AOTV在轨维护GEO卫星的轨道控制技术研究
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摘要
顺应我国太空技术的发展热潮，开展利用往返于空间站和地球静止轨道之间的可重复使用运载器对地球静止轨道卫星进行在轨维护技术的研究将是我国未来航天技术的一种发展趋势。气动力辅助变轨飞行器作为一种新型的跨大气层飞行的轨道转移飞行器，由于有效的利用了地球大气这种自然资源，因此与全推力变轨方式相比，可以有效的节约变轨成本。本文针气动力辅助变轨飞行器在轨维护地球静止轨道卫星的相关技术展开了研究，主要研究成果如下：
1．建立了气动力辅助变轨飞行器-空间站的在轨分离模型，并对两者分离之后的相关问题进行了研究。1）研究了气动力辅助变轨飞行器与空间站的分离模式，在此基础上，提出了AOTV与空间站在轨分离机构的设计方案和安全距离的概念。2）建立了离散型质能交换空间任务的动力学模型，推导了分离速度的求解公式，并分析了不同分离速度对空间站轨道的扰动情况。3）研究了气动力辅助变轨飞行器与空间站分离之后的相对运动过程，在分离速度大小一定的情况下，采用遗传算法优化得到分离速度的方向。4）研究了分离过程结束之后空间站的轨道保持问题。推导了任意编队构型下“虚拟中心”轨道根数的求解方法，采用LQR方法设计了轨道保持控制器，并仿真验证了控制器的有效性。
2．研究了大气层外最优变轨问题。1）在脉冲推力假设下，提出了一种求解最优转移轨道的解析方法，该方法仅需通过对单变量的超越方程进行求解，便可得到最优轨道参数；以离轨点位置、入轨点位置和转移时间为优化参数，采用智能优化算法求解了最优转移轨道；基于Lawden主矢量理论证明了解析法和智能优化算法的一阶最优性。2）在有限推力假设下，采用混合法研究了气动力辅助变轨飞行器从地球静止轨道至低轨道的轨道转移问题，结合发动机工作模式，给出了参数优化问题的数学模型，并采用序列二次规划算法进行求解。
3．研究了编队航天器整体轨道机动的轨迹规划方法。提出了一种新的路径规划方法：首先依据不同的飞行任务规划参考航天器的转移轨道，然后由周期性相对运动约束条件对伴随航天器的运动轨迹进行规划。仿真结果表明，该方法实现简单，能够满足编队航天器协同运动的约束条件。
4．研究了气动滑行模式下的最优变轨问题。1）深入分析了气动力辅助变轨过程，按飞行顺序将其划分为离轨段、大气飞行段和入轨段三个阶段，确定了优化对象为大气飞行段。2）建立了气动力辅助平面变轨问题的最优控制模型，包括无量纲动力学方程、约束条件和性能指标；采用Broyden打靶法对源自间接法的两点边值问题进行了求解，并对协态变量的初值猜测技术进行了讨论；采用Gauss伪谱法优化了热流、过载限制下的AOTV大气层内飞行轨迹。3）建立了气动力辅助异面变轨问题的最优控制模型，采用“遗传算法+Gauss伪谱法”二层优化方法对这类蕴含参数优化的最优控制问题进行求解，并与间接法和序列梯度恢复法进行了比较。
5．研究了气动巡航模式下的最优轨道转移问题。1）建立了大气内巡航飞行的动力学方程，为便于进行最优性分析，对方程进行了合理的简化。2）建立了气动巡航模式下异面变轨问题的最优控制模型，提出了相应的优化策略：采用序列二次规划方法对热流约束下的巡航飞行状态进行优化，以优化结果作为下降段优化任务中的性能指标，可以保证巡航模式下的大气内飞行全轨迹的最优性。3）以轨道根数形式的大气内飞行动力学方程为基础，推导了巡航阶段轨道面改变的解析解，避免了数值积分过程，可应用于巡航段的优化计算。
论文研究了基于气动力辅助变轨飞行器的面向地球静止轨道卫星在轨维护的相关技术，拓展了轨道转移飞行器的应用范畴，完成的工作可为地球静止轨道卫星自主在轨服务任务的总体方案与关键技术的研发提供借鉴与技术支撑。
Conforming to the developing upsurge of space technologies in our country, it is aintending space technology’s development trend of taking a research on the technologyof geostationary earth orbit (GEO) satellite’s on-orbit maintenance by using a reusablelaunch vehicle which travels between space station and geostationary earth orbit.Aeroassisted orbital transfer vehicle, to be a new type of trans-atmospheric orbitaltransfer vehicle, while compared with the all-propulsive mode, the cost for orbitchange can be saved effectively as a result of exploiting the atmosphere. The relatedtechnologies among GEO satellite’s on-orbit maintenance based on AOTV are studiedin this dissertation. The main work and contributions can be summarized as follows:
1. The on-orbit separation model for AOTV and space station is built, and thecorresponding problems after they are apart are studied.1) The separation mode forAOTV and space station is analyzed. On this basis, the design scheme of on-orbitseparation organ and the concept of safety distance are proposed.2) The dynamicalmodel for the mission of discrete mass-energy transfer is built. The formulation ofseparation velocity is deduced, and the disturbances to the space station’s orbit bydifferent separation velocities are analyzed.3) The process of relative motion after theseparation is studied. Under the circumstance of constant separation velocity, thedirection of separation velocity is optimized by genetic algorithm.4) The problem ofspace station’s orbital maintenance after the separation is studied. The method ofsolving the orbital elements of the virtual center for arbitrary configuration is proposed.The orbit keeping controller is designed based on Linear Quadratic Regulator (LQR)and the effectivity is validated by simulations.
