卫星集群导航与轨道控制方法研究
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摘要
随着新型航天任务的发展，卫星集群技术成为国际航天领域研究的一个重要方向。卫星集群是指多颗卫星保持在较近空间区域内运行，借助于星间通信链路实现信息交互和任务协作，以完成在轨任务的卫星系统。与传统卫星编队飞行技术相比，卫星集群技术具有特殊性：1）卫星集群不依赖星间相对测量信息，运行时成员卫星长期保持在一定的空间范围内，但并未规定精确的星间相位和距离联系，不必保持严格的空间构型；2）需具备长期自主运行能力，如长期自主导航、长期运行轨道设计、长期自主轨道保持与碰撞规避等。针对上述特殊性，本学文论文着重围绕卫星集群的长期自主导航、集群初始轨道建立和在轨安全运行策略展开深入研究，论文主要内容由以下部分组成：
针对卫星集群成员卫星采用平均轨道根数作为导航参数的自主导航问题，研究了多摄动影响下平均轨道根数的动力学模型。分析并给出适用于平均轨道根数建模的坐标系；推导瞬时轨道根数的数学描述，并在此基础上定义了文中使用的平均轨道根数；考虑近地空间任务的主要影响因素，推导地球非球形摄动带谐项、田谐项和大气阻力摄动对平均轨道根数变化率的影响，并结合轨道根数短周期项完成平均轨道根数到瞬时轨道根数的映射关系。
针对卫星集群成员卫星在轨长期自主精确估计平均轨道根数的问题，提出基于滤波的平均轨道根数在轨估计方法。首先，以平均轨道根数作为状态量并结合平均轨道根数变化率模型和高斯型摄动运动方程建立状态方程，以瞬时轨道根数作为量测值建立量测方程；其次，提出采用EKF和UKF滤波算法估计平均轨道根数，其中，为提高UKF滤波稳定性，并在不损失估计精度的条件下尽可能降低计算量，将球形单边采样方法应用于平方根形式的UKF滤波；最后，在无轨道控制、脉冲机动控制、连续推力控制三种工况下仿真验证了平均轨道根数滤波估计算法的有效性。
针对卫星集群星间相对距离长期有界的特殊要求，提出了入轨后初始轨道的建立方法。考虑非球形摄动带谐项和球形大气阻力摄动的影响，基于平均轨道根数提出了卫星集群星间相对距离有界的初始轨道约束条件；为建立卫星集群初始轨道，采用常值连续推力器，从燃料平衡方面，提出了基于环形控制策略的分布式轨道控制方法，对稳定性进行了详细的数学证明，并针对近圆轨道情况给出了简化的控制器；从燃料最优方面，提出了基于改进高斯伪谱法的最优轨道控制方法，将终端状态约束改进为线性逼近形式，并采用闭环方式改进误差因素对控制结果的影响；最后仿真验证了初始轨道条件和两类入轨控制算法的有效性。
针对在轨运行期间的安全保障问题，提出了卫星集群轨道保持方法和碰撞规避策略。当星间相对距离不能满足最远相对距离或最近相对距离约束时，利用星间相对运动关系、星间轨道根数关系，以及最远相对距离和最近相对距离约束，提出了卫星集群轨道保持策略和轨道保持算法；为保证相对距离较近时的运行安全，以碰撞预警级别作为判断是否进行规避的条件，给出了碰撞概率计算方法、碰撞发生时间区间近似计算方法，并分别提出了基于碰撞概率和基于相对距离的避让机动策略；考虑采用常值连续推力的情况提出了避让机动时间的约束；推导了碰撞规避后进行轨道控制的目标条件计算方法；最后，仿真验证了轨道保持和碰撞规避方法的有效性。
With the rapid development of the aerospace missions, the satellite cluster flight has become an important focus of the aerospace field all over the world. Satellite cluster is described as a kind of satellite system in which multiple satellites remain in close spatial region, satellite communication links are utilized to achieve information exchange and task collaboration. Compared with traditional satellite formation flying technology, satellite cluster has the particularities:1) satellite cluster does not depend on the relative measurement information, all the members remain in a certain region for long time, but does not provide a precise inter-satellite phase and distance contact, and do not maintain a strict configuration;2) the long-term autonomous abilities are needed, such as autonomous navigation, long-term orbit designed and establishment and the strategy for orbit-keeping and collision avoidance and so on. Based on these particularities, this dissertation focuses on the long term autonomous navigation, the establishment of the cluster flight and the strategy of cluster flight safety. The major contents of this dissertation are consisted of the following parts.
