初值不确定轨道可达区域计算
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摘要
为计算航天器轨道初值不确定造成的可达区域(RD),提出一种适用于椭圆参考轨道的计算方法。以航天器的名义轨道作为基线,定义一个随时间变化的移动参考平面,在此移动平面上建立名义轨道到可达区域上任一点的距离函数,函数的极大值点即为可达区包络的边界点,从而将问题转换为非线性方程组的求解问题,并对动力学模型部分线性化带来的误差进行了分析。随后采用变参数的自适应同伦算法对方程组进行求解。最后对航天器释放微小卫星的实例进行数值仿真,结果显示该方法可行有效。
A general method is developed to find the 3D envelope of the reachable domain(RD),which is caused by the initial orbit uncertainties,for ellipse reference orbits. A reference plane changed with the time is defined and the nominal orbit is regarded as a baseline. Then the function of the distance from the baseline to RD envelope is established in the reference plane along the nominal trajectory. So the RD envelope boundaries problem turns into an issue of solving nonlinear equations. Subsequently the error caused by using the linear dynamic model partially is evaluated. A variable parameter self-adaptation homotopy algorithm is developed to solve the nonlinear equations obtained. The simulation results of a satellite released example show that the method proposed is feasible and effective.
A general method is developed to find the 3D envelope of the reachable domain(RD),which is caused by the initial orbit uncertainties,for ellipse reference orbits. A reference plane changed with the time is defined and the nominal orbit is regarded as a baseline. Then the function of the distance from the baseline to RD envelope is established in the reference plane along the nominal trajectory. So the RD envelope boundaries problem turns into an issue of solving nonlinear equations. Subsequently the error caused by using the linear dynamic model partially is evaluated. A variable parameter self-adaptation homotopy algorithm is developed to solve the nonlinear equations obtained. The simulation results of a satellite released example show that the method proposed is feasible and effective.
引文
[1]Wen C X,Zhao Y S,Shi P.Precise determination of the reachable domain for a spacecraft with a single impulse[J].Journal of Guidance,Control and Dynamics,2014,37(6):1767-1779.
[2]雪丹,李俊峰,宝音贺西.平面脉冲作用下卫星轨道的可达范围研究[J].宇航学报,2009,30(1):88-92.[Xue Dan,Li Jun-feng,Bao-yin He-xi.Study on reachable domain for satellite trajectory with coplanar impulse applied[J].Journal of Astronautics,2009,30(1):88-92.]
[3]雪丹,李俊峰,蒋方华.卫星在轨道平面内的可达范围研究[J].力学学报,2010,42(2):337-342.[Xue Dan,Li Junfeng,Jiang Fang-hua.Reachable domain of a satellite with a coplanar impulse applied[J].Chinese Journal of Theoretical and Applied Mechanics,2010,42(2):337-342.]
[4]Xue D,Li J F,Bao-yin H X,et al.Reachable domain for spacecraft with a single impulse[J].Journal of Guidance,Control and Dynamics,2010,33(3):934-942.
[5]Wen C X,Zhao Y S,Shi P,et al.Orbital accessibility problem for spacecraft with a single impulse[J].Journal of Guidance,Control and Dynamics,2014,37(4):1260-1271.
[6]Holzinger M J,Scheeres D J,Hauser J.Optimal reachability sets using generalized independent parameters[C].American Control Conference(ACC),San Francisco,America,June 29,2011.
[7]Holzinger M J,Scheeres D J,Erwin R S.On-orbit operational range computation using Gauss's variational equations with J2perturbations[J].Journal of Guidance Control&Dynamics,2014,37(2):608-622.
[8]Zhang G,Cao X,Ma G.Reachable domain of spacecraft with a single tangent impulse considering trajectory safety[J].Acta Astronautica,2013,91(10):228-236.
[9]Li X H,He X S,Zhong Q F.et al.Reachable domain for satellite with two kinds of thrust[J].Acta Astronautica,2011,68(11):1860-1864.
[10]李雪华,和兴锁.连续推力作用下卫星轨道的相对可达区域研究[J].飞行力学,2011,29(1):63-65.[Li Xue-hua,He Xing-suo.Research on relative reachable domain of satellite trajectory generated after continuous-thrust applied[J].Flight Dynamics,2011,29(1):63-65.]
[11]魏广东.航天器轨道机动可达范围与轨道优化研究[D].哈尔滨:哈尔滨工业大学,2013.[Wei Guang-dong.Study on the range of spacecraft orbital maneuver and track optimization[D].Harbin:Harbin Institute of Technology,2013.]
