空间电磁对接/分离动力学与控制研究
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摘要
在轨服务技术代表了航天科学发展的前沿与重点方向，空间对接/分离为其关键基础技术。随着在轨航天器数目的增多以及空间任务复杂性的增强，常态化在轨服务需求逐渐凸现。空间电磁对接/分离技术为常态化在轨服务提供了一种新型对接/分离方式，能有效避免传统推力器方式所固有的推进剂消耗、羽流污染及光学干扰等，具有非接触、连续、可逆及同步控制能力。针对空间电磁对接/分离的动力学与控制问题，论文开展动力学及自对接性、姿/轨控制、角动量管理、六自由度仿真与地面试验系统设计研究，形成了一套较为完整的空间电磁对接/分离动力学模型与特性分析、控制算法及地面试验装置。
（1）空间电磁对接/分离动力学及自对接性。将星间电磁场作用以磁偶极子表征，采用电磁理论推导得到远场电磁力/力矩模型，包括直角坐标和球坐标两种形式。考虑星间电磁力的内力特性及Hill模型的线性特性，以质心轨道坐标系为参考系，运用Hill方程、电磁力模型和线性叠加原理推导建立了空间电磁对接/分离动力学模型。分析了空间电磁对接/分离的动力学特性，包括强非线性、耦合性、模型不确定性及控制能力特性。提出了电磁对接的自对接性概念，从地面(包括一维、二维情形)和空间电磁对接出发分析及理论证明了该自对接性，给出自对接可实现的电磁装置条件。
（2）柔性对接轨迹运动的鲁棒及自适应控制。考虑航天器柔性对接需求，采用glideslope方法设计了期望对接轨迹，并基于动力学模型及期望轨迹推导得到轨迹跟踪前馈控制律。针对空间电磁对接动力学的强非线性、耦合性及模型不确定性问题，采用内环反馈线性化+外环鲁棒H∞方法设计了满足柔性对接需求且对模型不确定性具有较强鲁棒性的轨迹跟踪偏差反馈控制律。考虑到鲁棒H∞方法的性能保守性，采用内环反馈线性化+外环ESO(Extended State Observer)及LQR(Linear Quadratic Regulator)方法，以及基于Lyapunov稳定性理论的自适应控制方法设计了轨迹跟踪偏差反馈控制律，并逐个通过仿真算例予以验证。另外，针对ESO的参数优化整定及估计误差、自适应控制律参数整定及其作用下闭环系统渐近稳定性开展理论分析，给出了相关参数的整定策略。
（3）安全分离轨迹运动的制导控制。星间电磁力的可逆性使得采用同一套电磁装置执行对接与分离成为可能，与柔性对接需求不同的是，电磁分离强调安全分离。面向伴星在轨释放背景，首先给出了空间电磁分离的几类基本假设。其次，基于主伴星恒定磁矩矢量模式仿真分析得出H-bar、V-bar及R-bar分离特性，给出了磁矩幅值与伴星分离运动特征参数的近似代数关系。最后，针对分离后伴星对主星或其他航天器自然椭圆近距离绕飞，采用循环追踪理论和微分同胚映射方法设计满足期望构型需求的安全电磁分离制导控制律，并开展了参数整定分析。
（4）姿态运动的分散协同鲁棒控制。考虑星间电磁力矩和地磁力矩对两航天器姿态运动的影响，分析了空间电磁对接/分离的姿态控制需求，指出对两航天器采用分散协同主动姿态控制的必要性。给定绝对/相对姿态偏差定义及其数学表达式，推导建立了单位四元数表示的绝对/相对姿态偏差运动方程。考虑磁力矩模型的不确定性，采用基于行为的分散协同策略、自适应控制及ESO方法设计了两航天器姿态控制律，理论分析了闭环系统的全局渐近稳定性。最后，通过仿真算例验证了分散协同鲁棒姿态控制下两航天器相对姿态运动的快速协同性及绝对姿态运动的渐近收敛性，对模型未建模动态及外界干扰具有较好鲁棒性。
（5）空间电磁对接/分离的角动量管理。将地磁场作用以磁偶极子表征，推导得到地磁力矩及星间电磁力矩在两航天器系统质心惯性系的投影分量模型。研究了基于地磁场作用的角动量管理策略及磁偶极子求解算法，包括：针对轨控作用力及其中一颗航天器的星间电磁力矩与地磁力矩相消需求，以V-bar、R-bar及H-bar对接为例，研究“正常模式的动量管理”；针对姿控执行机构角动量饱和情形，研究采用地磁力矩卸载多余角动量的“角动量卸载模式的动量管理”。鉴于采用地磁场作用的角动量管理策略具有被动性，初步研究了ACMM(AttitudeControl/Momentum Management)设计策略，包括“序列磁偶极子求解”和“ACMM控制”两部分。
（6）六自由度仿真与地面试验系统设计。面向基于空间电磁对接/分离的航天器近距离绕飞观测背景，开展空间电磁对接/分离的六自由度仿真分析，给出了仿真框架及重点验证了前述章节动力学模型与控制算法的可行性及性能。另外，开展电磁对接/分离地面试验系统设计及研制，给出了试验系统总体方案以及软/硬件设计成果。
总之，论文通过对空间电磁对接/分离动力学与控制研究，一方面从动力学与控制角度验证了该新型对接/分离技术的可行性，另一方面为下一步深入理论研究、地面演示验证试验及在轨试验提供了动力学模型、特性分析、控制算法及地面试验平台。
On-Orbit Servicing (OOS) technology, based on spacecraft docking and separationoperation, represents the frontier and important development trend of aerospace scienceresearch. The increase of on-orbit spacecraft number and spaceflight missioncomplexity highlights the requirement for regular OOS, for which the spaceelectromagnetic docking and separation technology would provide a novel docking andseparation style. This novel technology could resolve the inherent problems of thruster,such as propellant consumption and plume contamination, etc. and has non-contacting,continuous, reversible and synchronous control capability. Concentrating on dynamicsand control problems of space electromagnetic docking and separation, dynamics andself-docking characteristics, trajectory and attitude control, angular momentummanagement,6-DOF simulation and ground experiment system design are investigatedin this paper. The main research points are as follows.