Firstly, the formulations of the mean orbital elements are derived. The coordinate frames are analyzed, the proper frame for this dissertation is selected. The mathematical description of the osculating orbital elements is presented. The mean orbital elements are defined from the osculating orbital elements. A semi analytical dynamical model of mean orbital elements that includes zonal/tesseral/sectorial harmonics and drag is formulated to capture the daily, long-periodic, and secular evolution of the mean orbital elements.
Secondly, a new approach for onboard estimation of mean orbital elements is studied based on recursive filter for long-term autonomous navigation. The filter model of mean orbital elements is formulated. The Extend Kalman Filter (EKF) and Unscented Kalman Filter (UKF) are served as estimator The spherical simplex sigma-point selection and the square root form of UKF are fused for less computational cost and better numerical stability on-board A kind of direct computation method is presented for comparisons The effectiveness and robustness of the filter-based mean orbital elements estimation approach is validated by numerical simulations of three conditions, including without orbit maneuver, with impulsive orbit control and with continuous orbit control. And the accuracy is compared by the simulations.
Thirdly, the initial orbit establishment approaches are studied for distance bounded cluster flight. According to the special requirement of cluster flight mission, the distance-bounded natural orbit using mean orbital elements is derived under the perturbation of zonal harmonics and spherical drag. For fuel balance, a kind of distribute orbit controller is offered to establish cluster initial orbit, using cyclic strategy and constant continuous thrusters, and the stability of the orbit control law is proven. The controller is simplified for the near circular orbit mission. For fuel optimal, a kind of Improved Gauss Pseudospectral Method (IGPM) is offered. The nonlinear state integral constraint is transformed into the equivalent linear form for faster convergence speed. The closed-loop control strategy of IGPM is used to decrease the effects of undesired errors and uncertainties. The effectiveness of the initial orbit constraints and two kinds of orbit establishment approaches are validated by numerical simulations.
Finally, the cluster flight and collision avoidance strategies are studied to fulfill the safety requirements. A cluster-keeping strategy and cluster-keeping controller is developed for the relative distance of any pair of cluster members reaches the upper or lower bound using the relationships of relative distance, orbital elements and distant-bounded constraints. To ensure the safety, the collision warning level is used to evaluate the collision risk. The collision probability calculation methods are given. The prediction method of the time duration for collision is derived. Two collision avoidance maneuver strategies are given based on collision probability and relative distance, respectively. The thruster working duration constraint is offered. The desired conditions for postmaneuver orbit are designed. The effectiveness of strategies is validated by numerical simulation.
针对卫星集群成员卫星采用平均轨道根数作为导航参数的自主导航问题，研究了多摄动影响下平均轨道根数的动力学模型。分析并给出适用于平均轨道根数建模的坐标系；推导瞬时轨道根数的数学描述，并在此基础上定义了文中使用的平均轨道根数；考虑近地空间任务的主要影响因素，推导地球非球形摄动带谐项、田谐项和大气阻力摄动对平均轨道根数变化率的影响，并结合轨道根数短周期项完成平均轨道根数到瞬时轨道根数的映射关系。
针对卫星集群成员卫星在轨长期自主精确估计平均轨道根数的问题，提出基于滤波的平均轨道根数在轨估计方法。首先，以平均轨道根数作为状态量并结合平均轨道根数变化率模型和高斯型摄动运动方程建立状态方程，以瞬时轨道根数作为量测值建立量测方程；其次，提出采用EKF和UKF滤波算法估计平均轨道根数，其中，为提高UKF滤波稳定性，并在不损失估计精度的条件下尽可能降低计算量，将球形单边采样方法应用于平方根形式的UKF滤波；最后，在无轨道控制、脉冲机动控制、连续推力控制三种工况下仿真验证了平均轨道根数滤波估计算法的有效性。
针对卫星集群星间相对距离长期有界的特殊要求，提出了入轨后初始轨道的建立方法。考虑非球形摄动带谐项和球形大气阻力摄动的影响，基于平均轨道根数提出了卫星集群星间相对距离有界的初始轨道约束条件；为建立卫星集群初始轨道，采用常值连续推力器，从燃料平衡方面，提出了基于环形控制策略的分布式轨道控制方法，对稳定性进行了详细的数学证明，并针对近圆轨道情况给出了简化的控制器；从燃料最优方面，提出了基于改进高斯伪谱法的最优轨道控制方法，将终端状态约束改进为线性逼近形式，并采用闭环方式改进误差因素对控制结果的影响；最后仿真验证了初始轨道条件和两类入轨控制算法的有效性。
针对在轨运行期间的安全保障问题，提出了卫星集群轨道保持方法和碰撞规避策略。当星间相对距离不能满足最远相对距离或最近相对距离约束时，利用星间相对运动关系、星间轨道根数关系，以及最远相对距离和最近相对距离约束，提出了卫星集群轨道保持策略和轨道保持算法；为保证相对距离较近时的运行安全，以碰撞预警级别作为判断是否进行规避的条件，给出了碰撞概率计算方法、碰撞发生时间区间近似计算方法，并分别提出了基于碰撞概率和基于相对距离的避让机动策略；考虑采用常值连续推力的情况提出了避让机动时间的约束；推导了碰撞规避后进行轨道控制的目标条件计算方法；最后，仿真验证了轨道保持和碰撞规避方法的有效性。
