A Singularity-free Steering Law of Roof Array of Control Moment Gyros for Agile Spacecraft Maneuver

In this paper, a singularity-free steering law for single gimbal control moment gyros (CMGs) is addressed for agile spacecraft. The geometrical array considered particularly in this work is a roof array due to the simplicity of singularity envelope. A feasible angular momentum chart which can provide a singularity-free bound is employed. The chart allows a guaranteed maximum torque output and angular momentum at any time without concerning the geometrical singularity of the array. Furthermore, a new deterministic allocation algorithm, called half-leading steering logic, of gimbal angular rates, is also suggested instead of the well-known pseudo-inverse technique to meet control torque commands required and to keep away from the singularity. It is noted that a momentum vector recovery to the initial direction is also an important task for the CMG array to overcome the singularity and for the reliable operation of CMGs. An optimization technique is addressed to restore the gimbal vectors back to their original angular position after the attitude reorientation mission. The techniques proposed are demonstrated using illustrative numerical simulations.

     

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．     

基于飞轮的欠驱动航天器姿态控制器设计

在以飞轮作为姿态控制执行机构的航天器中,如果部分飞轮发生故障而使得航天器欠驱动时,姿态控制性能会急剧下降.本文对两个匕轮的刚性航天器,研究了姿态控制问题.在零动量的假设下,利用Backstepping方法,为欠驱动姿态控制系统设计了一个新型的姿态控制器.设计过程分两步进行:首先,根据姿态运动学模型,设计出可使航天器姿态全局渐近稳定的控制角速率;然后,根据姿态动力学模型,得到使航天器姿态全局渐近稳定的控制力矩.该控制器为非连续控制器,可使航天器姿态误差全局一致渐近收敛为零,并使系统具有良好的动态性能.计算机仿真表明,本文所设计出的控制器是可行的.     

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.     

Three‐Axis Global Magnetic Attitude Control of Earth‐Pointing Satellites in Circular Orbit

This paper addresses the controllability and global stability issues of a magnetically actuated satellite in the geomagnetic field. The variation of the geomagnetic field along the orbit, which is time varying in nature, makes the dynamics of the satellite time varying also. Sufficient conditions for controllability of such a time varying magnetic attitude control system are given. As a major contribution, it is proven that the three‐axis controllability of the spacecraft actuated by the magnetic actuators is possible and it does not depend on the initial angular velocity of the spacecraft. Global controllability is a precursor to global stability. Therefore, exponential stability for an arbitrarily high initial angular velocity and an arbitrary initial orientation is proven next for a proportional‐derivative control law using averaging theory. It is also proven that even an iso‐inertial satellite can be stabilized using the time invariant feedback control, which was hitherto not possible, even using time variant conventional control. Simulation results are presented under different initial orientations and angular velocities of the satellite in the presence of favorable and unfavorable gravity gradient torques to validate the proposed control method.     

Spacecraft attitude control and stabilization: Applications of geometric control theory to rigid body models

In this paper, we study the attitude control problem for spacecraft with gas jet or momentum exchange actuators, using the recent nonlinear geometric control theory. We give necessary and sufficient conditions for controllability of the system in the case that the gas jet actuators yield one, two, or three independent torques. In the case of momentum exchange devices, controllability is studied with three independent actuators, and controllability is shown to be impossible with fewer devices. The former conditions with gas jet actuators are presented in three equivalent ways, and an equivalence is established with an earlier condition by Baillieul. The local controllability problem is also studied in the case of gas jet actuators yielding two independent torques. Using these results, an algorithm stabilizing the controllable system around an equilibrium state and trajectory is outlined, as proposed by Hermes. In the situations considered, however, the linearized systems are not controllable.     

Reducing Base Reactions With Gyroscopic Actuation of Space-Robotic Systems

In this paper, control-moment gyroscopes (CMGs) are proposed as actuators for a spacecraft-mounted robotic arm to reduce reaction forces and torques on the spacecraft base. With the established kinematics and dynamics for a CMG robotic system, numerical simulations are performed for a general CMG system with an added payload. The analysis of an added payload’s effects on otherwise reactionless CMG systems motivates the examination of possible operations concepts to reduce base reactions and power consumption. Simulation results for an example closed-loop maneuver show that base reactions can be significantly reduced, or even eliminated, with CMG actuation while using the same amount of power as a robotic system driven by conventional joint motors.      