2. The problem of optimal orbital transfer outside the atmosphere is studied.1)Assuming the thrust is impulsive, the analytic method of solving optimal transfer orbitis presented. The parameters of optimal transfer orbit can be obtained only by solvinga transcendental equation with one variable. Regarding the deorbit position, reorbitposition and transfer time as the optimization parameters, the optimal transfer orbit isobtained by intelligent optimization algorithm. The first-order optimality of the twomethods are demonstrated based on the theory of Lawden’s prime vector.2) Assumingthe thrust is finite, the problem of orbital transfer from GEO to low earth orbit isstudied by the hybrid method. Combined with the work pattern of the engine, themathematical model of parameter optimization problem is presented and it is solved bySequential Quadratic Programming (SQP).
3. The problem of trajectory planning for spacecraft formation flying’s orbitmaneuver is studied. A new programming strategy is presented. Firstly the referencespacecraft’s transfer orbit is planned according to the flight mission, then the accompanied spacecraft’s trajectory is planned by the condition of periodic relativemotion. Simulation results show the approach is simple and can satisfy all therequirements of the coordinated maneuver.
4. The problem of optimal orbital transfer by aeroglid is studied.1) The process ofaeroassisted orbital transfer is analyzed in depth. It is divided into three phases whichare deorbit phase, atmospheric flight phase and reorbit phase. The atmospheric flightphase is established as the optimization object.2) The optimal control model of planarorbital transfer is built which contains nondimensional dynamical equations,constrained conditions and performance indices. The two point boundary valueproblem derived from the indirect problem is solved by the Broyden shooting method,and the technique of initial value guess for the costate variables is discussed. TheAOTV’s atmospheric flight trajectory is optimized by Gauss pseudospectral mehodwhen the heating rate and over loading are considered.3) The optimal control modelof nonplanar orbital transfer is built. Two-level optimization method of “Geneticalgorithm+Gauss pseudospectral method” is adopted to solve the optimal controlproblem which includes variable optimization, and compassion is carried on with theindirect method and sequential grads restoring method.
5. The problem of optimal orbital transfer by aerocruise is studied.1) Thedynamical equations by aerocruise are built. For the convenience of optimality analysis,the equations are simplified legitimately.2) The optimal control model of nonplanarorbital transfer by aerocruise is built, and the corresponding optimization strategy isproposed. The heating-rate-constrained aerocruise conditions which consist of cruisealtitude, cruise velocity and angle of attack are optimized by using SQP. Theoptimality of the aerocruise maneuver is guaranteed by considering the optimizedaerocruise conditions as performance index of descent trajectory optimization.3)Based on the dynamical equations which are expressed by orbital elements, theanalytical solution of the orbit transfer during the cruise phase is deduced. Thus theintegral process is avoided and the analytical solution can be applied into theoptimization computation of cruise phase.
