mars and Earth-Asteroid transfer.Comparisons with existing methods show that the proposed method can provide better transfer performances with high eciency.The proposed method extends the application of primer vector theory and provides a fast and accurate reference for preliminary mission design in spacecraft planetary exploration.
