有向通讯拓扑下多航天器系统分布式协同控制
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摘要
随着航天任务的复杂化，航天器的功能越来越多，若将所有功能全部集成到单一的航天器上，则不可避免地给航天任务的完成带来一定的风险。近年来，随着多智能体系统协同控制研究热潮的兴起，基于一致性的分布式协同控制在多航天器编队飞行中引起了广泛的研究。以图论为工具，由图的节点代表航天器，节点间的有向路径代表航天器间的信息传递关系，为多航天器系统协同控制的研究带来了极大的方便。本文在总结现有研究成果的基础上，基于一致性算法，在有向通讯拓扑下，对多航天器系统的分布式协同控制问题进行了深入研究，主要包括以下内容：
在有向通讯拓扑下分别针对领航航天器(期望姿态的表现形式)状态全局可知和局部可知两种情况，研究了多航天器系统协同跟踪问题。当领航航天器状态全局可知时，考虑由修正罗德里格参数(MRP)描述的跟随航天器误差动力学方程，针对跟随航天器存在模型不确定性以及受到外部干扰的情形提出了基于非回归项的分布式自适应协同姿态跟踪控制律，使得各跟随航天器达到姿态协同并跟踪具有时变角速度的领航航天器。当领航航天器状态局部可知时，即在仅有部分跟踪航天器可获取领航航天器状态的限制下，分别针对领航航天器静止、跟随航天器保持相对指向以及领航航天器具有时变角速度三种情形提出了分布式姿态协同控制算法。当领航航天器静止时，设计分布式协同控制算法，只要航天器间的有向通讯拓扑图具有有向生成树，根据Lyapunov稳定性原理及输入到状态稳定性理论证明了闭环系统的渐近稳定性，并将上述算法扩展到各跟随航天器保持相对指向的问题中。当领航航天器具有时变角速度时，为每个跟随航天器设计两个滑模估计器，在有限时间内各跟随航天器均可估计得到领航航天器的时变状态，进一步提出了不依赖于航天器惯量的分布式自适应协同跟踪控制律。
为了提高系统对干扰的鲁棒性并改善系统的收敛性能，开展了多航天器系统有限时间协同控制的研究。当不存在领航航天器时，借助反馈线性化的思想，提出了基于模型的分布式有限时间一致性算法，将二阶非线性系统降阶为一阶系统，进而证明一阶系统的有限时间稳定性。在仅有部分跟随航天器可获取领航航天器状态的情形下，设计包含邻居跟随航天器信息的快速终端滑模面，提出了不依赖于模型的分布式有限时间姿态调节控制律。构造Lyapunov函数，根据扩展有限时间Lyapunov稳定性定理证明了跟随航天器系统全局有限时间稳定。为削弱不连续控制带来的抖振，设计改进的边界层函数，克服了常规边界层内状态渐近稳定的缺陷，并证明系统的状态轨迹收敛到期望值的小邻域内。当领航航天器具有常值角速度时，设计连续的有限时间估计器，考虑到航天器转动惯量的不确定性及存在外部干扰的情形，提出了分布式有限时间自适应跟踪控制律。进一步指出，如果领航航天器的角加速度是有界的，那么对于跟踪时变角速度的领航航天器，所提出的控制律也是有效的。
基于一致性理论，考虑控制输入耦合的六自由度航天器运动模型，在有向通讯拓扑下对多航天器系统相对轨道及姿态的耦合协同控制问题进行了研究。在仅有部分跟随航天器可获取领航航天器信息的情形下，针对各跟随航天器存在未建模动态以及外部环境干扰等问题，提出了一种基于切比雪夫神经网络(CNN)的自适应L2增益控制律，使得各跟随航天器在轨道交会的同时姿态保持一致。针对跟踪航天器间相对速度和角速度难以测量的特点，设计了无需相对速度及角速度信息的分布式耦合自适应控制律，保证各跟随航天器保持特定的队形且具有期望的相对指向。当领航航天器为动态时，给出三个滑模估计器对领航航天器状态进行估计，设计仅需期望状态的CNN自适应更新算法，利用双曲正切函数的性质，提出了考虑控制输入饱和的分布式自适应协同控制律。
本文中，针对每个航天器所提出的控制算法都是仅依赖于其自身及相邻航天器的信息，因此所有的控制算法是都是分布式的。
As the increasing complexity of the space missions, the spacecraft need to becomemore and more powerful. It brings certain risks inevitably to the completion of the spacemission if all features are all integrated into one single spacecraft. Recently, distributedcoordinated control has gained much attention for multiple spacecraft formation flying.Using graph theory, the node represents the spacecraft, and the directed path betweentwo nodes represents the information transmission relationships among the spacecraft,which brings greater convenience to study the distributed coordinated control for multiplespacecraft system. The dissertation surveys the recent results on multi-agent systemsand spacecraft formation flying, and give a deep study on the distributed coordinatedcontrol for multiple spacecraft systems under a directed communication topology. Themain contents and contributions of this dissertation can be summarized as follows:
The coordinated tracking problem for spacecraft formation flying under a generaldirected graph is investigated. Two cases have been studied, namely, all the followerspacecraft can obtain the information of the leader spacecraft and only a subset of thefollower spacecraft has access to the leader spacecraft. In the first case, for the errordynamic equations of spacecraft described by the Modified Rodriguez Parameters (M-RP), a nonregressor-based adaptive cooperative tracking control algorithm is proposedfor multiple spacecraft formation flying dealing with modeling uncertainties and externaldisturbances. As a result, all follower spacecraft in the formation converge to the desiredattitude cooperatively and track the time-varying leader spacecraft. In the second case,under the constraint that only a subset of follower spacecraft has access to the leaderspacecraft, a distributed coordinated algorithm is proposed to guarantee that all the fol-lower spacecraft could track the stationary and/or dynamic leader spacecraft. For the casewhere the leader spacecraft has a constant attitude, a distributed controller is developedand it is then extended to achieve relative attitude maintenance. According to Lyapunovstability theory and the