Maneuvering Modeling and Simulation of AUV Dynamic Systems with Euler-Rodriguez Quaternion Method

The purpose of this study is to develop maneuvering models and systems of a simulator to improve the motion performance of autonomous underwater vehicles （AUVs） at the preliminary design stages in advance. The AUVs simulation systems based on the standard submarine equations of motion in six-degree-of-freedom （6-DOF） integrated with the Euler-Rodriguez quaternion method for representing singularity-free AUV attitude and time-saving calculation, and with a nonlinear control model for maneuvering and depth control simulations, time-marching in the fourth-order Runge-Kutta scheme. For validation of the simulation codes, results of the ISiMI AUV open-loop tests including turning test and zigzag test as well as an AUV simulator on the basis of Euler-angle method were used to compare with the quaternion-based AUV simulator. The computational results from the proposed simulator agree well with those from both the ISiMI AUV experiments and the Euler-angle based simulations. Additionally, a new maneuvering procedure, namely ＂put-out＂ was implemented to test directional stability for a large-scale AUV in the proposed AUV simulator that can be considered for vehicles in space as well as in constrained planes.

Quaternion-Based Adaptive Trajectory Tracking Control of a Rotor-Missile with Unknown Parameters Identification

This paper investigates the adaptive trajectory tracking control problem and the unknown parameter identification problem of a class of rotor-missiles with parametric system uncertainties.First,considering the uncertainty of structural and aerodynamic parameters,the six-degree-of-freedom(6Do F) nonlinear equations describing the position and attitude dynamics of the rotor-missile are established,respectively,in the inertial and body-fixed reference frames.Next,a hierarchical adaptive trajectory tracking controller that can guarantee closed-loop stability is proposed according to the cascade characteristics of the 6Do F dynamics.Then,a memory-augmented update rule of unknown parameters is proposed by integrating all historical data of the regression matrix.As long as the finitely excited condition is satisfied,the precise identification of unknown parameters can be achieved.Finally,the validity of the proposed trajectory tracking controller and the parameter identification method is proved through Lyapunov stability theory and numerical simulations.

Complex Decision Modeling Framework with Fairly Operators and Quaternion Numbers under Intuitionistic Fuzzy Rough Context

The main goal of informal computing is to overcome the limitations of hypersensitivity to defects and uncertainty while maintaining a balance between high accuracy,accessibility,and cost-effectiveness.This paper investigates the potential applications of intuitionistic fuzzy sets(IFS)with rough sets in the context of sparse data.When it comes to capture uncertain information emanating fromboth upper and lower approximations,these intuitionistic fuzzy rough numbers(IFRNs)are superior to intuitionistic fuzzy sets and pythagorean fuzzy sets,respectively.We use rough sets in conjunction with IFSs to develop several fairly aggregation operators and analyze their underlying properties.We present numerous impartial laws that incorporate the idea of proportionate dispersion in order to ensure that the membership and non-membership activities of IFRNs are treated equally within these principles.These operations lead to the development of the intuitionistic fuzzy rough weighted fairly aggregation operator(IFRWFA)and intuitionistic fuzzy rough ordered weighted fairly aggregation operator(IFRFOWA).These operators successfully adjust to membership and non-membership categories with fairness and subtlety.We highlight the unique qualities of these suggested aggregation operators and investigate their use in the multiattribute decision-making field.We use the intuitionistic fuzzy rough environment’s architecture to create a novel strategy in situation involving several decision-makers and non-weighted data.Additionally,we developed a novel technique by combining the IFSs with quaternion numbers.We establish a unique connection between alternatives and qualities by using intuitionistic fuzzy quaternion numbers(IFQNs).With the help of this framework,we can simulate uncertainty in real-world situations and address a number of decision-making problems.Using the examples we have released,we offer a sophisticated and systematically constructed illustrative scenario that is intricately woven with the complexity ofmedical evaluation in order to thoroughly assess the relevance and efficacy of the suggested methodology.

A holographic optical communication system based on RSA algorithm and quaternion function

A facile encryption way was successfully applied to the holographic optical encryption system with high speed,multidimensionality,and high capacity,which provided a better security solution for underwater communication.The reconstructed optical security system for information transmission was based on wavelengthλand focal length f that were keys to encryption and decryption.To finish the secure data transmission(λ,f)between sender and receiver,an extended Rivest-Shamir-Adleman(ERSA)algorithm for the encryption was achieved based on three-dimension quaternion function.Therein,the Pollard’s rho method was used for the evaluation and comparison of RSA and ERSA algorithms.The results demonstrate that the message encrypted by the ERSA algorithm has better security than that by RSA algorithm in the face of unpredictability and complexity of information transmission on the unsecure acoustic channel.

