Finite-time control of spacecraft and hardware in the loop tuning

A nonlinear disturbance observer based on a super twisting controller is designed and implemented on the uncertain spacecraft attitude control subsystem simulator. The reaction wheels' angular momentum and their rate saturation are concerned in the controller design. The super twisting algorithm (STA) is devised in a way to make the reaction wheels into rest at the end of the maneuver. A nonlinear-disturbance-observer (NDO) is applied in estimating the external disturbances, unmodeled inertia moment, the eccentricity of rotation and mass center of simulator, and the reaction wheel saturation constraint. The finite-time stability of the closed-loop system is established according to the Lyapunov theory. The simulation and experimental results of this newly designed controller-observer on the spacecraft attitude simulator are compared in uncertain conditions.     

On Melnikov's method in the study of chaotic motions of gyrostat

The homoclinic solutions of the attitude motion of a gyrostat with wheels along its principal axes are formulated using the procedure developed by Wittenburg. The generic Melnikov function for the attitude motion of a gyrostat subject to small non-linear damping torques and small periodic torques is derived. The derivation is based on the chaotic theory for a 'one and half' degrees of freedom system established by Wiggins and Shaw. The conditions for the physical parameters at the onset of the homoclinic solutions are given in detail. The chaotic criteria are investigated using Melnikov's function. In particular, the conditions of the physical parameters (moments of inertia, damping coefficients, amplitudes and frequencies of external excitation, moments of momentum of wheels) that ensure the convergence of Melnikov's integral are also worked out. In order to acquire some knowledge of long-term behaviours of the chaotic attitude motion, the fourth-order Runge-Kutta numerical algorithms are utilized to simulate its dynamics. The numerical experiment shows that the chaotic motions of the gyrostat are bounded, non-periodic and sensitive to initial conditions. One of the practical mechanical models of the gyrostat is the artificial satellite. The attitude motion of the three-axis stabilized gyrostat satellite, whose torque-free motion is the homoclinic orbits, will oscillate chaotically when it is subjected to the appropriate external disturbances.     

A simple stability criterion for spinning satellites with flexible appendages

For a rigid satellite only a rotation around the axis with maximum or minimum moment of inertia is stable. For satellites with flexible parts this well known rule is modified. Here the moment of inertia around the spin axis must exceed the lateral moments of inertia by some margin that depends on the properties of the flexible parts. The practical determination of this margin is the main subject of the paper. It is shown that stability limits can be derived from purely static considerations. The methods are illustrated by an extremely simple example that can be analyzed in closed form: a pair of thin radial booms with tip masses and root elasticity. For more realistic configurations results of numerical calculations are given that show the usefulness of the methods for engineering purposes. In addition these results are used to discuss the effects of parameters such as boom geometry, mass distribution, elasticity, and spin rate on the stability of the rotational motion. The paper is based on a method developed by McIntyre and Miyagi (1976). It implements this method by stressing the aspects of its practical application.     

On the problem of the time-optimal manipulator arm turning

Two kinds of manipulators making spatial movements are discussed. The problem of control which provides manipulator turning in the minimum possible time is considered. A control, satisfying the maximum principle of Pontryagin, has been designed for some set of boundary configurations. With this control a manipulator link in the process of turning oscillates around a position, corresponding to a minimum moment of inertia of a system with respect to an axis of rotation. Movement satisfying the maximum principle is compared to that for which the moment of inertia is minimal within the entire interval of time. The simplified equations as well as the complete ones are investigated     

基于惯量矩的椭圆拟合方法

数字图像中,Hough变换或最小二乘法无法对图像中物体直接进行椭圆拟合,需要边缘检测等预处理,过程复杂且计算量大,为此,提出一种直接用图像惯量矩来拟合椭圆的方法。选定图像中要拟合的目标物体,将彩色图像转换为概率密度灰度图;计算目标的质心和主轴转动惯量,并运用形心主轴惯量积为零的条件推导出椭圆旋转角度和形心主轴惯量矩的大小;由形心主轴惯量矩的大小得出椭圆长半轴和短半轴大小,从而得到拟合后椭圆的各项参数。彩色图像实验,验证了该方法拟合目标椭圆的有效性和鲁棒性。     