input-to-state stability theory, the resulting closed-loop systemsare asymptotically stable as long as the directed communication graph characterizing theinteraction among the followers and the leader contains a directed spanning tree. More-over, for the case where the leader spacecraft has a varying attitude, two sliding-modeestimators are presented for each follower to obtain the estimates of the leader’s attitude and angular velocity using only local information in finite time. Then, an adaptive attitudecoordinated tracking control law is synthesized in the presence of model uncertainties.
To improve the robustness of the system and obtain fast convergence performance,we design finite-time attitude coordinated control for multiple spacecraft systems. Forthe leaderless consensus problem, a model-dependent distributed finite-time consensusalgorithm is proposed using feedback linearization theory. On the sliding mode manifold,the finite-time consensus problem for multi-spacecraft systems with second-order non-linear dynamics becomes to the problem for first-order dynamics. For the leader space-craft coordinated tracking problem, a model-independent distributed finite-time attitudecoordination control algorithm for multiple spacecraft formation under a direct commu-nication topology is proposed using fast terminal sliding mode in the case that the leaderspacecraft reference state may only be available to a part of the following spacecraft. Byconstructing Lyapunov function, multiple spacecraft system is proved with global finite-time convergence based on the extended finite time Lyapunov theory and the proposecontrol algorithm can guarantee that the attitudes and angular velocities converge to thedesired values. In order to reduce the chatting of the discontinuous control, the modifiedboundary layer approach was adopted because of the asymptotic stability in the normalboundary layer. The modified control algorithm can guarantee that the attitudes and an-gular velocities converge to a neighborhood of the desired states in finite time. Whenthe leader spacecraft has a constant angular velocity, we propose a distributed continu-ous finite-time estimator and a distributed finite-time adaptive tracking control algorithmto deal with modeling uncertainties and external disturbances. Furthermore, the proposedalgorithm can track the leader spacecraft with a time-varying angular velocity if the leaderspacecraft’s angular acceleration is bounded.
Based on the consensus theory, the coupled cooperative control for relative orbitsand attitudes of a multiple spacecraft system is investigated under a directed communi-cation topology. Considering the nonlinear equations for the relative obits of near-earthspacecraft and the attitude motion equations in terms of the MRP, six degrees of free-dom (6DOF) motion equations with coupled control input, unknown nonlinearities, andexternal disturbance are built. In the case where the leader spacecraft state may only beavailable to only a subset of follower spacecraft, we proposes an adaptive L2gain con-trol algorithm based on Chebyshev Neural networks. It is shown that a fleet of followersrendezvous at a fixed point and point toward the same direction. Due to the fact that the relative velocities and relative angular velocities among the follower spacecraft as difcultto be measured, we propose a distributed coupled adaptive control algorithm without us-ing neighbor’s velocities and angular velocities such that all follower spacecraft maintaina desired formation and relative attitudes. In the case that the leader spacecraft are dy-namic, a distributed coupled coordinated tracking control algorithm and an adaptive lawusing only the leader spacecraft state combined with a distributed sliding mode estimatoris proposed subject to input saturation constraints.