(1) Dynamics and self-docking characteristics of space electromagneticdocking and separation. Hypothesizing the spacecraft electromagnets as magneticdipoles, the far-field electromagnetic force/torque models, with formats of Cartesiancoordinates and spherical coordinates, are derived by the electromagnetic theory.Referenced to the orbit coordinate frame at center of mass of the spacecraft pair, therelative motion dynamic models for the two spacecraft are derived based on Hill’sequations and far-field electromagnetic force model, and then the dynamic model ofspace electromagnetic docking and separation is got by directly subtracting the twodynamic models. Based on the dynamic model, its dynamics properties, includingstrong nonlinearity, coupling, model uncertainty and controllability, are analyzed. And,the concept of electromagnetic self-docking is put forward and proved from the ground(including one-dimensional and two-dimensional) and space cases and thecorresponding sufficient conditions of self-docking are given.
(2) Robust and adaptive control for soft docking trajectory motion.Considering spacecraft soft docking requirements, the desired docking trajectory isdesigned by applying the glideslope approach, and the feedforwad controller is derivedbased on the dynamic model. To resolve the control problems of space electromagneticdocking, such as strong nonlinearity, coupling and dynamic model uncertainty, a twoloop control frame with the inner loop of feedback linearization and outer loop of H∞method, is put forward and a soft trajectory tracking error feedback robust controller isfirstly designed, ensuring better robust capability to model uncertainty. Then,considering the conservative property of the H∞method, another two approaches,including inner loop feedback linearization with outer ESO(Extended State Observer) and LQR(Linear Quadratic Regulator), and the adaptive control method based onLyapunov stability theory, is explored to design the soft trajectory error feedbackcontroller, and verified by simulation cases. In addition, the estimation error of ESO andthe asymptotical stability of closed system with adaptive controller are theoreticallyanalyzed, and the tuning approach of parameters for ESO and adaptive controller arefollowed.
(3) Guidance control for safe separation trajectory motion. Reversible controlcapability of electromagnetic force makes it possible to utilize one electromagneticmechanism to accomplish docking and separation operation. Different from the softelectromagnetic docking, the electromagnetic separation emphasizes safety. With thebackground of on-orbit release partner satellite, several basic hypotheses for spaceelectromagnetic separation are given. Based on constant magnetic moment vectors, thecharacteristics of H-bar, V-bar and R-Bar electromagnetic separation are analyzed andput forward by numerical simulation, and the algebraic relationship between themagnetic moment and the separation relative motion of partner spacecraft is formulated.At last, concentrating on two normal elliptical close proximity fly-around mission aimedto the master or other spacecraft, the space electromagnetic separation guidancecontroller is designed based on the cyclic pursuit theorem and the differentiablehomeomorphic mapping, and the parameters tuning of which is analyzed.