基于气动力矩和模型预测的LEO卫星角动量管理算法

为抑制气动力矩对近地轨道(LEO)卫星姿态控制系统的影响,改善卫星电磁环境,设计一种基于气动力矩和模型预测的LEO卫星角动量管理算法,利用气动力矩管理卫星角动量并通过磁力矩器辅助提高角动量管理效率和可靠性.利用所设计的角动量管理算法构建卫星姿态动力学的线性化模型和姿态控制律,预测角动量变化趋势;通过在卫星太阳阵常规运动上附加额外的小角度偏转,将LEO卫星主导摄动力矩的气动力矩转化为管理卫星角动量的控制力矩.仿真实验表明,与传统的角动量管理策略相比,所设计的角动量管理算法通过将气动力矩转化为角动量管理控制力矩,能够有效节省卫星角动量管理的消耗.此外,该算法在不增加物理机构的前提下可以作为卫星的备用角动量管理策略,能够显著增强卫星姿态系统的可靠性和鲁棒性.     

Controllability of Spacecraft Attitude Using Control Moment Gyroscopes

This technical note describes an application of nonlinear controllability theory to the problem of spacecraft attitude control using control moment gyroscopes (CMGs). Nonlinear controllability theory is used to show that a spacecraft carrying one or more CMGs is controllable on every angular momentum level set in spite of the presence of singular CMG configurations, that is, given any two states having the same angular momentum, any one of them can be reached from the other using suitably chosen motions of the CMG gimbals. This result is used to obtain sufficient conditions on the momentum volume of the CMG array that guarantee the existence of gimbal motions which steer the spacecraft to a desired spin state or rest attitude.      

Momentum unloading excessive reaction-wheel system of a spacecraft

Wide use of electromechanical actuators in attitude control systems of spacecraft is intimately connected with improvement of these actuators using unloading methods—relieving excessive momentum. As applied to electromechanical actuators of the type of reaction wheels, the problem of unloading momentum for the case of excessive flywheel system is studied. The key feature of the work is the use of arbitrary parameters in the general solution of the undefined system of linear algebraic equations as additional control parameters. For the minimum excessive flywheel system and magnetorquers of the unloading system creating the additional external moment, control algorithms are synthesized which guarantee asymptotic stability of the zero solution to model equations describing the flywheel motion. The performance of the proposed algorithms and specific features of the process of unloading momentums of the flywheels are studied, as exemplified by the controlled motion of the spacecraft in stabilization of the regime of three-axial orbital orientation.     

Bending collapse of thin-walled rectangular section columns

This paper reviews the existing methods of collapse analysis for thin-walled rectangular section tubes subjected to bending about a principal axis and suggests a new collapse mechanism that gives an improved analytical solution for the moment–rotation relationship. The new model is kinematically admissible and completely analytical. It involves two unknown constants, half the length of the folding wave and the rolling radius in the calculation, which are determined by minimising a mean crumpling moment. The new analytical solution shows good agreement with experimental results.     

Problems of Evolution of Rotations of a Rigid Body under the Action of Perturbing Moments

The rotatory motion of a nearly dynamically spherical rigidbody, which contains a viscoelastic element, is considered. This elementis simulated by a moving mass, connected by a spring and damper to thepoint, situated on one of a principal axis of inertia. The smallparameters caused by the proximity of moments of inertia and thepresence of moving mass are considered to be of the same order. Thespherical coordinates defining the position of the angular velocityvector are introduced. The system of differential equations is obtainedand investigated, the special cases of motion are considered. Theauthors investigate perturbed rotational motions of a rigid body,similar to the regular precession in the Lagrange case, under the actionof the moment that is slowly changing in time and the restoring momentdepending on the angle of nutation. In two problems it is assumed thatthe angular velocity of the body is large and its direction is close tothe axes of dynamic symmetry. In the first problem it is assumed thattwo projections of the vector of the perturbing moment onto principalaxes of inertia of the body are small as compared to the restoringmoment, while the third one is of the same order of the magnitude as themoment in question. In the second problem it is assumed that theperturbing moments are small as compared to the restoring one. Averagedsystems of equations of motion are obtained and investigated in thefirst and the second approximations. Examples are considered.     

