Distributed fixed‐time attitude coordination control for multiple rigid spacecraft

In this paper, the fixed‐time attitude coordination control for multiple rigid spacecraft under an undirected communication graph is investigated. By using the backstepping technique, the distributed fixed‐time observer, and the method of “adding a power integrator,” a distributed fixed‐time attitude coordination control law is designed for a group of spacecraft. The proposed control scheme is nonsingular and can guarantee a group of rigid spacecraft simultaneously tracking a common desired attitude within fixed time even when the time‐varying reference attitude is available only to a subset of the group members. Rigorous analysis is provided to show that the attitude consensus tracking errors can converge to the origin in finite time which is bounded by a fixed constant independent of initial conditions. Numerical simulations are carried out to demonstrate the effectiveness of the proposed control law.     

Global finite-time attitude consensus tracking control for a group of rigid spacecraft

The problem of finite-time attitude consensus for multiple rigid spacecraft with a leader–follower architecture is investigated in this paper. To achieve the finite-time attitude consensus, at the first step, a distributed finite-time convergent observer is proposed for each follower to estimate the leader's attitude in a finite time. Then based on the terminal sliding mode control method, a new finite-time attitude tracking controller is designed such that the leader's attitude can be tracked in a finite time. Finally, a finite-time observer-based distributed control strategy is proposed. It is shown that the attitude consensus can be achieved in a finite time under the proposed controller. Simulation results are given to show the effectiveness of the proposed method.     

Finite‐time attitude control of multiple rigid spacecraft using terminal sliding mode

This paper investigates the control problem of finite‐time attitude synchronization and tracking for a group of rigid spacecraft in the presence of environmental disturbances. A new fast terminal sliding manifold is developed for multiple spacecraft formation flying under the undirected graph topology. On the basis of the finite‐time control and adaptive control strategies, two novel decentralized finite‐time control laws are proposed to force the spacecraft attitude error dynamics to converge to small regions in finite time, and adaptive control is applied to reject the disturbance. The finite‐time convergence and stability of the closed‐loop system can be guaranteed by Lyapunov theory. Simulation examples are provided to illustrate the feasibility of the control algorithm. Copyright © 2014 John Wiley & Sons, Ltd.     

Finite‐time attitude stabilization for rigid spacecraft

This paper investigates the finite‐time attitude stabilization problem for rigid spacecraft in the presence of inertia uncertainties and external disturbances. Three nonsingular terminal sliding mode (NTSM) controllers are designed to make the spacecraft system converge to its equilibrium point or a region around its equilibrium point in finite time. In addition, these novel controllers are singularity‐free, and the presented adaptive NTSM control (ANTSMC) laws are chattering‐free. A rigorous proof of finite‐time convergence is developed. The proposed ANTSMC algorithms combine NTSM, adaptation and a constant plus power rate reaching law. Because the algorithms require no information about inertia uncertainties and external disturbances, they can be used in practical systems, where such knowledge is typically unavailable. Simulation results support the theoretical analysis.Copyright © 2013 John Wiley & Sons, Ltd.     

Fixed‐time attitude tracking control for spacecraft based on adding power integrator technique

In this article, the fixed‐time attitude tracking problem for rigid spacecraft is investigated based on the adding‐a‐power‐integrator control technique. First, a fixed‐time attitude tracking controller is designed to guarantee fixed‐time convergence of tracking errors. Then, by considering the presence of random disturbance and actuator faults, an adaptive fault‐tolerant attitude tracking controller is designed to guarantee tracking errors converge to a residual set of zero in a fixed time. The complete bounds on settling time are derived independently of initial conditions. The simulation results illustrate the highly precise and robust attitude control performance obtained by using the proposed controllers.     

通信时延和联合连通拓扑下多刚体系统分布式姿态一致性控制

本文研究了通信时延和联合连通切换拓扑条件下的多刚体系统分布式姿态一致性控制问题. 通过构建有 效的辅助向量并选择合适的Lyapunov-Krasovskii函数, 分别对恒定通信时延和时变通信时延两种不同情况下的控 制器进行了设计. 数值仿真结果表明, 本文提出的方法能够有效地解决这类分布式姿态一致性控制问题. 多刚体; 姿态一致性; 联合连通拓扑; 时变时延; Lyapunov函数     

The leader-following attitude control of multiple rigid spacecraft systems

In this paper, we consider the leader-following consensus problem for a multiple rigid spacecraft system whose attitude is represented by the unit quaternion. Most results on this problem rely on the assumption that every follower can access the state of the leader and are obtained via a decentralized control manner. By developing a nonlinear distributed observer for the leader system, we can solve this problem via a distributed control scheme under the mild assumptions that the state of the leader can reach every follower through a path and that the communication between followers is bidirectional. Moreover, our result can accommodate a class of desired angular velocities generated by a marginally stable linear autonomous system.     