[12]张云鹤.航天器可达区域分析及摄动情况下相对运动精确轨道控制[D].哈尔滨:哈尔滨工业大学,2010.[Zhang Yun-he.Analysis of reachable domain of spacecraft and accurate orbit control of relative motion with perturbation[D].Harbin:Harbin Institute of Technology,2010.]
[13]Layne T W.Numerical linear algebra aspects of globally convergent homotopy methods[J].SIAM Review,1986,28(4):529-545.
[14]Vinh H X,Gilbert E G,Howe R M.et al.Reachable domain for interception at hyperbolic speeds[J].Acta Astronautica,1995,35(1):1-8.
[15]Waybum T L,Seader J D.Homotopy continuation methods for computer-aided process design[J].Computer and Chemical Engineering,1987,11(1):7-25.
[16]李霞.非线性方程组的同伦算法及应用[D].秦皇岛:燕山大学,2005.[Li Xia.Homotopy algorithm and application for nonlinear equations[D].Qinhuangdao:Yanshan University,2005.]
[2]雪丹,李俊峰,宝音贺西.平面脉冲作用下卫星轨道的可达范围研究[J].宇航学报,2009,30(1):88-92.[Xue Dan,Li Jun-feng,Bao-yin He-xi.Study on reachable domain for satellite trajectory with coplanar impulse applied[J].Journal of Astronautics,2009,30(1):88-92.]
[3]雪丹,李俊峰,蒋方华.卫星在轨道平面内的可达范围研究[J].力学学报,2010,42(2):337-342.[Xue Dan,Li Junfeng,Jiang Fang-hua.Reachable domain of a satellite with a coplanar impulse applied[J].Chinese Journal of Theoretical and Applied Mechanics,2010,42(2):337-342.]
[4]Xue D,Li J F,Bao-yin H X,et al.Reachable domain for spacecraft with a single impulse[J].Journal of Guidance,Control and Dynamics,2010,33(3):934-942.
[5]Wen C X,Zhao Y S,Shi P,et al.Orbital accessibility problem for spacecraft with a single impulse[J].Journal of Guidance,Control and Dynamics,2014,37(4):1260-1271.
[6]Holzinger M J,Scheeres D J,Hauser J.Optimal reachability sets using generalized independent parameters[C].American Control Conference(ACC),San Francisco,America,June 29,2011.
[7]Holzinger M J,Scheeres D J,Erwin R S.On-orbit operational range computation using Gauss's variational equations with J2perturbations[J].Journal of Guidance Control&Dynamics,2014,37(2):608-622.
[8]Zhang G,Cao X,Ma G.Reachable domain of spacecraft with a single tangent impulse considering trajectory safety[J].Acta Astronautica,2013,91(10):228-236.
[9]Li X H,He X S,Zhong Q F.et al.Reachable domain for satellite with two kinds of thrust[J].Acta Astronautica,2011,68(11):1860-1864.
[10]李雪华,和兴锁.连续推力作用下卫星轨道的相对可达区域研究[J].飞行力学,2011,29(1):63-65.[Li Xue-hua,He Xing-suo.Research on relative reachable domain of satellite trajectory generated after continuous-thrust applied[J].Flight Dynamics,2011,29(1):63-65.]
[11]魏广东.航天器轨道机动可达范围与轨道优化研究[D].哈尔滨:哈尔滨工业大学,2013.[Wei Guang-dong.Study on the range of spacecraft orbital maneuver and track optimization[D].Harbin:Harbin Institute of Technology,2013.]
[12]张云鹤.航天器可达区域分析及摄动情况下相对运动精确轨道控制[D].哈尔滨:哈尔滨工业大学,2010.[Zhang Yun-he.Analysis of reachable domain of spacecraft and accurate orbit control of relative motion with perturbation[D].Harbin:Harbin Institute of Technology,2010.]
[13]Layne T W.Numerical linear algebra aspects of globally convergent homotopy methods[J].SIAM Review,1986,28(4):529-545.
[14]Vinh H X,Gilbert E G,Howe R M.et al.Reachable domain for interception at hyperbolic speeds[J].Acta Astronautica,1995,35(1):1-8.
[15]Waybum T L,Seader J D.Homotopy continuation methods for computer-aided process design[J].Computer and Chemical Engineering,1987,11(1):7-25.
[16]李霞.非线性方程组的同伦算法及应用[D].秦皇岛:燕山大学,2005.[Li Xia.Homotopy algorithm and application for nonlinear equations[D].Qinhuangdao:Yanshan University,2005.]