(4) Decentralized and coordinated robust control for attitude motion.Considering the effects of inter-satellite electromagnetic torque and the Earth's magnetictorque to the attitude motions of the spacecraft pair, the requirements of attitude controlare studied and the necessity of decentralized coordinate active attitude controlapproach is pointed out. Defining and formulating the absolute and relative attitudedeviation, the dynamic and kinematics models of absolute and relative attitude deviationmotion with the unit quaternion expression are derived. The attitude controller isdesigned by utilizing behavior-based decentralized control approach, adaptive controland ESO method, and then the global asymptotical stability of the closed system istheoretically analyzed. At last, the quick coordination of relative attitude, asymptoticalconvergence of absolute attitude, and robust capability to model uncertainty andexternal disturbances, are verified by simulation cases for the closed attitude controlsystem with decentralized coordinate attitude controllers.
(5) Angular momentum management for space electromagnetic docking andseparation. Treating the Earth's magnetic field as magnetic dipoles, the projectionmodels of the Earth's magnetic torque and the inter-satellite electromagnetic torque onthe inertial coordinate frame centered at the center of mass of the spacecraft pair isderived. Then, the angular momentum management approach and correspondingsolution algorithms for magnetic dipoles are studied, including the following two. First, considering the requirements of trajectory motion control and one spacecraft'sinter-satellite electromagnetic torque counteracting with the Earth's magnetic torque,taking V-bar, R-bar and H-bar docking for example, the "normal angular momentummanagement" approaches are explored. Second, considering the angular momentumsaturation case of attitude control actuation mechanism, the "angular momentumreduction management" approach is studied by applying the Earth's magnetic torque.Because the designed angular momentum management approaches are negative, anAttitude Control/Momentum Management (ACMM) approach is studied, whichincludes the "sequence magnetic dipoles solution" and the "ACMM control".
(6)6-DOF simulation and ground experiment system design. With thebackground of spacecraft close proximity fly-around observation based on spaceelectromagnetic docking and separation technology, a6-DOF numerical simulation caseof space electromagnetic docking and separation is implemented. A simulation frame isconstructed, and the feasibility and performance of previous dynamic models andcontrol algorithms are verified. Additionally, a ground experiment system is studied anddesigned, and the general system scheme, design results of hardware and software arepresented.
In conclusion, the research of dynamics and control for the space electromagneticdocking and separation technology, on one hand, verifies the feasibility of this noveltechnology from the dynamics and control aspect; on the other hand, provides dynamicmodels, characteristics analysis, control algorithms and ground experiment base forfuture theoretical research, ground demonstration and verification experiments, orfurther on-orbit experiments.
（1）空间电磁对接/分离动力学及自对接性。将星间电磁场作用以磁偶极子表征，采用电磁理论推导得到远场电磁力/力矩模型，包括直角坐标和球坐标两种形式。考虑星间电磁力的内力特性及Hill模型的线性特性，以质心轨道坐标系为参考系，运用Hill方程、电磁力模型和线性叠加原理推导建立了空间电磁对接/分离动力学模型。分析了空间电磁对接/分离的动力学特性，包括强非线性、耦合性、模型不确定性及控制能力特性。提出了电磁对接的自对接性概念，从地面(包括一维、二维情形)和空间电磁对接出发分析及理论证明了该自对接性，给出自对接可实现的电磁装置条件。