空间多刚体系统姿态的协同控制

将一种针对多个一般非线性系统的基于输出反馈的协同控制方法应用在采用四元数法描述的空间多个刚体姿态的协同控制系统中去，给出了空间多刚体系统姿态协同控制问题有解的充分条件，并设计了多刚体系统姿态的协同控制律．算例仿真结果表明，此法设计的协同控制器能够稳定控制描述各个刚体系统的姿态四元数，使其渐近稳定．     

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.     

Distributed attitude and translation consensus for networked rigid bodies based on unit dual quaternion

This paper provides unified solutions for distributed attitude and translation consensus problems for networked fully actuated rigid bodies under the fixed and undirected communication topology with the tool of unit dual quaternion. We investigate two kinds of consensus, that is, leaderless consensus and leader‐following consensus with a static leader. Firstly, the dynamics of rigid bodies are presented by unit dual quaternion. The control inputs of rigid bodies are also obtained from unit dual quaternion. Secondly, we propose a distributed consensus law in the form of dual quaternion to guarantee that the attitudes and translations of all rigid bodies reach consensus, respectively, without a leader. Thirdly, the leader‐following consensus problem with a static leader is studied. With the proposed leader‐following consensus law, the states of all rigid bodies converge to the corresponding states of the static leader, including the attitude and the translation. Finally, numerical examples are provided to validate the effectiveness of the theoretical results. Copyright © 2017 John Wiley & Sons, Ltd.     

Distributed observer‐based leader‐follower attitude consensus control for multiple rigid bodies using rotation matrices

This paper addresses the distributed observer‐based leader‐follower attitude consensus control problem for multiple rigid bodies. An intrinsic distributed observer is proposed for each follower to estimate the leader's trajectory, which is only available to a subset of followers. The proposed observer can guarantee that the estimated attitude evolves on rotation matrices all the time, and it provides us with a simple way to design the attitude consensus control law. The dynamics of rigid bodies and distributed observer are both modeled directly on rotation matrices, so that the singularity and ambiguity can be avoided. Furthermore, adopting the idea of disturbance observer on vector space, a gyro bias observer on the rotation matrices is proposed. Based on the distributed observer, three types of attitude consensus control law are proposed, which are respectively on the basis of full‐state, biased angular velocity, and external disturbance combined with biased angular velocity. Finally, the SimMechanics experiments are provided to illustrate effectiveness of the proposed theoretical results.     

Distributed attitude synchronization control for multiple flexible spacecraft without modal variable measurement

This paper solves the attitude synchronization and tracking problem for a group of flexible spacecraft without flexible‐mode variable measurement. The spacecraft formation is studied in a leader‐following synchronization scheme with a dynamic virtual leader. With the application of adaptive sliding‐mode control technique, a distributed modified Rodriguez parameters‐based dynamic controller is proposed for flexible spacecraft without requiring modal variable measurement. It is proved that the attitude synchronization and tracking can be achieved asymptotically under the control strategy through the Lyapunov's stability analysis. Furthermore, a distributed robust continuous control algorithm is designed to guarantee the ultimate boundedness of both the attitude tracking error and the modal variable observation error when bounded external disturbances exist. Some numerical simulation examples for multiple flexible spacecraft formation are given to demonstrate the effectiveness of the proposed method.     

Optimal control on Lie groups with applications to attitude control

In this paper we solve a class of optimal control problems on Lie groups in the sense that we derive differential equations which the optimal controls must satisfy. These results are applied to the attitude control of a spacecraft modeled as a rigid body. Specifically, we derive control laws (both in open-loop and closed-loop form) to maneuver the spacecraft between two given rotational states in finite time. The laws are such that a cost functional measuring the over-all angular velocity during the spacecraft’s motion is minimized. They do not require recourse to numerical methods and hence can be easily implemented in an on-board attitude control system. After dealing with a three-axis controlled spacecraft we also discuss the case that only torques about two principal axes of an axisymmetric spacecraft can be exerted.     

