基于四元数的航天器姿态非线性控制器

针对由四元数描述的航天器姿态控制系统进行了非线性反馈控制器设计.首先,得到一类含角速度测量的反馈控制律.该控制律不仅可以保证闭环系统是全局渐近稳定的,而且保证了2个期望的平衡位置都是稳定的.然后,利用基于四元数的滤波器取代角速度测量,得到一类无需角速度测量的反馈控制律.该控制律同样保证了闭环系统的全局渐近稳定性和2个稳定的期望平衡位置.值得注意的是,2个稳定的期望平衡位置,将促使由任意初始姿态出发的轨迹都就近收敛至任意期望平衡位置.最后,数值仿真展示了所得反馈控制律的优势.     

Finite‐time angular velocity observers for rigid‐body attitude tracking with bounded inputs

The attitude tracking of a rigid body without angular velocity measurements is addressed. A continuous angular velocity observer with fractional power functions is proposed to estimate the angular velocity via quaternion attitude information. The fractional power gains can be properly tuned according to a homogeneous method such that the estimation error system is uniformly almost globally finite‐time stable, irrespective of control inputs. To achieve output feedback attitude tracking control, a quaternion‐based nonlinear proportional‐derivative controller using full‐state feedback is designed first, yielding uniformly almost globally finite‐time stable of the attitude tracking system as well as bounded control torques a priori. It is then shown that the certainty equivalent combination of the observer and nonlinear proportional‐derivative controller ensures finite‐time convergence of the attitude tracking error for almost all initial conditions. The proposed methods not only avoid high‐gain injection, as opposed to the semi‐global results, but also overcome the unwinding problem associated with some quaternion‐based observers and/or controllers. Numerical simulations are presented to verify the effectiveness of the proposed methods. Copyright © 2016 John Wiley & Sons, Ltd.     

航天器姿态输出反馈抗干扰跟踪控制

针对采用四元数描述的航天器姿态运动模型研究输出反馈抗干扰跟踪控制问题.首先在姿态运动模型的基础上,结合四元数的性质设计扩张状态观测器(extended state observer,ESO)来估计角速度和干扰力矩,从理论上保证了ESO中的四元数状态满足范数约束,并证明了观测误差的收敛性;进一步利用互连和阻尼分配无源控制(interconnection and damping assignment passivity-based control,IDA--PBC)理论设计控制律,通过姿态和角速度误差状态变换以及引入误差积分项,使得期望的姿态和角速度误差,以及积分项误差运动方程中均出现阻尼项,提高了系统的抗干扰性能,最后利用Laypunov函数证明了闭环系统一致最终有界稳定.仿真结果验证了所设计ESO和IDA--PBC控制律的有效性.     

深空探测航天器姿态的自抗扰控制

本文针对一种带有挠性附件和液体晃动的深空探测航天器姿态控制问题,提出了自抗扰控制律.该控制律可以自主、有效地抑制挠性附件弹性振动和液体晃动对姿态角运动的耦合作用以及处理大范围的扰动和系统不确定性.基于四元数生成角速度跟踪指令,把控制问题由姿态角控制转化为角速度控制.通过设计扩张状态观测器实时估计并补偿角速度通道总扰动并结合角速度偏差反馈,使得角速度快速跟踪指令,进而实现控制目标.仿真结果验证了控制律的有效性和鲁棒性.     

Output feedback control for attitude tracking

In this paper the problem of attitude tracking control for a rigid spacecraft is addressed. It is assumed that only attitude measurements are available, and thus spacecraft's angular velocity has to be properly estimated. Two alternative schemes are proposed in which the unit quaternion is adopted to represent the orientation. In the first scheme, a second-order model-based observer is adopted to estimate the angular velocity used in the control law. In the second scheme, an estimate of the angular velocity error is obtained through a lead filter. Sufficient conditions ensuring local exponential stability of the two controllers are derived via Lyapunov analysis.     

干扰环境下的挠性航天器姿态跟踪控制

挠性航天器在姿态机动过程会受环境干扰力矩的作用,研究有扰情况下挠性航天器的姿态跟踪控制问题.首先,设计了干扰观测器在线估计频率已知的外部干扰信号,然后,基于干扰观测器设计了非线性反馈姿态跟踪控制器以跟踪目标姿态,并且该控制器只需要误差四元数和角速度的反馈信息.其次,采用Lyapunov方程和Barbalat引理证明了控...     