（2）柔性对接轨迹运动的鲁棒及自适应控制。考虑航天器柔性对接需求，采用glideslope方法设计了期望对接轨迹，并基于动力学模型及期望轨迹推导得到轨迹跟踪前馈控制律。针对空间电磁对接动力学的强非线性、耦合性及模型不确定性问题，采用内环反馈线性化+外环鲁棒H∞方法设计了满足柔性对接需求且对模型不确定性具有较强鲁棒性的轨迹跟踪偏差反馈控制律。考虑到鲁棒H∞方法的性能保守性，采用内环反馈线性化+外环ESO(Extended State Observer)及LQR(Linear Quadratic Regulator)方法，以及基于Lyapunov稳定性理论的自适应控制方法设计了轨迹跟踪偏差反馈控制律，并逐个通过仿真算例予以验证。另外，针对ESO的参数优化整定及估计误差、自适应控制律参数整定及其作用下闭环系统渐近稳定性开展理论分析，给出了相关参数的整定策略。
（3）安全分离轨迹运动的制导控制。星间电磁力的可逆性使得采用同一套电磁装置执行对接与分离成为可能，与柔性对接需求不同的是，电磁分离强调安全分离。面向伴星在轨释放背景，首先给出了空间电磁分离的几类基本假设。其次，基于主伴星恒定磁矩矢量模式仿真分析得出H-bar、V-bar及R-bar分离特性，给出了磁矩幅值与伴星分离运动特征参数的近似代数关系。最后，针对分离后伴星对主星或其他航天器自然椭圆近距离绕飞，采用循环追踪理论和微分同胚映射方法设计满足期望构型需求的安全电磁分离制导控制律，并开展了参数整定分析。
（4）姿态运动的分散协同鲁棒控制。考虑星间电磁力矩和地磁力矩对两航天器姿态运动的影响，分析了空间电磁对接/分离的姿态控制需求，指出对两航天器采用分散协同主动姿态控制的必要性。给定绝对/相对姿态偏差定义及其数学表达式，推导建立了单位四元数表示的绝对/相对姿态偏差运动方程。考虑磁力矩模型的不确定性，采用基于行为的分散协同策略、自适应控制及ESO方法设计了两航天器姿态控制律，理论分析了闭环系统的全局渐近稳定性。最后，通过仿真算例验证了分散协同鲁棒姿态控制下两航天器相对姿态运动的快速协同性及绝对姿态运动的渐近收敛性，对模型未建模动态及外界干扰具有较好鲁棒性。
（5）空间电磁对接/分离的角动量管理。将地磁场作用以磁偶极子表征，推导得到地磁力矩及星间电磁力矩在两航天器系统质心惯性系的投影分量模型。研究了基于地磁场作用的角动量管理策略及磁偶极子求解算法，包括：针对轨控作用力及其中一颗航天器的星间电磁力矩与地磁力矩相消需求，以V-bar、R-bar及H-bar对接为例，研究“正常模式的动量管理”；针对姿控执行机构角动量饱和情形，研究采用地磁力矩卸载多余角动量的“角动量卸载模式的动量管理”。鉴于采用地磁场作用的角动量管理策略具有被动性，初步研究了ACMM(AttitudeControl/Momentum Management)设计策略，包括“序列磁偶极子求解”和“ACMM控制”两部分。
（6）六自由度仿真与地面试验系统设计。面向基于空间电磁对接/分离的航天器近距离绕飞观测背景，开展空间电磁对接/分离的六自由度仿真分析，给出了仿真框架及重点验证了前述章节动力学模型与控制算法的可行性及性能。另外，开展电磁对接/分离地面试验系统设计及研制，给出了试验系统总体方案以及软/硬件设计成果。
总之，论文通过对空间电磁对接/分离动力学与控制研究，一方面从动力学与控制角度验证了该新型对接/分离技术的可行性，另一方面为下一步深入理论研究、地面演示验证试验及在轨试验提供了动力学模型、特性分析、控制算法及地面试验平台。
On-Orbit Servicing (OOS) technology, based on spacecraft docking and separationoperation, represents the frontier and important development trend of aerospace scienceresearch. The increase of on-orbit spacecraft number and spaceflight missioncomplexity highlights the requirement for regular OOS, for which the spaceelectromagnetic docking and separation technology would provide a novel docking andseparation style. This novel technology could resolve the inherent problems of thruster,such as propellant consumption and plume contamination, etc. and has non-contacting,continuous, reversible and synchronous control capability. Concentrating on dynamicsand control problems of space electromagnetic docking and separation, dynamics andself-docking characteristics, trajectory and attitude control, angular momentummanagement,6-DOF simulation and ground experiment system design are investigatedin this paper. The main research points are as follows.
(1) Dynamics and self-docking characteristics of space electromagneticdocking and separation. Hypothesizing the spacecraft electromagnets as magneticdipoles, the far-field electromagnetic force/torque models, with formats of Cartesiancoordinates and spherical coordinates, are derived by the electromagnetic theory.Referenced to the orbit coordinate frame at center of mass of the spacecraft pair, therelative motion dynamic models for the two spacecraft are derived based on Hill’sequations and far-field electromagnetic force model, and then the dynamic model ofspace electromagnetic docking and separation is got by directly subtracting the twodynamic models. Based on the dynamic model, its dynamics properties, includingstrong nonlinearity, coupling, model uncertainty and controllability, are analyzed. And,the concept of electromagnetic self-docking is put forward and proved from the ground(including one-dimensional and two-dimensional) and space cases and thecorresponding sufficient conditions of self-docking are given.