欠驱动刚体航天器姿态运动规划的遗传算法

研究欠驱动刚体航天器姿态的非完整运动规划问题．航天器利用3个动量飞轮可以控制其姿态和任意定位,当其中一轮失效,航天器姿态通常表现为不可控．在系统角动量为零的情况下,系统的姿态控制问题可转化为无漂移系统的运动规划问题．基于优化控制理论,提出了求解欠驱动刚体航天器的姿态运动控制遗传算法,并且数值仿真表明：该方法对欠驱动航天器姿态运动的控制是有效的．     

带有两个动量飞轮刚体航天器的姿态非完整运动规划问题

航天器利用三个动量飞轮可以控制其姿态和任意定位.当其中一个动量飞轮失效,在某些特定的情况下,如何控制航天器的姿态问题还没有有效的方法.利用最优控制方法研究了带有两个动量飞轮的刚体航天器姿态优化控制问题.为此考虑系统角动量为零的情况下,将航天器姿态运动方程化为非完整形式约束方程,系统的控制问题可转化为无漂移系统的非完整运动规划问题.通过Ritz近似理论得到求解带有两个动量飞轮航天器姿态的运动规划控制算法.通过数值仿真,表明该方法对航天器姿态运动规划控制是有效的.     

姿态变化一致有界的姿态稳定控制器设计

针对航天器姿态稳定控制问题, 设计一种迭代学习姿态控制器. 将连续非周期运动的姿态跟踪过程分解为队列重复运动, 采用前一周期的姿态跟踪误差修正后一周期的控制输入, 分别对未知参数和干扰构建有界迭代学习律, 给出航天器姿态稳定控制器, 并从理论上分析了闭环系统的渐近稳定性和姿态跟踪误差的一致有界性. 通过在轨捕获非合作目标过程中航天器姿态跟踪控制问题的数值仿真, 验证了迭代学习控制器的鲁棒性和强抗干扰性.

     

目标形状特征的新定义

为了解决描述图形几何形状难问题,提出描述图形形状的特征矢量。根据目标轮廓的几何形状定义了轮廓的向心矩、偏心矩、惯性矩,这些特征与轮廓形状和面积有关。利用轮廓的最小包络矩形,提出了向心矩比、偏心矩比和惯性矩比,其值变化范围在0到1之间,且无量纲。这些特征具有旋转、平移和尺度不变性。     

Controllability of spacecraft systems in a central gravitationalfield

The configuration space for rigid spacecraft systems in a central gravitational field can be modeled by SO(3)× IR³, where the special orthogonal group SO(3) represents the attitude dynamics and IR³ is for the orbital motion. The attitude dynamics of the spacecraft system is affected by the orbital elements through the well-known gravity-gradient torque. On the other hand, the effects of attitude-orbit coupling can also possibly be used to alter orbital motions by controlling the attitude. This controllability property is the primary issue of this paper. The control systems for spacecraft with either reaction wheels or gas jets being used as attitude controllers are proven in this study to be controllable. Rigorously establishing these results necessitates starting with the formal definitions of controllability and Poisson stability. It is then shown that if the drift vector field of the system is weakly positively Poisson stable and the Lie algebra rank condition is satisfied, controllability can be concluded. The Hamiltonian structure of the spacecraft model provides a natural route of verifying the property of weakly positive Poisson stability. Accordingly, the controllability is obtained after confirming the Lie algebra rank condition. Developing a methodology in deriving Lie brackets in the tangent space of T(SO(3)×IR³), i.e., the second tangent bundle is thus deemed necessary. A general formula is offered for the computation of Lie brackets of second tangent vector fields in TT(SO(3)^m×IRⁿ), in light of its importance in the fields of mechanics, robotics, optimal control, and nonlinear control, among others. With these tools, the controllability results can be proved. The analysis in this paper gives some insight into the attitude-orbit coupling effects and may potentially lead towards new techniques in designing controllers for large spacecraft systems     

