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.     

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．     

Time-varying formation control with attitude synchronization of multiple rigid body systems

In this article, we study the leader-following formation control problem for a group of rigid body systems whose followers' motions are described by dual quaternion equations. A few features are as follows. First, we introduce an exosystem to generate the leader's trajectory as well as the formation configuration, which can produce a large class of time-varying signals so that we can achieve a variety of time-varying formations. Second, to overcome the communication constraint described by a digraph, we extend the distributed observer to estimate not only the desired attitude and angular velocity but also the leader's position and linear velocity. Third, a novel distributed control law is synthesized to furnish a rigorous performance analysis of the closed-loop system. The effectiveness of our design is illustrated by a numerical example.     

The attitude control problem

A general framework for the analysis of the attitude tracking control problem for a rigid body is presented. A large family of globally stable control laws is obtained by using the globally nonsingular unit quaternion representation in a Lyapunov function candidate whose form is motivated by the consideration of the total energy of the rigid body. The controllers share the common structure of a proportional-derivative feedback plus some feedforward which can be zero (the model-independent case), the Coriolis torque compensation, or an adaptive compensation. These controller structures are compared in terms of the requirement on the a priori model information, guaranteed transient performance, and robustness. The global stability of the Luh-Walker-Paul robot end-effector controller is also analyzed in this framework     

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.     

Spacecraft Anti‐Unwinding Attitude Control Using Second‐Order Sliding Mode

This paper presents an anti‐unwinding control method for the attitude stabilization of a rigid spacecraft. Quaternion has double stable equilibrium and this may cause unwinding problems in spacecraft attitude control if both the equilibria are not considered in control design. Here, the initial condition of scalar quaternion is included in sliding surface and an anti‐unwinding control method is formulated in second‐order sliding mode. The presented second‐order sliding mode controller can alleviate chattering and ensure a smooth control for actuator. Further, to eliminate the need of advance information about bounds of uncertainty and external disturbance, adaptive laws are applied to estimate the controller gains. The closed‐loop stability is proved using the Lyapunov stability theory. In conclusion, a simulation is conducted in the presence of inertia uncertainty and external disturbances and it is found that the presented control method is efficient to negate the effect of inertia uncertainty and external disturbances, alleviate chattering, eliminate unwinding, and ensure high accuracy and steady state precision.     

Attitude Control of Multiple Rigid Bodies with Uncertainties and Disturbances

Decentralized attitude synchronization and tracking control for multiple rigid bodies are investigated in this paper. In the presence of inertia uncertainties and environmental disturbances, we propose a class of decentralized adaptive sliding mode control laws. An adaptive control strategy is adopted to reject the uncertainties and disturbances. Using the Lyapunov approach and graph theory, it is shown that the control laws can guarantee a group of rigid bodies to track the desired time-varying attitude and angular velocity while maintaining attitude synchronization with other rigid bodies in the formation. Simulation examples are provided to illustrate the feasibility and advantage of the control algorithm.      

基于对偶四元数的机器人方位与手眼关系同时标定方法

针对相机姿态估计及机器人运动学正解存在测算偏差时,手眼标定及机器人坐标系-世界坐标系标定结果不能准确收敛到全局最优解的问题,提出了一种基于对偶四元数理论的机器人方位与手眼关系同时标定方法.该方法首先将标定方程中坐标系刚体变换关系用螺旋轴、旋转角度和平移量参数化表示,再结合全局优化算法对平移量进行优化.搭建了PUMA560机器人数值仿真系统和工业机器人实测实验平台,将该方法与经典的四元数和对偶四元数标定方法进行了比较分析.仿真和实测结果表明,在相机姿态估计及机器人运动学正解存在测量误差的情况下,该方法无需初值估计和数据筛选依然可以保证求解结果的最优性.     

基于对偶四元数的卫星主从式编队姿轨跟踪的优化控制

在对偶四元数的框架下研究了主从式编队卫星相对姿态和相对位置跟踪控制的优化问题.首先,给出了用对偶四元数描述的编队卫星六自由度的相对运动模型.接着,把系统模型拆分为标称系统和扰动系统,对于标称系统,使用李雅普诺夫优化控制技术和轨迹跟踪优化的方法来得到非线性系统的次优解,而对于扰动系统,利用滑模控制来确保闭环系统的鲁棒性,为此把最优控制和滑模控制结合起来提出了一种优化的积分滑模控制器,并通过李雅普诺夫方法严格地证明了整个闭环系统的全局渐近稳定性.最后,通过数学仿真来验证设计方法的有效性和可行性,结果表明本文的方法能够实现编队卫星姿轨跟踪的精确控制,收敛速度较快,得到的性能指标更小,且对模型参数不确定性和外部有界干扰具有较强鲁棒性.     