(2) Robust and adaptive control for soft docking trajectory motion.Considering spacecraft soft docking requirements, the desired docking trajectory isdesigned by applying the glideslope approach, and the feedforwad controller is derivedbased on the dynamic model. To resolve the control problems of space electromagneticdocking, such as strong nonlinearity, coupling and dynamic model uncertainty, a twoloop control frame with the inner loop of feedback linearization and outer loop of H∞method, is put forward and a soft trajectory tracking error feedback robust controller isfirstly designed, ensuring better robust capability to model uncertainty. Then,considering the conservative property of the H∞method, another two approaches,including inner loop feedback linearization with outer ESO(Extended State Observer) and LQR(Linear Quadratic Regulator), and the adaptive control method based onLyapunov stability theory, is explored to design the soft trajectory error feedbackcontroller, and verified by simulation cases. In addition, the estimation error of ESO andthe asymptotical stability of closed system with adaptive controller are theoreticallyanalyzed, and the tuning approach of parameters for ESO and adaptive controller arefollowed.
(3) Guidance control for safe separation trajectory motion. Reversible controlcapability of electromagnetic force makes it possible to utilize one electromagneticmechanism to accomplish docking and separation operation. Different from the softelectromagnetic docking, the electromagnetic separation emphasizes safety. With thebackground of on-orbit release partner satellite, several basic hypotheses for spaceelectromagnetic separation are given. Based on constant magnetic moment vectors, thecharacteristics of H-bar, V-bar and R-Bar electromagnetic separation are analyzed andput forward by numerical simulation, and the algebraic relationship between themagnetic moment and the separation relative motion of partner spacecraft is formulated.At last, concentrating on two normal elliptical close proximity fly-around mission aimedto the master or other spacecraft, the space electromagnetic separation guidancecontroller is designed based on the cyclic pursuit theorem and the differentiablehomeomorphic mapping, and the parameters tuning of which is analyzed.
(4) Decentralized and coordinated robust control for attitude motion.Considering the effects of inter-satellite electromagnetic torque and the Earth's magnetictorque to the attitude motions of the spacecraft pair, the requirements of attitude controlare studied and the necessity of decentralized coordinate active attitude controlapproach is pointed out. Defining and formulating the absolute and relative attitudedeviation, the dynamic and kinematics models of absolute and relative attitude deviationmotion with the unit quaternion expression are derived. The attitude controller isdesigned by utilizing behavior-based decentralized control approach, adaptive controland ESO method, and then the global asymptotical stability of the closed system istheoretically analyzed. At last, the quick coordination of relative attitude, asymptoticalconvergence of absolute attitude, and robust capability to model uncertainty andexternal disturbances, are verified by simulation cases for the closed attitude controlsystem with decentralized coordinate attitude controllers.
(5) Angular momentum management for space electromagnetic docking andseparation. Treating the Earth's magnetic field as magnetic dipoles, the projectionmodels of the Earth's magnetic torque and the inter-satellite electromagnetic torque onthe inertial coordinate frame centered at the center of mass of the spacecraft pair isderived. Then, the angular momentum management approach and correspondingsolution algorithms for magnetic dipoles are studied, including the following two. First, considering the requirements of trajectory motion control and one spacecraft'sinter-satellite electromagnetic torque counteracting with the Earth's magnetic torque,taking V-bar, R-bar and H-bar docking for example, the "normal angular momentummanagement" approaches are explored. Second, considering the angular momentumsaturation case of attitude control actuation mechanism, the "angular momentumreduction management" approach is studied by applying the Earth's magnetic torque.Because the designed angular momentum management approaches are negative, anAttitude Control/Momentum Management (ACMM) approach is studied, whichincludes the "sequence magnetic dipoles solution" and the "ACMM control".
(6)6-DOF simulation and ground experiment system design. With thebackground of spacecraft close proximity fly-around observation based on spaceelectromagnetic docking and separation technology, a6-DOF numerical simulation caseof space electromagnetic docking and separation is implemented. A simulation frame isconstructed, and the feasibility and performance of previous dynamic models andcontrol algorithms are verified. Additionally, a ground experiment system is studied anddesigned, and the general system scheme, design results of hardware and software arepresented.
In conclusion, the research of dynamics and control for the space electromagneticdocking and separation technology, on one hand, verifies the feasibility of this noveltechnology from the dynamics and control aspect; on the other hand, provides dynamicmodels, characteristics analysis, control algorithms and ground experiment base forfuture theoretical research, ground demonstration and verification experiments, orfurther on-orbit experiments.
引文
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