SE(3)上一般力学控制系统的运动描述与飞行器建模

与Lie群上的简单力学控制系统不同,Lie群上的一般力学控制系统需要考虑势能在位形空间中的变化,故其Lagrange算子不再是左不变的,这意味着根据定义Euler-Poincaré方程不能直接应用于此类系统。为此,本文首先建立矩阵Lie群SE(3)上的一般力学控制系统的数学描述,重新定义Lagrange算子为左不变动能减势能;然后基于连续Lagrange-d’Alembert法则推导得到了含有势能函数的Euler-Poincaré方程,用来刻画SE(3)上一般力学控制系统的动态;最后给出了四旋翼无人直升机和无人飞艇建模的应用实例。     

Robust image-based coordinated control for spacecraft formation flying

This paper addresses a coordinated control problem for Spacecraft Formation Flying (SFF). The distributed followers are required to track and synchronize with the leader spacecraft. By using the feature points in the two-dimensional image space, an integrated 6-degree-of-freedom dynamic model is formulated for spacecraft relative motion. Without sophisticated three-dimensional reconstruction, image features are directly utilized for the controller design. The proposed image-based controller can drive the follower spacecraft in the desired configuration with respect to the leader when the real-time captured images match their reference counterparts. To improve the precision of the formation configuration, the proposed controller employs a coordinated term to reduce the relative distance errors between followers. The uncertainties in the system dynamics are handled by integrating the adaptive technique into the controller, which increases the robustness of the SFF system. The closed-loop system stability is analyzed using the Lyapunov method and algebraic graph theory. A numerical simulation for a given SFF scenario is performed to evaluate the performance of the controller.     

SE(3)上航天器姿轨耦合固定时间容错控制

针对相对运动航天器姿轨一体化控制问题,考虑执行器故障和控制输入饱和的影响,提出了一种基于滑模的模糊自适应固定时间容错控制方法。首先,在李群SE（3）的框架下建立并推导相对运动航天器姿轨一体化误差动力学模型;其次,引入执行器故障和控制输入饱和的问题,采用双幂次快速终端滑模面,并结合模糊自适应方法设计了固定时间稳定的容错控制器,可以实现执行器故障情况下相对运动航天器的高精度快速跟踪控制;然后,运用Lyapunov方法证明了系统的稳定性,该控制器不仅能不依赖于系统的初始状态实现滑模趋近和到达阶段的固定时间稳定性,而且由于采用模糊逼近方法结合自适应更新策略可以实时高精度地估计系统的总扰动信息,因此可以达到快速高精度的容错控制目标;最后,对所提出的的控制方法进行数值仿真分析,结果验证了该方法的有效性和可行性。     

Coordinated attitude control for flexible spacecraft formation with actuator configuration misalignment

This paper investigates the coordinated attitude control problem for flexible spacecraft formation with the consideration of actuator configuration misalignment. First, an integral-type sliding mode adaptive control law is designed to compensate the effects of flexible mode, environmental disturbance and actuator installation deviation. The basic idea of the Integral-type Sliding Mode Control (ISMC) is to design a proper sliding manifold so that the sliding mode starts from the initial time instant, and thus the robustness of the system can be guaranteed from the beginning of the process and the reaching phase is eliminated. Then, considering the nominal system of spacecraft formation based on directed topology, an attitude cooperative control strategy is developed for the nominal system with or without communication delay. The proposed control law can guarantee that for each spacecraft in the spacecraft formation, the desired attitude objective can be achieved and the attitude synchronization can be maintained with other spacecraft in the formation. Finally, simulation results are given to show the effectiveness of the proposed control algorithm.     