The related technologies of GEO satellite’s on-orbit maintenance based on AOTVare studied in this dissertation. The accomplished work expands the applicationdomain of orbital transfer vehicle. It will provide scheme references and theoreticalsupport for the over design and key technology development of GEO satellite’son-orbit autonomous servicing.
1．建立了气动力辅助变轨飞行器-空间站的在轨分离模型，并对两者分离之后的相关问题进行了研究。1）研究了气动力辅助变轨飞行器与空间站的分离模式，在此基础上，提出了AOTV与空间站在轨分离机构的设计方案和安全距离的概念。2）建立了离散型质能交换空间任务的动力学模型，推导了分离速度的求解公式，并分析了不同分离速度对空间站轨道的扰动情况。3）研究了气动力辅助变轨飞行器与空间站分离之后的相对运动过程，在分离速度大小一定的情况下，采用遗传算法优化得到分离速度的方向。4）研究了分离过程结束之后空间站的轨道保持问题。推导了任意编队构型下“虚拟中心”轨道根数的求解方法，采用LQR方法设计了轨道保持控制器，并仿真验证了控制器的有效性。
2．研究了大气层外最优变轨问题。1）在脉冲推力假设下，提出了一种求解最优转移轨道的解析方法，该方法仅需通过对单变量的超越方程进行求解，便可得到最优轨道参数；以离轨点位置、入轨点位置和转移时间为优化参数，采用智能优化算法求解了最优转移轨道；基于Lawden主矢量理论证明了解析法和智能优化算法的一阶最优性。2）在有限推力假设下，采用混合法研究了气动力辅助变轨飞行器从地球静止轨道至低轨道的轨道转移问题，结合发动机工作模式，给出了参数优化问题的数学模型，并采用序列二次规划算法进行求解。
3．研究了编队航天器整体轨道机动的轨迹规划方法。提出了一种新的路径规划方法：首先依据不同的飞行任务规划参考航天器的转移轨道，然后由周期性相对运动约束条件对伴随航天器的运动轨迹进行规划。仿真结果表明，该方法实现简单，能够满足编队航天器协同运动的约束条件。
4．研究了气动滑行模式下的最优变轨问题。1）深入分析了气动力辅助变轨过程，按飞行顺序将其划分为离轨段、大气飞行段和入轨段三个阶段，确定了优化对象为大气飞行段。2）建立了气动力辅助平面变轨问题的最优控制模型，包括无量纲动力学方程、约束条件和性能指标；采用Broyden打靶法对源自间接法的两点边值问题进行了求解，并对协态变量的初值猜测技术进行了讨论；采用Gauss伪谱法优化了热流、过载限制下的AOTV大气层内飞行轨迹。3）建立了气动力辅助异面变轨问题的最优控制模型，采用“遗传算法+Gauss伪谱法”二层优化方法对这类蕴含参数优化的最优控制问题进行求解，并与间接法和序列梯度恢复法进行了比较。
5．研究了气动巡航模式下的最优轨道转移问题。1）建立了大气内巡航飞行的动力学方程，为便于进行最优性分析，对方程进行了合理的简化。2）建立了气动巡航模式下异面变轨问题的最优控制模型，提出了相应的优化策略：采用序列二次规划方法对热流约束下的巡航飞行状态进行优化，以优化结果作为下降段优化任务中的性能指标，可以保证巡航模式下的大气内飞行全轨迹的最优性。3）以轨道根数形式的大气内飞行动力学方程为基础，推导了巡航阶段轨道面改变的解析解，避免了数值积分过程，可应用于巡航段的优化计算。
论文研究了基于气动力辅助变轨飞行器的面向地球静止轨道卫星在轨维护的相关技术，拓展了轨道转移飞行器的应用范畴，完成的工作可为地球静止轨道卫星自主在轨服务任务的总体方案与关键技术的研发提供借鉴与技术支撑。
Conforming to the developing upsurge of space technologies in our country, it is aintending space technology’s development trend of taking a research on the technologyof geostationary earth orbit (GEO) satellite’s on-orbit maintenance by using a reusablelaunch vehicle which travels between space station and geostationary earth orbit.Aeroassisted orbital transfer vehicle, to be a new type of trans-atmospheric orbitaltransfer vehicle, while compared with the all-propulsive mode, the cost for orbitchange can be saved effectively as a result of exploiting the atmosphere. The relatedtechnologies among GEO satellite’s on-orbit maintenance based on AOTV are studiedin this dissertation. The main work and contributions can be summarized as follows:
1. The on-orbit separation model for AOTV and space station is built, and thecorresponding problems after they are apart are studied.1) The separation mode forAOTV and space station is analyzed. On this basis, the design scheme of on-orbitseparation organ and the concept of safety distance are proposed.2) The dynamicalmodel for the mission of discrete mass-energy transfer is built. The formulation ofseparation velocity is deduced, and the disturbances to the space station’s orbit bydifferent separation velocities are analyzed.3) The process of relative motion after theseparation is studied. Under the circumstance of constant separation velocity, thedirection of separation velocity is optimized by genetic algorithm.4) The problem ofspace station’s orbital maintenance after the separation is studied. The method ofsolving the orbital elements of the virtual center for arbitrary configuration is proposed.The orbit keeping controller is designed based on Linear Quadratic Regulator (LQR)and the effectivity is validated by simulations.