深空探测柔性太阳帆航天器动力学建模与姿态控制

太阳帆利用太阳辐射压力提供太空航行的必要动力,由于具有理论上的无限速度和无需消耗任何燃料等优势,被认为是完成未来深空探测任务的有效技术途径之一.柔性太阳帆航天器的动力学模型包括多体动力学、刚柔耦合动力学和太阳辐射光压模型,复杂的动力学特性导致其姿态控制设计具有很强的挑战性.针对带有控制杆的柔性太阳帆航天器,本文采用拉格朗日方程和有限元法,给出了面向控制的解析式动力学模型.所推导的刚柔耦合动力学模型,刻画了太阳帆航天器的本质动力学特性,即双框架控制杆的短周期运动,姿态与柔性太阳帆的耦合效应,以及在太阳光压恢复力矩下的姿态静稳定性和长周期运动.基于带控制杆的太阳帆航天器的双时间尺度特性,提出了双回路控制结构,用于实现航天器俯仰轴和偏航轴的姿态控制.将内回路设计为PD控制器,用于实现质心位置的调整.将外回路设计为PID控制器,用于阻尼姿态运动,并实现在平衡太阳光压力矩下的姿态保持.从而将柔性太阳帆航天器的复杂姿态控制问题转化为两个低阶子问题,实现了在不同频带上的控制设计.仿真结果验证了动力学建模和姿态控制设计方法的有效性.     

Decentralised finite-time attitude synchronisation and tracking control for rigid spacecraft

The problem of finite-time attitude synchronisation and tracking for a group of rigid spacecraft nonlinear dynamics is investigated in this paper. First of all, in the presence of environmental disturbance, a novel decentralised control law is proposed to ensure that the spacecraft attitude error dynamics can converge to the sliding surface in finite time; then the final practical finite-time stability of the attitude error dynamics can be guaranteed in small regions. Furthermore, a modified finite-time control law is proposed to address the control chattering. The control law can guarantee a group of spacecraft to attain desired time-varying attitude and angular velocity while maintaining attitude synchronisation with other spacecraft in the formation. Simulation examples are provided to illustrate the feasibility of the control algorithm presented in this paper.     

Finite‐Time Sliding Mode Trajectory Tracking Control of Uncertain Mechanical Systems

The problem of finite‐time tracking control is studied for uncertain nonlinear mechanical systems. To achieve finite‐time convergence of tracking errors, a simple linear sliding surface based on polynomial reference trajectory is proposed to enable the trajectory tracking errors to converge to zero in a finite time, which is assigned arbitrarily in advance. The sliding mode control technique is employed in the development of the finite‐time controller to guarantee the excellent robustness of the closed‐loop system. The proposed sliding mode scheme eliminates the reaching phase problem, so that the closed‐loop system always holds the invariance property to parametric uncertainties and external disturbances. Lyapunov stability analysis is performed to show the global finite‐time convergence of the tracking errors. A numerical example of a rigid spacecraft attitude tracking problem demonstrates the effectiveness of the proposed controller.     

Global finite-time attitude regulation using bounded feedback for a rigid spacecraft

This paper investigates the problem of global attitude regulation control for a rigid spacecraft under input saturation. Based on the technique of finite-time control and the switching control method, a novel global bounded finite-time attitude regulation controller is proposed. Under the proposed controller, it is shown that the spacecraft attitude can reach the desired attitude in a finite time. In addition, the bound of a proposed attitude controller can be adjusted to any small level to accommodate the actuation bound in practical implementation.     

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.

     

A specified‐time control framework for control‐affine systems and rigid bodies: A time‐rescaling approach

This paper addresses the specified‐time control problem for control‐affine systems and rigid bodies, wherein the specified‐time duration can be designed in advance according to the task requirements. By using the time‐rescaling approach, a novel framework to solve the specified‐time control problem is proposed, and the original systems are converted to the transformation systems based on which the specified‐time control laws for both control‐affine systems and rigid bodies are studied. Compared with the existing approaches, our proposed specified‐time control laws can be derived from the known stabilization control laws. To our best knowledge, it is the first time that transformation system–based specified‐time control framework for control‐affine system and rigid body dynamics is proposed. To further improve the convergence performance of specified‐time control, a finite‐time attitude synchronization control law for rigid bodies on rotation matrices is proposed, and thereby, the finite‐time–based specified‐time control law is designed eventually. In the end, numerical simulations and SimMechanics experiments are provided to illustrate effectiveness of the theoretical results.     

Adaptive finite‐time attitude stabilization for rigid spacecraft with actuator faults and saturation constraints

The attitude stabilization problem for rigid spacecraft in the presence of inertial uncertainties, external disturbances, actuator saturations, and actuator faults is addressed in this paper. First, a novel fast terminal sliding mode manifold is designed to avoid the singularity problem while providing high control ability. In addition, fast terminal sliding mode control laws are proposed to make the spacecraft system trajectory fast converge onto the fast terminal sliding mode surface and finally evolve into small region in finite time, which cannot be achieved by the previous literatures. Based on the real sliding mode context, a practical adaptive fast terminal sliding mode control law is presented to guarantee attitude stabilization in finite time. Also, simulation results are presented to illustrate the effectiveness of the control strategies. Copyright © 2015 John Wiley & Sons, Ltd.