Spacecraft formation-containment flying control with time-varying translational velocity

This paper investigates the problem of Spacecraft Formation-Containment Flying Control (SFCFC) when the desired translational velocity is time-varying. In SFCFC problem, there are multiple leader spacecraft and multiple follower spacecraft and SFCFC can be divided into leader spacecraft’s formation control and follower spacecraft’s containment control. First, under the condition that only a part of leader spacecraft can have access to the desired time-varying translational velocity, a velocity estimator is designed for each leader spacecraft. Secondly, based on the estimated translational velocity, a distributed formation control algorithm is designed for leader spacecraft to achieve the desired formation and move with the desired translational velocity simultaneously. Then, to ensure all follower spacecraft converge to the convex hull formed by the leader spacecraft, a distributed containment control algorithm is designed for follower spacecraft. Moreover, to reduce the dependence of the designed control algorithms on the graph information and increase system robustness, the control gains are changing adaptively and the parametric uncertainties are handled, respectively. Finally, simulation results are provided to illustrate the effectiveness of the theoretical results.     

航天器有限时间输出反馈姿态控制

研究在角速度不可测时航天器的有限时间姿态控制问题。基于有限时间控制技术,提出了由修正Rodrigues参数进行姿态描述的航天器输出反馈姿态控制算法。首先设计了单个航天器的输出反馈姿态控制器,在没有角速度反馈时也能够保证航天器姿态在有限时间内调节到期望姿态。之后,设计了无需绝对角速度和相对角速度信息的多航天器分布式输出反馈姿态控制器。使用Lyapunov理论和图论,对闭环系统全局有限时间稳定性进行了严格的证明。最后对提出的控制算法进行了数值仿真,其结果验证了所设计的航天器输出反馈控制算法的可行性和有效性。     

应用分力合成主动振动抑制方法的最优飞行器大角度机动控制策略

 针对当代带大型挠性附件的空间飞行器,提出了分力合成主动振动抑制方法,并且分析了方法的鲁棒性。该方法可以保证挠性飞行器在实现指定的刚体运动的同时,抑制掉对系统影响较大的挠性振动模态,对频率不确定性的鲁棒性使得该方法易于工程实践。对于使用常幅值力矩喷气执行机构的航天器,设计了应用分力合成方法的时间—燃料最优机动控制律,数值仿真结果验证了方法的有效性。     

Pattern control for large-scale spacecraft swarms in elliptic orbits via density fields

Space swarms, enabled by the miniaturization of spacecraft, have the potential capability to lower costs, increase efficiencies, and broaden the horizons of space missions. The formation control problem of large-scale spacecraft swarms flying around an elliptic orbit is considered. The objective is to drive the entire formation to produce a specified spatial pattern. The relative motion between agents becomes complicated as the number of agents increases. Hence, a density-based method is adopted...     

利用厄密特多项式的配置和非线性规划进行小推力最优变轨

提出了一种计算在反平方场中采用小推力变轨的最优轨道的直接方法,这种方法采用了近段发展起来的使用分段的多项式来代替状态和控制变量的直接优化方法,然后最优控制问题就转化成可以用数值方法解决的非线性规划问题。     

Solar Pressure Attitude Stabilization of Earth-Pointing Spacecraft

The development of a solar pressure control system for three-axis attitude control of Earth-oriented spacecraft is presented. A controller configuration consisting of two rotatable mirrorlike surfaces, representing the minimum hardware implementation, is considered. Optimal control theory is applied to synthesize a feedback control law directly governing the differential rotation of the control surfaces. The system performance is evaluated through the response analysis of a satellite subject to destabilizing gravity gradient torques as well as external disturbances. Even under such adverse conditions, the results indicate a moderately sized controller to be quite effective in maintaining the desired Earth-pointing spacecraft orientation. The validity of the optimal control law is established for all times of the year, and the feasibility of implementing suboptimal control policies is also examined.     