欠驱动航天器双飞轮—单喷气姿态最优控制原理及方法

欠驱动航天器的姿态控制能够增强航天器的可靠性.本文针对欠驱动航天器姿态控制, 从喷气姿态阻尼的角动量等效原理出发, 推导脉宽调制公式, 得到燃料消耗最小时给定姿态、非给定姿态两种情况下的喷气最优组合方案.同时, 为了实现喷气全局最优, 提出欠驱动飞轮姿态控制策略, 实现了运动航天器机动至预期姿态.进一步分析欠驱动飞轮航天器的姿态控制原理及稳定性, 提出了共面双飞轮-单喷气的配置方案, 通过双飞轮组合稳定航天器的角速度, 使得航天器到达预期姿态机动时燃料全局最省.结合绕两个旋转轴的姿态机动路径规划方法, 通过姿态机动时序关系的实时分配可实现航天器姿态机动与稳定控制.最后, 通过航天器姿态控制仿真和对比分析, 发现共面双飞轮-单喷气的欠驱动姿态阻尼及姿轨控制方案能够在较少硬件配置下实现对航天器的姿态控制, 且消耗燃料最少.     

Attitude manoeuvre of spacecraft with long cantilever beam appendage by momentum wheel

Attitude manoeuvre of spacecraft with a long cantilever beam appendage by momentum wheel is studied. The dynamics equation of the main body is derived by conservation of angular momentum. The dynamics equation of the appendage is derived by force equilibrium principle. Two feedback control strategies of the momentum wheel are applied for the attitude manoeuvre of the main body. The lateral vibration of the appendage is suppressed by active control in proportion to its lateral displacement and velocity. The variation of residual nutation angle of the spacecraft or the residual transversal angular velocity of the main body in the manoeuvre process is researched with changes of steady state time of the manoeuvre, appendage parameters, control parameters on the appendage and appendage location. In addition, spacecraft response is researched when there are no active controls on the appendage.     

The parameters optimisation design for variable speed control momentum gyroscopes

Control momentum gyroscopes (CMGs) have many advantages over other actuators for the attitude control of a spacecraft. Compared with the single-gimbal control moment gyroscopes (SGCMGs), the mass and power of the flywheel of variable-speed control moment gyroscopes (VSCMGs) are greatly increased. In this paper, a new solving strategy of singularity problem is proposed, which concludes the exchangeable momentum and steering law, and the parameters of VSCMGs are designed based on the constraint of singular problem. The configuration characteristics of VSCMGs with the constraint of upper and lower bounds of the flywheel regulation speed are revealed. The steering characteristics of weighted pseudo-inverse with null motion (WPINM) are analysed, then the flywheel torque requirement of WPINM is evaluated based on the geometry theory. At last, the parameter design problem of VSCMGs is cast as multi-objectives and bi-level programming problem. The bi-level programming is transformed into a single-level programming problem by using of the Karush–Kuhn–Tucker condition. Finally, the intelligent algorithm of particle swarm optimisation is presented to solve the nonlinear multi-objective problem.     

Near-optimal nonholonomic motion planning for a system of coupledrigid bodies

How does a falling cat change her orientation in midair without violating angular momentum constraint? This has become an interesting problem to both control engineers and roboticists. In this paper, we address this problem together with a constructive solution. First, we show that a falling cat problem is equivalent to the constructive nonlinear controllability problem. Thus, the same principle and algorithm used by a falling cat can be used for space robotic applications, such as reorientation of a satellite using rotors and attitude control of a space structure using internal motion, and other robotic tasks, such as dextrous manipulation with multifingered robotic hands and nonholonomic motion planning for mobile robots. Then, using ideas from Ritz approximation theory, we develop a simple algorithm for motion planning of a falling cat. Finally, we test the algorithm through simulation on two widely accepted models of a falling cat. It is interesting to note that one set of simulation results closely resembles the real trajectories employed by a falling cat     

CG伪谱法在欠驱动航天器姿态机动最优控制中的应用

使用Chebyshev-Gauss(CG)伪谱法研究带动量轮和推力器的欠驱动航天器姿态最优控制问题.基于欧拉姿态角和动量矩定理导出两类航天器姿态运动模型,采用Clenshaw-Curtis积分近似得到性能指标函数中的积分项,应用重心拉格朗日插值逼近状态变量和控制变量,将连续最优控制问题离散为具有代数约束的非线性规划(NLP)问题,通过序列二次规划(SQP)算法求解.数值仿真结果表明,对两类欠驱动航天器的姿态机动最优控制均能达到设计控制要求,得到的姿态最优曲线与验证得到的曲线几乎完全重叠.     

多航天器系统分布式有限时间姿态协同跟踪控制

基于一致性算法, 在有向通讯拓扑下, 研究存在状态约束的多航天器系统分布式有限时间姿态协同跟踪控制问题. 在仅有部分跟随航天器可以获取领航航天器状态, 并且跟随航天器之间存在不完全信息交互的情形下, 设计了分布式快速终端滑模面, 提出了不依赖于模型的分布式有限时间姿态协同跟踪控制律. 根据有限时间Lyapunov 稳定性定理, 证明了系统的状态在有限时间内收敛于领航航天器状态的小邻域内. 最后通过仿真算例验证了所提出算法的有效性.