In this dissertation, the proposed algorithms for each follower spacecraft is onlydependent on its own information and the information of its neighbor spacecraft. Thus,the proposed algorithms are distributed.
在有向通讯拓扑下分别针对领航航天器(期望姿态的表现形式)状态全局可知和局部可知两种情况，研究了多航天器系统协同跟踪问题。当领航航天器状态全局可知时，考虑由修正罗德里格参数(MRP)描述的跟随航天器误差动力学方程，针对跟随航天器存在模型不确定性以及受到外部干扰的情形提出了基于非回归项的分布式自适应协同姿态跟踪控制律，使得各跟随航天器达到姿态协同并跟踪具有时变角速度的领航航天器。当领航航天器状态局部可知时，即在仅有部分跟踪航天器可获取领航航天器状态的限制下，分别针对领航航天器静止、跟随航天器保持相对指向以及领航航天器具有时变角速度三种情形提出了分布式姿态协同控制算法。当领航航天器静止时，设计分布式协同控制算法，只要航天器间的有向通讯拓扑图具有有向生成树，根据Lyapunov稳定性原理及输入到状态稳定性理论证明了闭环系统的渐近稳定性，并将上述算法扩展到各跟随航天器保持相对指向的问题中。当领航航天器具有时变角速度时，为每个跟随航天器设计两个滑模估计器，在有限时间内各跟随航天器均可估计得到领航航天器的时变状态，进一步提出了不依赖于航天器惯量的分布式自适应协同跟踪控制律。
为了提高系统对干扰的鲁棒性并改善系统的收敛性能，开展了多航天器系统有限时间协同控制的研究。当不存在领航航天器时，借助反馈线性化的思想，提出了基于模型的分布式有限时间一致性算法，将二阶非线性系统降阶为一阶系统，进而证明一阶系统的有限时间稳定性。在仅有部分跟随航天器可获取领航航天器状态的情形下，设计包含邻居跟随航天器信息的快速终端滑模面，提出了不依赖于模型的分布式有限时间姿态调节控制律。构造Lyapunov函数，根据扩展有限时间Lyapunov稳定性定理证明了跟随航天器系统全局有限时间稳定。为削弱不连续控制带来的抖振，设计改进的边界层函数，克服了常规边界层内状态渐近稳定的缺陷，并证明系统的状态轨迹收敛到期望值的小邻域内。当领航航天器具有常值角速度时，设计连续的有限时间估计器，考虑到航天器转动惯量的不确定性及存在外部干扰的情形，提出了分布式有限时间自适应跟踪控制律。进一步指出，如果领航航天器的角加速度是有界的，那么对于跟踪时变角速度的领航航天器，所提出的控制律也是有效的。
基于一致性理论，考虑控制输入耦合的六自由度航天器运动模型，在有向通讯拓扑下对多航天器系统相对轨道及姿态的耦合协同控制问题进行了研究。在仅有部分跟随航天器可获取领航航天器信息的情形下，针对各跟随航天器存在未建模动态以及外部环境干扰等问题，提出了一种基于切比雪夫神经网络(CNN)的自适应L2增益控制律，使得各跟随航天器在轨道交会的同时姿态保持一致。针对跟踪航天器间相对速度和角速度难以测量的特点，设计了无需相对速度及角速度信息的分布式耦合自适应控制律，保证各跟随航天器保持特定的队形且具有期望的相对指向。当领航航天器为动态时，给出三个滑模估计器对领航航天器状态进行估计，设计仅需期望状态的CNN自适应更新算法，利用双曲正切函数的性质，提出了考虑控制输入饱和的分布式自适应协同控制律。
本文中，针对每个航天器所提出的控制算法都是仅依赖于其自身及相邻航天器的信息，因此所有的控制算法是都是分布式的。
As the increasing complexity of the space missions, the spacecraft need to becomemore and more powerful. It brings certain risks inevitably to the completion of the spacemission if all features are all integrated into one single spacecraft. Recently, distributedcoordinated control has gained much attention for multiple spacecraft formation flying.Using graph theory, the node represents the spacecraft, and the directed path betweentwo nodes represents the information transmission relationships among the spacecraft,which brings greater convenience to study the distributed coordinated control for multiplespacecraft system. The dissertation surveys the recent results on multi-agent systemsand spacecraft formation flying, and give a deep study on the distributed coordinatedcontrol for multiple spacecraft systems under a directed communication topology. Themain contents and contributions of this dissertation can be summarized as follows:
The coordinated tracking problem for spacecraft formation flying under a generaldirected graph is investigated. Two cases have been studied, namely, all the followerspacecraft can obtain the information of the leader spacecraft and only a subset of thefollower spacecraft has access to the leader spacecraft. In the first case, for the errordynamic equations of spacecraft described by the Modified Rodriguez Parameters (M-RP), a nonregressor-based adaptive cooperative tracking control algorithm is proposedfor multiple spacecraft formation flying dealing with modeling uncertainties and externaldisturbances. As a result, all follower spacecraft in the formation converge to the desiredattitude cooperatively and track the time-varying leader spacecraft. In the second case,under the constraint that only a subset of follower spacecraft has access to the leaderspacecraft, a distributed coordinated algorithm is proposed to guarantee that all the fol-lower spacecraft could track the stationary and/or dynamic leader spacecraft. For the casewhere the leader spacecraft has a constant attitude, a distributed controller is developedand it is then extended to achieve relative attitude maintenance. According to Lyapunovstability theory and the input-to-state stability theory, the resulting closed-loop systemsare asymptotically stable as long as the directed communication graph characterizing theinteraction among the followers and the leader contains a directed spanning tree. More-over, for the case where the leader spacecraft has a varying attitude, two sliding-modeestimators are presented for each follower to obtain the estimates of the leader’s attitude and angular velocity using only local information in finite time. Then, an adaptive attitudecoordinated tracking control law is synthesized in the presence of model uncertainties.