Split-Tetraquaternion Algebra and Applications

In this paper, from the spacetime algebra associated with the Minkowski space ℝ3,1by means of a change of signature, we describe a quaternionic representation of the split-tetraquaternion algebra which incorporates the Pauli algebra, the split-biquaternion algebra and the split-quaternion algebra, we relate these algebras to Clifford algebras and we show the emergence of the stabilized Poincaré-Heisenberg algebra from the split-tetraquaternion algebra. We list without going into details some of their applications in Physics and in Born geometry.

The quaternion beam model for hard-magnetic flexible cantilevers

The recently developed hard-magnetic soft(HMS)materials manufactured by embedding high-coercivity micro-particles into soft matrices have received considerable attention from researchers in diverse fields,e.g.,soft robotics,flexible electronics,and biomedicine.Theoretical investigations on large deformations of HMS structures are significant foundations of their applications.This work is devoted to developing a powerful theoretical tool for modeling and computing the complicated nonplanar deformations of flexible beams.A so-called quaternion beam model is proposed to break the singularity limitation of the existing geometrically exact(GE)beam model.The singularity-free governing equations for the three-dimensional(3D)large deformations of an HMS beam are first derived,and then solved with the Galerkin discretization method and the trustregion-dogleg iterative algorithm.The correctness of this new model and the utilized algorithms is verified by comparing the present results with the previous ones.The superiority of a quaternion beam model in calculating the complicated large deformations of a flexible beam is shown through several benchmark examples.It is found that the purpose of the HMS beam deformation is to eliminate the direction deviation between the residual magnetization and the applied magnetic field.The proposed new model and the revealed mechanism are supposed to be useful for guiding the engineering applications of flexible structures.

Standard Dual Quaternion Optimization and Its Applications in Hand-Eye Calibration and SLAM

Several common dual quaternion functions,such as the power function,the magnitude function,the 2-norm function,and the kth largest eigenvalue of a dual quaternion Hermitian matrix,are standard dual quaternion functions,i.e.,the standard parts of their function values depend upon only the standard parts of their dual quaternion variables.Furthermore,the sum,product,minimum,maximum,and composite functions of two standard dual functions,the logarithm and the exponential of standard unit dual quaternion functions,are still standard dual quaternion functions.On the other hand,the dual quaternion optimization problem,where objective and constraint function values are dual numbers but variables are dual quaternions,naturally arises from applications.We show that to solve an equality constrained dual quaternion optimization(EQDQO)problem,we only need to solve two quaternion optimization problems.If the involved dual quaternion functions are all standard,the optimization problem is called a standard dual quaternion optimization problem,and some better results hold.Then,we show that the dual quaternion optimization problems arising from the hand-eye calibration problem and the simultaneous localization and mapping(SLAM)problem are equality constrained standard dual quaternion optimization problems.

Data encryption based on a 9D complex chaotic system with quaternion for smart grid

With the development of smart grid, operation and control of a power system can be realized through the power communication network, especially the power production and enterprise management business involve a large amount of sensitive information, and the requirements for data security and real-time transmission are gradually improved. In this paper, a new 9-dimensional(9D) complex chaotic system with quaternion is proposed for the encryption of smart grid data. Firstly, we present the mathematical model of the system, and analyze its attractors, bifurcation diagram, complexity,and 0–1 test. Secondly, the pseudo-random sequences are generated by the new chaotic system to encrypt power data.Finally, the proposed encryption algorithm is verified with power data and images in the smart grid, which can ensure the encryption security and real time. The verification results show that the proposed encryption scheme is technically feasible and available for power data and image encryption in smart grid.

Hermite Positive Definite Solution of the Quaternion Matrix Equation Xm + B*XB = C

This paper discusses the necessary and sufficient conditions for the existence of Hermite positive definite solutions of the quaternion matrix equation Xm+ B*XB = C (m > 0) and its iterative solution method. According to the characteristics of the coefficient matrix, a corresponding algebraic equation system is ingeniously constructed, and by discussing the equation system’s solvability, the matrix equation’s existence interval is obtained. Based on the characteristics of the coefficient matrix, some necessary and sufficient conditions for the existence of Hermitian positive definite solutions of the matrix equation are derived. Then, the upper and lower bounds of the positive actual solutions are estimated by using matrix inequalities. Four iteration formats are constructed according to the given conditions and existence intervals, and their convergence is proven. The selection method for the initial matrix is also provided. Finally, using the complexification operator of quaternion matrices, an equivalent iteration on the complex field is established to solve the equation in the Matlab environment. Two numerical examples are used to test the effectiveness and feasibility of the given method. .

