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.

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%。

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。

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。

基于多分支架构的目标三维位姿实时估计方法

针对车路协同应用场景中目标尺度与位置值域跨度大导致的位姿实时估计精度低、回归求解模型收敛慢的问题,提出了一种基于多分支架构的目标三维位姿实时估计方法。在目标二维检测算法模型架构基础上,设计位姿估计分支结构,用于输出目标姿态四元数、目标相对相机的三维空间位置及目标长宽高。在训练阶段,为位姿估计分支设计了相应的损失函数,采用向量单位化算子回归姿态四元数、对数重映射算法回归目标尺寸与目标到相机距离;在推理阶段,根据模型输出的四元数和目标到相机距离解算出目标三维位姿,实现精确的位姿估计。在OVRC数据集的位姿精度验证中,位置坐标误差的均方差最大为1.94 m,姿态角误差的均方差最大为3.98°;在Kitti数据集的相对精度测试实验中,相比PVNet方法,检测精度提升了3.22%,相比3DBB方法,推理效率提升一倍。

Sigmoid变换的滤波-x四元数最小均方算法

滤波-x最小均方(Filtered-x Least Mean Square,FxLMS)算法是主动噪声控制系统中常用的算法,对中低频噪声有较好的控制作用,但在某些环境噪声中传统的算法可能达不到期望的抑制效果。提出一种基于sigmoid变换的滤波-x四元数最小均方算法,该算法利用四元数的空间特性使噪声信号在超复数域内部相互耦合和关联,并通过sigmoid函数对误差信号进行非线性变换来约束噪声信号以减低对权值更新的影响力度,避免权值在更新过程中发散,从而实现优异的收敛性能以及增强的鲁棒性。同时通过研究步长分析该算法的稳态特性,并在汽车、工厂噪声环境下验证提出算法性能的优越性,仿真结果支持了该结论。

混沌驱动四元数旋转三维星座加密的WFRFT通信方法

针对现有一维混沌映射序列分布不均和映射参数范围有限的问题,提出一种改进型的一维逻辑正弦混沌映射,在此基础上设计了一种混沌驱动四元数旋转三维星座加密的多参数加权分数傅里叶变换(Chaos driven Quaternion Rotation 3D constellation Encrypted-Multiple Parameters Weighted-type Fractional Fourier Transform,CQR3DE-MPWFRFT)通信方法。Logistic映射和Sine映射耦合,提出L-S混沌映射,将需要传输的信息进行三维星座调制。通过L-S混沌映射产生的混沌密钥驱动生成四元数,对生成的三维星座图进行旋转加密。进行多参数加权分数傅里叶变换(Multiple Parameters Weighted-type Fractional Fourier Transform,MPWFRFT)之后,完成数字调制。仿真结果表明:该混沌映射参数范围更大,随机性更好;所设计的CQR3DE-MPWFRFT方法利用L-S混沌驱动四元数实现了二维星座到三维星座的旋转加密,其星座点与传统调制相比星座空间更大,相较于MPWFRFT方法系统误码率性能有一定的提升,即使窃听方密钥只有10-15的差异,仍然无法完成窃听,能够提高信息在物理层的传输安全。

修正共轭梯度算法求解四元数Sylvester张量方程

本文提出一类张量形式的修正共轭梯度算法求解四元数Sylvester张量方程.证明在不计舍入误差的情况下,所提方法可在有限迭代步内获得张量方程组的解.进一步,通过选择特殊类型的初始张量,可获得方程组的唯一极小Frobenius范数解.通过数值算例验证了所提出算法的可行性和有效性.

风场扰动下植保四旋翼无人机的建模与控制

由于四旋翼植保无人机的飞行高度较低,在实际飞行中易受到环境风场的影响。为此,根据Newton-Euler方程建立了风场环境下四旋翼飞行器的动力学模型,并设计了基于内外环PID控制策略的控制器。其中,姿态角控制器采用基于四元数的反馈控制器,并使用Lyapunov稳定性判据验证了其全局渐近稳定性;姿态角速率控制器采用PID控制器;位置控制器由速度PID控制器和位置P控制器组成。通过在Gazebo中进行风场模拟仿真实验和实际飞行试验,对设计的四旋翼飞行器控制系统进行参数调试和验证,结果表明:控制器具备在风场环境下控制四旋翼无人机稳定飞行的能力。

四元数亚正定系统混参分裂迭代方法

随着四元数的广泛应用,大型四元数结构矩阵方程的求解成为科学计算的重要课题。针对四元数亚正定系统AX=B,在新自共轭正定和斜自共轭分裂迭代(new positive definite and skew-self-conjugate splitting,NPSS)基础上,通过引入双参数和松弛加速技术,构建出两种新的混参分裂迭代格式,即非对称新自共轭正定和斜自共轭分裂迭代(asymmetric new positive definite and skew-self-conjugate splitting,ANPSS),以及超松弛非对称新自共轭正定和斜自共轭分裂迭代(successive over relaxation asymmetric new positive definite and skew-self-conjugate splitting,SANPSS),同时运用四元数矩阵特征值理论,证明了这两种迭代的收敛性,并给出相关参数的取值范围。采用四元数矩阵的复表示方法,在MATLAB环境下实现该系统的数值求解。数值算例表明,多参数的灵活选取,显示出所提混参分裂迭代相比NPSS迭代具有更高的收敛效率。