分区四元数姿态控制

提出了一种基于分区控制策略的四元数姿态控制律. 其基本思想是基于姿态四元数误差分区设计目标角速度, 由此将问题降阶为一个角速度跟踪问题; 基于不同的角速度跟踪误差, 设计了切换类型的抗干扰姿态控制律. 该控制策略可以使得姿态快速收敛, 并且在合适的参数选择条件之下还能同时满足控制力矩的饱和约束. 通过综合相平面和Lyapunov函数的分析方法严格证明了闭环系统全局收敛的性质. 最后, 通过数值仿真验证了本文提出的控制方案的有效性.     

Global set stabilization of the spacecraft attitude control problem based on quaternion

In this paper, we develop a global set stabilization method for the attitude control problem of spacecraft system based on quaternion. The control law that uses both optimal control and finite‐time control techniques can globally stabilize the attitude of spacecraft system to a set of equilibria. First, for the kinematic subsystem, we design a virtual optimal angular velocity. To obtain the global minimum of the performance index, this optimal angular velocity is only discontinuous in initial values. It can be regarded as a combination of open loop control and closed loop control. Then for the dynamic subsystem, we design a finite‐time control law that can force the angular velocity to track the virtual optimal angular velocity. It is proved that the closed loop system satisfies global set stability in the absence of disturbances. In the presence of disturbances, the system trajectory will converge to a neighborhood of the equilibrium set. Rigorous analysis shows that by introducing finite‐time control techniques, the closed loop system possesses a better disturbance rejection property. The control method is more natural and energy‐efficient. The effectiveness of the proposed method is demonstrated by simulation results. Copyright © 2009 John Wiley & Sons, Ltd.     

A special case of spacecraft optimal attitude control

The problem of optimal control of a spacecraft reorientation from an arbitrary initial attitude to a prescribed angular attitude is studied. The reorientation time is given. The case when the quadratic norm of the angular velocity vector of the spacecraft is minimized is studied. Using the necessary optimality conditions in the form of Pontryagin??s maximum principle and the quaternion method for spacecraft motion control, an analytical solution of this problem is obtained. Formal equations are derived and expressions for the optimal control program are obtained. For a dynamically symmetric spacecraft, the angular velocity is obtained in the analytical form. Results of the mathematical simulation of the spacecraft dynamics under the optimal control are presented that demonstrate the practical usefulness of the proposed algorithm for the spacecraft attitude control.     

基于四元数和卡尔曼滤波的两轮车姿态稳定方法

针对自平衡两轮车姿态角的在线估计问题,采用四元数的姿态解算算法,利用Levenberg-Marquardt非线性最小二乘法对自平衡两轮车陀螺仪信号拟合,建立了随机漂移误差数学模型,应用卡尔曼滤波融合陀螺仪和加速度计输出的信号,补偿了陀螺仪输出角速度的随机漂移误差,得到了自平衡两轮车姿态的最优估计。实验结果表明,这种姿态估计算法是有效的,有利于车体的自平衡控制。     

Stabilization of a 3D axially symmetric pendulum

Stabilizing controllers are developed for a 3D pendulum assuming that the pendulum has a single axis of symmetry and that the center of mass lies on the axis of symmetry. This assumption allows development of a reduced model that forms the basis for controller design and global closed-loop analysis; this reduced model is parameterized by the constant angular velocity component of the 3D pendulum about its axis of symmetry. Several different controllers are proposed. Controllers based on angular velocity feedback only, asymptotically stabilize the hanging equilibrium. Then controllers are introduced, based on angular velocity and reduced attitude feedback, that asymptotically stabilize either the hanging equilibrium or the inverted equilibrium. These problems can be viewed as stabilization of a Lagrange top. Finally, if the angular velocity about the axis of symmetry is assumed to be zero, controllers are introduced, based on angular velocity and reduced attitude feedback, that asymptotically stabilize either the hanging equilibrium or the inverted equilibrium. This problem can be viewed as stabilization of a spherical pendulum.     

六组合传感器的测量算法研究

基于六组合高精度陀螺(如激光陀螺、光纤陀螺等)传感器测量载体的三向角速率和三向加速度的数据,对三向姿态角进行求解测量算法的研究。利用一种四元数法的数学间接计算方法,即利用四维空间中的四元数的性质和运算规则来研究三维空间中刚体转动的问题,在科研试飞测量中具有很好的实际应用价值。     

无需角速度的含通信时延卫星编队飞行自适应姿态协同跟踪控制

针对编队卫星姿态协同跟踪控制中存在相异星间通信时变时间延迟的问题,提出了采用一阶滤波器来设计含通信时延的输出反馈控制器, 并通过引入参数在线自适应辨识技术,以实现利用卫星姿态误差信息来实现对卫星的转动惯量进行在线估计.对于系统稳定性的分析, 通过构造一新型Lyapunov函数,证明该控制器不仅能够有效地克服通信时间延迟对编队系统协同性的影响,同时可论证无需角速度信息反馈的闭环系统的有界稳定性.最后,将提出的算法应用于只需要角速度信息反馈的卫星编队飞行的协同控制,仿真结果表明该方法的可行性与有效性,具有实际的应用前景.     