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.     

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.     

Motion trajectory of human arms based on the dual quaternion with motion tracker

In this paper, we present an algorithm for human motion capture of the real-time motion trajectory of human arms based on wireless inertial 3D motion trackers. It aims to improve the accuracy of inertial motion captures and quickly reconstruct some human movements. To evaluate the performance of the proposed dual quaternion algorithm, we present the prototype design. The wireless inertial measurement system and Kinect device are introduced simultaneously in capturing human motion. The dual quaternion algorithm incorporates features of the quaternion rotation and translation. So the singular points of Euler angles can be avoided. Dual quaternion algorithm and DCM(direction cosine matrix) are used to reconstruct human arm movements respectively. Compared with the computing speed in Matlab, the speed of the dual quaternion is faster than it of DCM. To the end, we propose a 3D ADAMS human robotic model for simulating the motion trajectory using dual quaternion algorithm. The results show that the dual quaternion can achieve capabilities of a positive DCM solving, which completed between body segments rotating and translating the coordinate system transformation. Also it can effectively drive in real-time a human model to animate movement, and provide a good algorithm.     

Finite-time Attitude Control: A Finite-time Passivity Approach

This paper studies the finite-time attitude control problem for a rigid body. It is known that linear asymptotically stabilizing control laws can be derived from passivity properties for the system which describes the kinematic and dynamic motion of the attitude. Our approach expands this framework by defining finite-time passivity and exploring the corresponding properties. For a rigid body, the desired attitude can be tracked in finite time using the designed finite-time attitude control law. Some finitetime passivity properties for the feedback connection systems are also shown. Numerical simulations are provided to demonstrate the effectiveness of the proposed control law.      

航天器位姿运动一体化直接自适应容错控制研究

针对航天器近距离操作过程中追踪航天器位姿控制系统执行器故障问题,提出了一种直接自适应容错控制方法,保证了追踪航天器在发生执行器故障下的自身稳定性和对目标航天器位姿状态的渐近跟踪性能.基于对偶四元数的航天器位姿一体化控制系统模型,首先,假设故障已知,设计标称控制信号;然后,设计自适应更新律对标称控制信号中的未知参数进行估计,构成自适应控制信号;最后,利用多Lyapunov函数对多故障模式下的系统性能进行分析.仿真结果表明了所提方法的有效性.     

Spacecraft coordination control in 6DOF: Integrator backstepping vs passivity-based control

In this paper, we present three nonlinear control solutions for 6DOF spacecraft formation control, adopted from Euler-Lagrange system theory. The quaternion parametrization results in dual equilibrium points in the closed loop system, and the controllers are proved to render these uniformly asymptotically stable. We also present a theoretical comparison of the three control solutions, together with simulation results to visualize the performance of the controllers.     

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.     

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.     

Attitude control without angular velocity measurement: a passivityapproach

It is well known that the linear feedback of the quaternion of the attitude error and the angular velocity globally stabilizes the attitude of a rigid body. In this note, we show that the angular velocity feedback can be replaced by a nonlinear filter of the quaternion, thus removing the need for direct angular velocity measurement. In contrast to other approaches, this design exploits the inherent passivity of the system; a model-based observer reconstructing the velocity is not needed. An application of the proposed scheme is illustrated for the robot control problem. Simulation results are included to illustrate the theoretical results     

对偶四元数线阵遥感影像几何定位

提出以对偶四元数为数学工具进行线阵CCD(电荷耦合元件)遥感影像几何定位的全新技术方法。利用对偶四元数建立遥感通用传感器严密成像模型,将光线束的位置和姿态统一用对偶四元数表示,通过传感器扫描光线在空间中的螺旋运动,实现像点到其对应地面点物方坐标的变换,从而克服了成像几何参数(外方位元素)之间的强相关性。按照空间刚体变换线性蒙皮混合理论,可以把刚体变换矩阵分解为平移和旋转两个部分,对平移部分进行线性插值,对旋转部分进行球面插值,从而实现线阵CCD遥感影像外方位元素的解算。按照所建立的成像几何模型,利用某地区Geoeye-1遥感影像进行几何定位实验,实验结果表明新算法获得的几何定位精度优于传统算法,能够解决定位参数之间的相关性问题。