To improve the robustness of the system and obtain fast convergence performance,we design finite-time attitude coordinated control for multiple spacecraft systems. Forthe leaderless consensus problem, a model-dependent distributed finite-time consensusalgorithm is proposed using feedback linearization theory. On the sliding mode manifold,the finite-time consensus problem for multi-spacecraft systems with second-order non-linear dynamics becomes to the problem for first-order dynamics. For the leader space-craft coordinated tracking problem, a model-independent distributed finite-time attitudecoordination control algorithm for multiple spacecraft formation under a direct commu-nication topology is proposed using fast terminal sliding mode in the case that the leaderspacecraft reference state may only be available to a part of the following spacecraft. Byconstructing Lyapunov function, multiple spacecraft system is proved with global finite-time convergence based on the extended finite time Lyapunov theory and the proposecontrol algorithm can guarantee that the attitudes and angular velocities converge to thedesired values. In order to reduce the chatting of the discontinuous control, the modifiedboundary layer approach was adopted because of the asymptotic stability in the normalboundary layer. The modified control algorithm can guarantee that the attitudes and an-gular velocities converge to a neighborhood of the desired states in finite time. Whenthe leader spacecraft has a constant angular velocity, we propose a distributed continu-ous finite-time estimator and a distributed finite-time adaptive tracking control algorithmto deal with modeling uncertainties and external disturbances. Furthermore, the proposedalgorithm can track the leader spacecraft with a time-varying angular velocity if the leaderspacecraft’s angular acceleration is bounded.
Based on the consensus theory, the coupled cooperative control for relative orbitsand attitudes of a multiple spacecraft system is investigated under a directed communi-cation topology. Considering the nonlinear equations for the relative obits of near-earthspacecraft and the attitude motion equations in terms of the MRP, six degrees of free-dom (6DOF) motion equations with coupled control input, unknown nonlinearities, andexternal disturbance are built. In the case where the leader spacecraft state may only beavailable to only a subset of follower spacecraft, we proposes an adaptive L2gain con-trol algorithm based on Chebyshev Neural networks. It is shown that a fleet of followersrendezvous at a fixed point and point toward the same direction. Due to the fact that the relative velocities and relative angular velocities among the follower spacecraft as difcultto be measured, we propose a distributed coupled adaptive control algorithm without us-ing neighbor’s velocities and angular velocities such that all follower spacecraft maintaina desired formation and relative attitudes. In the case that the leader spacecraft are dy-namic, a distributed coupled coordinated tracking control algorithm and an adaptive lawusing only the leader spacecraft state combined with a distributed sliding mode estimatoris proposed subject to input saturation constraints.
In this dissertation, the proposed algorithms for each follower spacecraft is onlydependent on its own information and the information of its neighbor spacecraft. Thus,the proposed algorithms are distributed.
引文
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