Shape control of spacecraft formation using a virtual spring-damper mesh

This paper derives a distance-based formation control method to maintain the desired formation shape for spacecraft in a gravitational potential field. The method is an analogy of a vir-tual spring-damper mesh. Spacecraft are connected virtually by spring-damper pairs. Convergence analysis is performed using the energy method. Approximate expressions for the distance errors and control accelerations at steady state are derived by using algebraic graph representations and results of graph rigidity. Analytical results indicate that if the underlying graph of the mesh is rigid, the convergence to a static shape is assured, and higher formation control precision can be achieved by increasing the elastic coefficient without increasing the control accelerations. A numerical exam-ple of spacecraft formation in low Earth orbit confirms the theoretical analysis and shows that the desired formation shape can be well achieved using the presented method, whereas the orientation of the formation can be kept pointing to the center of the Earth by the gravity gradient. The method is decentralized, and uses only relative measurement information. Constructing a distributed virtual structure in space can be the general application area. The proposed method can serve as an active shape control law for the spacecraft formations using propellantless internal forces.     

Discrete time multiple spacecraft formation flying attitude optimal control in presence of relative state constraints

This paper addresses the challenge of synchronized multiple spacecraft attitude reorientation in presence of pointing and boundary constraints with limited inter-spacecraft communication link. Relative attitude pointing constraint among the fleet of spacecraft has also been modeled and considered during the attitude maneuvers toward the desired states. Formation fling control structure that consists of decentralized path planners based on virtual structure approach joint with discrete time optimal local controller is designed to achieve the mission’s goals. Due to digital computing of spacecraft’s onboard computer, local optimal controller based on discrete time prediction and correction algorithm has been utilized. The time step of local optimal algorithm execution is designed so that the spacecraft track their desired attitudes with appropriate error bound. The convergence of the proposed architecture and stability of local controller’s tracking error within appropriate upper bound are proved. Finally, a numerical simulation of a stereo imaging scenario is presented to verify the performance of the proposed architecture and the effectiveness of the algorithm.     

航天器姿控系统的PD型学习观测器故障重构

针对满足Lipschitz条件的航天器姿态控制系统这一非线性系统中存在的执行器加性故障、空间干扰与测量噪声问题,提出了基于PD型迭代学习观测器的故障重构方法。该方法具有期望的鲁棒性能指标,能够在系统存在空间干扰与测量噪声情况下实现对突变故障与时变故障等故障类型的精确重构。基于线性矩阵不等式技术给出系统化PD型迭代学习观测器的设计方法,并根据Lyapunov稳定性理论对上述设计方法的稳定性条件进行了理论证明,同时利用鲁棒技术抑制空间干扰与测量噪声对执行器故障重构的影响,通过线性矩阵不等式工具箱求解观测器参数矩阵。最后,将该方法应用到航天器姿态控制系统中,仿真结果证明了该方法的有效性。     

基于综合指标的最优冗余陀螺配置确定方法

陀螺是航天器控制系统中的关键姿态敏感器,其主要采取冗余措施进行配置。针对航天器控制系统设计中如何进行陀螺冗余配置的问题,提出了一种确定最优冗余陀螺配置的方法,该方法综合考虑了系统的可靠性、精度、成本代价等综合指标。首先,以工程中普遍采用的陀螺斜置式为对象,系统性给出了陀螺斜置式的安装结构,并以测量误差最小为目标确定出确定安装数目下的最优陀螺冗余安装结构。其次,结合实际工程经验对陀螺冗余配置的综合性能指标进行详细系统的分析。然后,利用优化评价方法以综合指标为基础对不同安装数目下的陀螺冗余安装结构进行综合评价,确定出陀螺冗余配置的最优安装数目,即最优冗余陀螺配置。最后,利用该方法对实际工程中的斜置式陀螺冗余配置进行分析和计算。结果表明,当陀螺的安装数目为7时为最优冗余配置,该结论对实际工程具有理论指导作用。     

Spacecraft attitude maneuver control using two parallel mounted 3-DOF spherical actuators