2. The problem of optimal orbital transfer outside the atmosphere is studied.1)Assuming the thrust is impulsive, the analytic method of solving optimal transfer orbitis presented. The parameters of optimal transfer orbit can be obtained only by solvinga transcendental equation with one variable. Regarding the deorbit position, reorbitposition and transfer time as the optimization parameters, the optimal transfer orbit isobtained by intelligent optimization algorithm. The first-order optimality of the twomethods are demonstrated based on the theory of Lawden’s prime vector.2) Assumingthe thrust is finite, the problem of orbital transfer from GEO to low earth orbit isstudied by the hybrid method. Combined with the work pattern of the engine, themathematical model of parameter optimization problem is presented and it is solved bySequential Quadratic Programming (SQP).
3. The problem of trajectory planning for spacecraft formation flying’s orbitmaneuver is studied. A new programming strategy is presented. Firstly the referencespacecraft’s transfer orbit is planned according to the flight mission, then the accompanied spacecraft’s trajectory is planned by the condition of periodic relativemotion. Simulation results show the approach is simple and can satisfy all therequirements of the coordinated maneuver.
4. The problem of optimal orbital transfer by aeroglid is studied.1) The process ofaeroassisted orbital transfer is analyzed in depth. It is divided into three phases whichare deorbit phase, atmospheric flight phase and reorbit phase. The atmospheric flightphase is established as the optimization object.2) The optimal control model of planarorbital transfer is built which contains nondimensional dynamical equations,constrained conditions and performance indices. The two point boundary valueproblem derived from the indirect problem is solved by the Broyden shooting method,and the technique of initial value guess for the costate variables is discussed. TheAOTV’s atmospheric flight trajectory is optimized by Gauss pseudospectral mehodwhen the heating rate and over loading are considered.3) The optimal control modelof nonplanar orbital transfer is built. Two-level optimization method of “Geneticalgorithm+Gauss pseudospectral method” is adopted to solve the optimal controlproblem which includes variable optimization, and compassion is carried on with theindirect method and sequential grads restoring method.
5. The problem of optimal orbital transfer by aerocruise is studied.1) Thedynamical equations by aerocruise are built. For the convenience of optimality analysis,the equations are simplified legitimately.2) The optimal control model of nonplanarorbital transfer by aerocruise is built, and the corresponding optimization strategy isproposed. The heating-rate-constrained aerocruise conditions which consist of cruisealtitude, cruise velocity and angle of attack are optimized by using SQP. Theoptimality of the aerocruise maneuver is guaranteed by considering the optimizedaerocruise conditions as performance index of descent trajectory optimization.3)Based on the dynamical equations which are expressed by orbital elements, theanalytical solution of the orbit transfer during the cruise phase is deduced. Thus theintegral process is avoided and the analytical solution can be applied into theoptimization computation of cruise phase.
The related technologies of GEO satellite’s on-orbit maintenance based on AOTVare studied in this dissertation. The accomplished work expands the applicationdomain of orbital transfer vehicle. It will provide scheme references and theoreticalsupport for the over design and key technology development of GEO satellite’son-orbit autonomous servicing.
引文
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