基于六加速度计的陀螺仪漂移补偿算法的研究

为满足机动无人机姿态测量的需求,尝试了一种新的陀螺仪漂移补偿方案：对6只加速度计按回转轴对称布局,从而解算出角速度;并利用Kalman滤波对该解算角速度与陀螺仪的输出进行融合,通过反馈校正来实现对陀螺仪漂移的补偿。仿真结果证明：该方案能有效补偿陀螺仪漂移,具有一定工程应用价值。     

基于自适应互补滤波的四旋翼飞行器姿态解算

在四旋翼无人机中,姿态传感器采用捷联式惯导惯性检测单元(IMU),其中包括加速度计、陀螺仪、电子罗盘和空气压力高度计.这些传感器在工作过程中存在温度漂移以及噪声干扰,为了得到准确的姿态数据,首先建立了传感器四元数模型,在频域中设计互补滤波器,并设计了PI自适应补偿系数,对传感器数据进行融合、补偿和修正,有效地避免了系统模型误差对姿态估计的影响.修正后的角速度通过一阶龙格-库塔法、四元数算法完成飞行器的姿态解算.传统互补滤波器在噪声大时滤波效果不理想,故加入PI控制,形成一种效果更好的自适应滤波算法,根据仿真结果,该算法滤波后的信号比传统互补滤波的结果更加平滑,更接近理想波形.     

Robust attitude stabilization of spacecraft using nonlinearquaternion feedback

This paper considers the problem of three-axis attitude stabilization of a rigid spacecraft. A nonlinear control law which uses the feedback of the unit quaternion and the measured angular velocities is proposed and is shown to provide global asymptotic stability. The control law does not require the knowledge of the system parameters and is, therefore, robust to modeling errors. The significance of the control law is that it can be used for large-angle maneuvers with guaranteed stability     

卫星姿态跟踪的非线性PI控制器设计

针对刚体卫星的姿态跟踪问题,提出了一种新的非线性PI控制器。它不同于传统的全状态反馈控制方案,无需姿态角速度的测量信号,而是通过引入一个一阶低通滤波器来产生伪角速度信号,进而对其进行反馈。同时,采用积分控制以减少或抑制由于常值干扰力矩引起的常值姿态误差。通过Lyapunov方法分析证明了整个闭环系统是渐近稳定的。最后,仿真结果验证了所提出的输出反馈控制律在实现姿态跟踪和干扰抑制方面的有效性。     

Almost global finite‐time stabilization of rigid body attitude dynamics using rotation matrices

This work considers continuous finite‐time stabilization of rigid body attitude dynamics using a coordinate‐free representation of attitude on the Lie group of rigid body rotations in three dimensions, SO(3). Using a Hölder continuous Morse–Lyapunov function, a finite‐time feedback stabilization scheme for rigid body attitude motion to a desired attitude with continuous state feedback is obtained. Attitude feedback control with finite‐time convergence has been considered in the past using the unit quaternion representation. However, it is known that the unit quaternion representation of attitude is ambiguous, with two antipodal unit quaternions representing a single rigid body attitude. Continuous feedback control using unit quaternions may therefore lead to the unstable unwinding phenomenon if this ambiguity is not resolved in the control design, and this has adverse effects on actuators, settling time, and control effort expended. The feedback control law designed here leads to almost global finite‐time stabilization of the attitude motion of a rigid body with Hölder continuous feedback to the desired attitude. As a result, this control scheme avoids chattering in the presence of measurement noise, does not excite unmodeled high‐frequency structural dynamics, and can be implemented with actuators that can only provide continuous control inputs. Numerical simulation results for a spacecraft in low Earth orbit, obtained using a Lie group variational integrator, confirm the theoretically obtained stability and robustness properties of this attitude feedback stabilization scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

Linearization of attitude-control error dynamics

Some useful properties of direction-cosine and quaternion attitude formulations that include specification of attitude error and the inversion of rigid-body rotational dynamics are reviewed. The inversion procedure is then applied to a measure of attitude error to realize a new model-follower control system that exhibits linear attitude-error dynamics. Error analyses and simulation results for spacecraft attitude-control systems are presented to demonstrate the more robust performance obtainable from an exact linear-error formulation over that obtained from either direction-cosine or quaternion formulations with simple linear feedback control laws