Cyclic Solution and Optimal Approximation of the Quaternion Stein Equation

In this paper, two different methods are used to study the cyclic structure solution and the optimal approximation of the quaternion Stein equation AXB - X = F . Firstly, the matrix equation equivalent to the target structure matrix is constructed by using the complex decomposition of the quaternion matrix, to obtain the necessary and sufficient conditions for the existence of the cyclic solution of the equation and the expression of the general solution. Secondly, the Stein equation is converted into the Sylvester equation by adding the necessary parameters, and the condition for the existence of a cyclic solution and the expression of the equation’s solution are then obtained by using the real decomposition of the quaternion matrix and the Kronecker product of the matrix. At the same time, under the condition that the solution set is non-empty, the optimal approximation solution to the given quaternion circulant matrix is obtained by using the property of Frobenius norm property. Numerical examples are given to verify the correctness of the theoretical results and the feasibility of the proposed method. .

QUATERNIONIC SLICE REGULAR FUNCTIONS AND QUATERNIONIC LAPLACE TRANSFORMS

The functions studied in the paper are the quaternion-valued functions of a quaternionic variable.It is shown that the left slice regular functions and right slice regular functions are related by a particular involution,and that the intrinsic slice regular functions play a central role in the theory of slice regular functions.The relation between left slice regular functions,right slice regular functions and intrinsic slice regular functions is revealed.As an application,the classical Laplace transform is generalized naturally to quaternions in two different ways,which transform a quaternion-valued function of a real variable to a left or right slice regular function.The usual properties of the classical Laplace transforms are generalized to quaternionic Laplace transforms.

深海AUV无动力垂直下潜运动特性研究

深海AUV(自主水下机器人)采用无动力下潜方式能有效节约能源,但是水平或小纵倾角姿态下潜用时较长,水平偏移大。为提高下潜速度,减小下潜偏移距离,对AUV无动力垂直下潜过程进行研究。使用四元数代替欧拉角得到AUV运动方程,并加入洋流和浮力数学模型,通过Simulink仿真模块建立AUV垂直下潜运动仿真方法,解决垂直下潜产生的姿态角解算奇异性问题。通过设置不同仿真工况,得到AUV垂直下潜运动状态量受负浮力、重浮心距离、舵角、初始纵倾角及环境扰动力的作用规律。结果表明,AUV采用垂直下潜方式,可实现较大的下潜速度,同时减小水平偏移距离;洋流扰动是垂直下潜运动产生水平偏移的主要原因;下潜深度6000 m时,浮力变化扰动导致末端下潜速度减小30%,下潜时间增加21%。

基于四元多特征稀疏表示的彩色壁画图像超分辨率重建

蕴含复杂纹理信息及丰富色彩信息的彩色壁画图像在采用传统的基于通道分离的超分辨率方法进行重建时,由于只对图像的亮度信息进行处理,忽略了彩色壁画图像本身包含的众多细节信息和通道间的相关信息,容易造成重建后的图像出现边缘模糊、色彩伪影等问题。针对这些问题,提出将Lαβ色彩空间三个通道的信息与局部方差相结合运用于四元数模型,以此来表征彩色壁画图像的细节、亮度和色彩信息。在此基础上,构建了一个基于细节-亮度-色彩信息的多特征字典模型,从而在有效利用壁画图像各通道色彩信息的同时增强重建图像的细节信息。实验结果表明,该方法在主、客观指标方面均有较好表现,对于彩色壁画图像的整体重建效果较好。

梯度隐藏的安全聚类与隐私保护联邦学习

联邦学习是一种前沿的分布式机器学习算法,它在保障用户对数据控制权的同时实现了多方协同训练。然而,现有的联邦学习算法在处理Non-IID数据、梯度信息泄露和动态用户离线等方面存在诸多问题。为了解决这些问题,基于四元数、零共享与秘密共享等技术,提出了一种梯度隐藏的安全聚类与隐私保护联邦学习SCFL。首先,借助四元数旋转技术隐藏首轮模型梯度,并且在确保梯度特征分布不变的情况下实现安全的聚类分层,从而解决Non-IID数据导致的性能下降问题;其次,设计了一种链式零共享算法,采用单掩码策略保护用户模型梯度;然后,通过门限秘密共享来提升对用户离线情况的鲁棒性。与其他现有算法进行多维度比较表明,SCFL在Non-IID数据分布下准确度提高3.13%~16.03%,整体运行时间提高3~6倍。同时,任何阶段均能保证信息传输的安全性,满足了精确性、安全性和高效性的设计目标。