A parallel configuration using two 3-degree-of-freedom (3-DOF) spherical electromag-netic momentum exchange actuators is investigated for large angle spacecraft attitude maneuvers. First, the full dynamic equations of motion for the spacecraft system are derived by the Newton-Euler method. To facilitate computation, virtual gimbal coordinate frames are established. Second, a nonlinear control law in terms of quaternions is developed via backstepping method. The pro-posed control law compensates the coupling torques arising from the spacecraft rotation, and is robust against the external disturbances. Then, the singularity problem is analyzed. To avoid sin-gularities, a modified weighed Moore-Pseudo inverse velocity steering law based on null motion is proposed. The weighted matrices are carefully designed to switch the actuators and redistribute the control torques. The null motion is used to reorient the rotor away from the tilt angle saturation state. Finally, numerical simulations of rest-to-rest maneuvers are performed to validate the effec-tiveness of the proposed method.     

Stabilization of the attitude of a rigid spacecraft with external disturbances using finite-time control techniques

In this paper, we consider the attitude stabilization problem for a rigid spacecraft with external disturbances. To obtain a better disturbance rejection property, we employ finite-time control techniques. In the absence of disturbances, by employing continuous finite-time control method, a continuous finite-time controller is designed such that the attitude of the rigid spacecraft will converge to the origin in finite time. In the presence of disturbances, by employing terminal sliding mode method, a discontinuous finite-time control law is proposed such that the states will eventually converge to a small region of the origin, which can be rendered as small as desired. Numerical simulation results show the effectiveness of the method.     

Composite control method for stabilizing spacecraft attitude in terms of Rodrigues parameters

In this paper, the attitude stabilization problem of a rigid spacecraft described by Rodrigues parameters is investigated via a composite control strategy, which combines a feedback control law designed by a finite time control technique with a feedforward compensator based on a linear disturbance observer (DOB) method. By choosing a suitable coordinate transformation, the spacecraft dynamics can be divided into three second-order subsystems. Each subsystem includes a certain part and an uncertain part. By using the finite time control technique, a continuous finite time controller is designed for the certain part. The uncertain part is considered to be a lumped disturbance, which is estimated by a DOB, and a corresponding feedforward design is then implemented to compensate the disturbance. Simulation results are employed to confirm the effectiveness of the proposed approach.     

机载跟踪雷达的次最优控制

 本文把机载跟踪雷达的目标视为匀速直线运动叠加一阶马尔柯夫过程,在视线坐标系内建立状态方程和观测方程。采用二次型性能指标,用E-coupling法求得次最优控制律。模拟计算表明,采用该控制律的系统具有很高的跟踪精度,比经典比例控制大约提高一个数量级,和最优控制相当。     

Attitude coordination for spacecraft formation with multiple communication delays

Communication delays are inherently present in information exchange between spacecraft and have an effect on the control performance of spacecraft formation. In this work, attitude coordination control of spacecraft formation is addressed, which is in the presence of multiple communication delays between spacecraft. Virtual system-based approach is utilized in case that a constant reference attitude is available to only a part of the spacecraft. The feedback from the virtual systems to the spacecraft formation is introduced to maintain the formation. Using backstepping control method, input torque of each spacecraft is designed such that the attitude of each spacecraft converges asymptotically to the states of its corresponding virtual system. Furthermore, the backstepping technique and the Lyapunov–Krasovskii method contribute to the control law design when the reference attitude is time-varying and can be obtained by each spacecraft. Finally, effectiveness of the proposed methodology is illustrated by the numerical simulations of a spacecraft formation.     

一种基于轨道根数约束的最优制导方法

针对航天器空间变轨的制导问题,研究了一种基于轨道根数约束的最优制导方法。在地心惯性坐标系下直接建立航天器的最优控制模型,给出了位置速度表达式和协态变量初值之间的关系;进一步,在不约束真近点角的前提下,推导了5个轨道根数的约束方程,并通过对轨道根数和最优控制理论中协态方程的特性分析,获得了另外两个约束方程。协态变量初值可直接通过求解7个完整约束方程组获得,进而得到最优推力方向。仿真验证了所提制导方法的有效性。