Attitude guidance and tracking for spacecraft with two reaction wheels

This paper addresses the guidance and tracking problem for a rigid-spacecraft using two reaction wheels (RWs). The guidance problem is formulated as an optimal control problem on the special orthogonal group SO(3). The optimal motion is solved analytically as a function of time and is used to reduce the original guidance problem to one of computing the minimum of a nonlinear function. A tracking control using two RWs is developed that extends previous singular quaternion stabilisation controls to tracking controls on the rotation group. The controller is proved to locally asymptotically track the generated reference motions using Lyapunov's direct method. Simulations of a 3U CubeSat demonstrate that this tracking control is robust to initial rotation errors and angular velocity errors in the controlled axis. For initial angular velocity errors in the uncontrolled axis and under significant disturbances the control fails to track. However, the singular tracking control is combined with a nano-magnetic torquer which simply damps the angular velocity in the uncontrolled axis and is shown to provide a practical control method for tracking in the presence of disturbances and initial condition errors.     

Two‐Layer Terminal Sliding Mode Attitude Control of Satellites Equipped with Reaction Wheels

This paper addresses the global stability and robust attitude tracking problem of a near polar orbit satellite subject to unknown disturbances and uncertainties. It is assumed that the satellite is fully actuated by a set of reaction wheels (RW) as control actuators because of their relative simplicity, versatility and high accuracy. The terminal sliding mode control (TSMC) approach is utilized in a two‐level architecture to achieve control objectives. In the lower layer a detumbling‐like controller is designed which guarantees the finite‐time detumbling and tracking of the desired angular velocities and based on this result a robust attitude tracking controller is designed in the upper layer to achieve 3‐axis attitude tracking in the presence of unknown disturbances and bounded uncertainties. Robust stability and tracking properties of designed controllers are proved using the Lyapunov theory. Finally, a set of numerical simulation results are provided to illustrate the effectiveness and performance of the proposed control method.     

Defining the axis of a helix

A simple method for finding the axis of a helix is presented. Although described in terms of protein alpha helices, the method is generally applicable to helices whose defining units are more or less regularly spaced. Absolute mathematical regularity of the helical parameters is not required. The procedure can be applied at several levels of rigor. At its simplest it involves simple vector operations only and yields two points that define the axis along with the axis direction cosines. No regression analysis is needed. The minimum length helix required for the algorithm is four residues, which define an axis segment between residues 2 and 3. In its more rigorous form the algorithm scans along the chain one residue at a time, yielding a set of axis segments to which a linear least squares regression fits the axis. Non-linear, iterative procedures are not necessary. For each consecutive set of four residues the pitch, radius, rise per residue, rotation per residue about the axis and number of residues per turn are also obtained. Methods are also outlined for distinguishing between smoothly curved and sharply kinked helices and for extracting from these structures the radius of curvature and the location and angle of the kink.     

3D stable biped walking control and implementation on real robot

A combination of walking control methods was proposed and implemented on a biped robot. The LIPM-based model predictive control (MPC) was adopted to generate a basic stable walking pattern. The stability of pitch and yaw rotation was improved through pitch and yaw momentum control as a supplementation of MPC. It is found that biped robot walking tends to deviate from the planned walking direction if not considering the rotation friction torque in yaw axis under the support foot. There are basically two methods to control yaw momentum, waist and swing arms rotation control. However, the upper body is often needed to accomplish other tasks. Therefore, a yaw momentum control method based on swing leg dynamics was proposed. This idea does not depend on upper body’s motion and is highlighted in this paper. Through experiments, the feasibility of the combination of the control methods proved to be practical in keeping biped robot walking stable both in linear and rotation motion. The pros and cons of the yaw momentum control method were also tested and discussed through comparison experiments, such as walking on flat and uneven terrain, walking with different payloads.     

Feedback stabilization of uniform rigid body rotation

This abstract discusses the stabilization of uniform rigid body rotation about an arbitrary axis by feedback control. The class of feedback control laws considered is linear and is shown to robustly stabilize rotation with respect to inertia uncertainty. The methodology developed in this paper is based on the energy-momentum method of stability analysis and fully exploits the underlying geometry. The methodology is illustrated with several examples.