With the rapid development of the aerospace missions, the satellite cluster flight has become an important focus of the aerospace field all over the world. Satellite cluster is described as a kind of satellite system in which multiple satellites remain in close spatial region, satellite communication links are utilized to achieve information exchange and task collaboration. Compared with traditional satellite formation flying technology, satellite cluster has the particularities:1) satellite cluster does not depend on the relative measurement information, all the members remain in a certain region for long time, but does not provide a precise inter-satellite phase and distance contact, and do not maintain a strict configuration;2) the long-term autonomous abilities are needed, such as autonomous navigation, long-term orbit designed and establishment and the strategy for orbit-keeping and collision avoidance and so on. Based on these particularities, this dissertation focuses on the long term autonomous navigation, the establishment of the cluster flight and the strategy of cluster flight safety. The major contents of this dissertation are consisted of the following parts.
Firstly, the formulations of the mean orbital elements are derived. The coordinate frames are analyzed, the proper frame for this dissertation is selected. The mathematical description of the osculating orbital elements is presented. The mean orbital elements are defined from the osculating orbital elements. A semi analytical dynamical model of mean orbital elements that includes zonal/tesseral/sectorial harmonics and drag is formulated to capture the daily, long-periodic, and secular evolution of the mean orbital elements.
Secondly, a new approach for onboard estimation of mean orbital elements is studied based on recursive filter for long-term autonomous navigation. The filter model of mean orbital elements is formulated. The Extend Kalman Filter (EKF) and Unscented Kalman Filter (UKF) are served as estimator The spherical simplex sigma-point selection and the square root form of UKF are fused for less computational cost and better numerical stability on-board A kind of direct computation method is presented for comparisons The effectiveness and robustness of the filter-based mean orbital elements estimation approach is validated by numerical simulations of three conditions, including without orbit maneuver, with impulsive orbit control and with continuous orbit control. And the accuracy is compared by the simulations.
Thirdly, the initial orbit establishment approaches are studied for distance bounded cluster flight. According to the special requirement of cluster flight mission, the distance-bounded natural orbit using mean orbital elements is derived under the perturbation of zonal harmonics and spherical drag. For fuel balance, a kind of distribute orbit controller is offered to establish cluster initial orbit, using cyclic strategy and constant continuous thrusters, and the stability of the orbit control law is proven. The controller is simplified for the near circular orbit mission. For fuel optimal, a kind of Improved Gauss Pseudospectral Method (IGPM) is offered. The nonlinear state integral constraint is transformed into the equivalent linear form for faster convergence speed. The closed-loop control strategy of IGPM is used to decrease the effects of undesired errors and uncertainties. The effectiveness of the initial orbit constraints and two kinds of orbit establishment approaches are validated by numerical simulations.
Finally, the cluster flight and collision avoidance strategies are studied to fulfill the safety requirements. A cluster-keeping strategy and cluster-keeping controller is developed for the relative distance of any pair of cluster members reaches the upper or lower bound using the relationships of relative distance, orbital elements and distant-bounded constraints. To ensure the safety, the collision warning level is used to evaluate the collision risk. The collision probability calculation methods are given. The prediction method of the time duration for collision is derived. Two collision avoidance maneuver strategies are given based on collision probability and relative distance, respectively. The thruster working duration constraint is offered. The desired conditions for postmaneuver orbit are designed. The effectiveness of strategies is validated by numerical simulation.
引文
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