基于惯性测量单元的旋挖钻机钻具姿态测量方法

为实时获取钻孔过程中钻具的姿态信息,提高机手掌握成孔垂直度,设计了一种基于惯性测量单元的钻具姿态测量方法。该方法采用三轴加速度计、磁力计和陀螺仪构成惯性测量单元,建立基于四元数的姿态测量非线性模型,并采用基于四元数的扩展卡尔曼滤波算法,有效降低振动等干扰信号的影响,提高钻具姿态解算的准确性。实验结果表明,该方法能够有效避免振动对动态测量的干扰,实现旋挖钻机姿态的准确测量,为旋挖钻机施工提供实时、准确的姿态监测手段,为桩基施工质量提供重要保障。

Pythagorean-hodograph曲线的最小旋转Euler-Rodrigues标架优化方法

针对空间Pythagorean-hodograph(PH)曲线的有理最小旋转标架(RMF)问题,基于五次空间PH曲线的Euler-Rodrigues(ER)标架提出一种最小旋转标架的优化方法。PH曲线由Bézier方法来构造,再利用Bernstein多项式及四元数来表示,曲线的ER标架得到简单表示。当PH曲线的ER标架沿曲线弧的旋转角最小时,此时最小旋转ER标架也称曲线的RMF。在计算曲线的RMF的过程中,关键问题是求解旋转角度函数。由于有较多有理多项式的积分,一般难以找到角度函数的具体函数形式。运用最佳平方逼近的方法,构造一个多项式来近似表示旋转角度函数,对比不同次数多项式与角度函数的误差,得到合适次数的多项式近似角度函数。将多项式近似角度函数与直接计算角度函数求解曲线最小旋转ER标架所用时间对比,分析各自的计算量大小。数据结果证明,最佳平方逼近的方法可大大减少计算量,同时实现较小误差的目的。

基于Quaternion-EKF的未标定机器人视觉伺服系统位姿估算

针对单目未标定机器人视觉伺服系统中目标位姿估算问题,设计了一个基于Quaternion(四元数)的扩展卡尔曼滤波器。该算法引入四元数描述目标姿态角,以四元数、目标在相机坐标系中的位置、运动速度作为状态向量,以目标特征点在成像平面的像素坐标为观测向量。利用MATLAB分析协方差矩阵R、Q对算法的影响,并确定最优的协方差矩阵。文末通过MATLAB仿真和实验研究对该算法进行了验证,并与传统EKF进行了比较,结果表明,本文提出的算法能显著提高目标位姿估算精度,可以满足应用要求。

基于光滑粒子流体动力学的波浪中航行体入水数值模拟

航行体在波浪条件下高速入水的运动响应和载荷特性是其研发设计过程中需要重点考虑的问题,为了对该问题进行精准预测,采用无网格光滑粒子流体动力学(smoothed particle hydrodynamics,SPH)方法,提出了一种新型周期性波浪边界技术,利用四元数法计算物体六自由度运动,建立了波浪条件下入水模拟的数值水池。通过对静水中方块体垂直落水和航行体倾斜入水运动轨迹和冲击载荷的模拟,对比于实验参考结果,验证了数值模型的计算精度。随后,在SPH数值波浪水池中对航行体在不同波浪相位角下的高速入水过程开展研究,结果表明航行体弹道稳定性受到波浪相位角影响显著,0°相位角入水时弹道最为稳定。该新型SPH数值水池能够实现航行体波浪中入水过程的精确预报。

Mixed noise removal for color images using quaternion representation

In order to effectively restore color noisy images with the mixture of Gaussian noise and impulse noise,a new algorithm is proposed using the quaternion-based holistic processing idea for color images.First,a color image is represented by a pure quaternion matrix.Secondly,according to the different characteristics of the Gaussian noise and the impulse noise,an algorithm based on quaternion directional vector order statistics is used to detect the impulse noise. Finally,the quaternion optimal weights non-local means filter （QOWNLMF）for Gaussian noise removal is improved for the mixed noise removal.The detected impulse noise pixels are not considered in the calculation of weights.Experimental results on five standard images demonstrate that the proposed algorithm performs better than the commonly used robust outlyingness ratio-nonlocal means （ROR-NLM）algorithm and the optimal weights mixed filter （OWMF）.

DUAL QUATERNION CURVE INTERPOLATION ALGORITHM FOR FORMATION SATELLITES

The traditional algorithms for formation flying satellites treat the satellite position and attitude sepa- rately. A novel algorithm combining satellite attitude with position is proposed. The principal satellite trajectory is obtained by dual quaternion interpolation, then the relative position and attitude of the deputy satellite are ob- tained by dual quaternion modeling on the principal satellite. Through above process, relative position and atti- tude are unified. Compared with the orbital parameter and the quaternion methods, the simulation result proves that the algorithm can unify position and attitude, and satisfy the precision requirement of formation flying satel- lites.