     

Attitude control of spacecraft simulator without angular velocity measurement

In this paper the attitude control of a spacecraft simulator using Reaction Wheels (RW) as the actuators is investigated. The main goal of the current study is to bring the RWs to the rest at the end of the maneuver without angular velocity measurement. A modified feedback linearization controller is applied by considering the Euler angles of the simulator as the output and the RWs angular momentums as the internal state variables. The stability of the proposed controller and the internal dynamics is analyzed using Lyapunov theory. Two modified sliding mode observers are designed to estimate the angular velocities of the spacecraft attitude control subsystem simulator. The proposed observers do not use the control input and the detailed knowledge of the model and thus it can be implemented easily. The global stability of the system is proved. The proposed controller and observers are finally evaluated numerically and experimentally on an attitude spacecraft simulator.     

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.     

挠性卫星姿态机动三段式轨迹规划与滚动跟踪控制

以新颖成像模式对挠性敏捷卫星姿态的快速机动控制为需求,本文针对金字塔构型控制力矩陀螺(CMG)群为执行机构的挠性卫星,提出基于三段式正弦角加速度的姿态路径规划方法及具有滚动优化思想的跟踪算法。在姿态路径规划方法设计中,融合谱分析及非线性优化方法,设计了兼顾卫星姿态机动快速性及抑制挠性附件振动性能的姿态轨迹;为实现对规划姿态轨迹的高精度跟踪,综合加权优化指标及奇异性、执行机构能力等约束,设计了金字塔构型CMG群框架角速度的非线性模型预测(NMPC)跟踪控制律。在转动惯量存在测量误差及空间干扰情况下,多种姿态机动仿真表明,本文提出的控制方法是有效的,且表现出较强的鲁棒性。     

Decentralized sliding‐mode control for attitude synchronization in spacecraft formation

This paper addresses attitude synchronization and tracking problems in spacecraft formation in the presence of model uncertainties and external disturbances. A decentralized adaptive sliding mode control law is proposed using undirected interspacecraft communication topology and analyzed based on algebraic graph theory. A multispacecraft sliding manifold is derived, on which each spacecraft approaches desired time‐varying attitude and angular velocity while maintaining attitude synchronization with the other spacecraft in the formation. A control law is then developed to ensure convergence to the sliding manifold. The stability of the resulting closed‐loop system is proved by application of Barbalat's Lemma. Simulation results demonstrate the effectiveness of the proposed attitude synchronization and tracking methodology. Copyright © 2012 John Wiley & Sons, Ltd.     

Output feedback second order sliding mode control for spacecraft attitude and translation motion

This paper studies an output feedback control problem for spacecraft position and attitude control when uncertainties related to system parameters and external disturbances are present. Firstly, a new finite-time control law is designed using second order sliding mode concepts. In the presence of external disturbances and inertia uncertainties, the new control law provides finite-time convergence and high tracking precision. Secondly, a new sliding-mode-based filter is developed to estimate the first time derivatives of attitude and position in finite time. Instead of the translational and angular velocity variables, the estimated derivative values are used for the controller design. The proposed controller with this filter is an output feedback controller since translational and angular velocity measurements are not required. The closed-loop system under this controller is non-homogeneous and the stability is proven by using concepts of a strong Lyapunov function and Lyapunov stability theory. The trajectories of the closed-loop system can be controlled to converge to a ball centered at the origin that can be made as small as desired. Numerical simulations of position and attitude control of spacecraft are given to demonstrate the performance of the proposed controller and filter.     

Nonlinear attitude and shape control of spacecraft with articulatedappendages and reaction wheels

Three-dimensional attitude and shape control problems are studied for a class of spacecraft with articulated appendages and reaction wheels. A number of special cases of such attitude control problems have been studied previously. We provide a unified formulation and a comprehensive set of results for planning of attitude and shape maneuvers of a spacecraft, assuming that joint actuators and reaction wheels provide a sufficiently rich set of inputs. The development is based on a nonlinear, drift-free, control model that characterizes the attitude and shape change dynamics, assuming zero angular momentum of the system. Controllability results are presented for the general case, and specialized results are identified for interesting multibody spacecraft configurations. These results are made explicit by providing computable formulas for the Lie brackets in terms of the spacecraft geometry, mass properties, and shape. Constructive motion planning approaches are described to achieve spacecraft attitude and shape change maneuvers. A distinct feature of these approaches is that they require only simple computations, as is desirable for online implementation. Emphasis is given to the interplay between the shape change dynamics and the attitude change dynamics in achieving the maneuver planning objectives     

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