Quaternion Method Research Articles

Finite-time adaptive synchronization of fractional-order delayed quaternion-valued fuzzy neural networks

Based on direct quaternion method, this paper explores the finite-time adaptive synchronization (FAS) of fractional-order delayed quaternion-valued fuzzy neural networks (FODQVFNNs). Firstly, a useful fractional differential inequality is created, which offers an effective way to investigate FAS. Then two novel quaternion-valued adaptive control strategies are designed. By means of our newly proposed inequality, the basic knowledge about fractional calculus, reduction to absurdity as well as several inequality techniques of quaternion and fuzzy logic, several sufficient FAS criteria are derived for FODQVFNNs. Moreover, the settling time of FAS is estimated, which is in connection with the order and initial values of considered systems as well as the controller parameters. Ultimately, the validity of obtained FAS criteria is corroborated by numerical simulations.

Quaternion Methods and Regular Models of Celestial and Space Flight Mechanic: Using Euler (Rodrigues–Hamilton) Parameters to Describe Orbital (Trajectory) Motion. II: Perturbed Spatial Restricted Three-Body Problem

Quaternion Methods and Regular Models of Celestial and Space Flight Mechanic: Using Euler (Rodrigues–Hamilton) Parameters to Describe Orbital (Trajectory) Motion. II: Perturbed Spatial Restricted Three-Body Problem

Application of extended reality technology for real-time navigation in clinical operation

To explore the application of extended reality (XR) technology in clinical surgeries for improving the success rate of surgeries. To assist the surgeons to better understand the location, size and geometric shape of the lesions and reduce potential radiation exposure in minimally invasive surgical navigation based on two-dimensional images, we constructed three-dimensional models based on CT data and used XR technology to achieve intraoperative navigation. An improved quaternion method was used to improve the accuracy of electromagnetic positioning, with which the system error of positioning accuracy was reduced to below 2 mm. A 5G network was used to optimize the server GPU programming algorithm, and real-time video stream coding strategy and network design were adopted to reduce data transmission jam and delay in the remote surgery network, which achieved an average delay of less than 60 ms. A Gaussian distribution deformation model was used to simulate collision detection and stress deformation of the tissues to achieve a tactile perception effect. The intraoperative navigation system based on XR technology allowed more accurate determination of the location of the lesions, effectively reduced the surgical risk, and avoided the risk of intraoperative radiation exposure. The low latency and high fidelity of 5G network achieved real-time interaction during the surgery to provide a technical basis for multi-terminal remote cooperative surgery. The combination of force feedback technology and XR technology enables the surgeons to conduct deep immersion preoperative planning and virtual surgery to improve the success rate of surgery and shorten the learning curve.

Quaternion Methods and Regular Models of Celestial and Space Flight Mechanic: Using Euler (Rodrigues-Hamilton) Parameters to Describe Orbital (Trajectory) Motion. II: Perturbed Spatial Restricted Three-Body Problem

The article considers the problem of regularizing the features of the classical equations of celestial mechanics and space flight mechanics (astrodynamics), which use variables that characterize the shape and size of the instantaneous orbit (trajectory) of the moving body under study, and Euler angles that describe the orientation of the used rotating (intermediate) coordinate system or the orientation of the instantaneous orbit, or the plane of the orbit of a moving body in an inertial coordinate system. Singularity-type features (division by zero) of these classical equations are generated by Euler angles and complicate the analytical and numerical study of orbital motion problems. These singularities are effectively eliminated by using the four-dimensional Euler (Rodrigues-Hamilton) parameters and Hamiltonian rotation quaternions. In this (second) part of the work, new regular quaternion models of celestial mechanics and astrodynamics are obtained that do not have the above features and are built within the framework of a perturbed spatial limited three-body problem (for example, the Earth, the Moon (or the Sun) and a spacecraft (or an asteroid)): equations of trajectory motion written in non-holonomic or orbital or ideal coordinate systems, for the description of the rotational motion of which the Euler (Rodrigues-Hamilton) parameters and quaternions of Hamilton rotations are used. New regular quaternion equations of the perturbed spatial restricted three-body problem are also obtained, constructed using two-dimensional ideal rectangular Hansen coordinates, Euler parameters and quaternion variables, as well as using complex compositions of Hansen coordinates and Euler parameters (Cayley-Klein parameters). The advantage of the proposed orbital motion equations constructed using the Euler parameters over the equations constructed using the Euler angles is due to the well-known advantages of the quaternion kinematic equations in the Euler parameters included in the proposed equations over the kinematic equations in the Euler angles included in the classical equations.

Measurement Method and Experiment of Hydraulic Support Group Attitude and Straightness Based on Binocular Vision

Hydraulic supports are important equipment used in coal mining. Detecting the real-time attitude and straightness of hydraulic support group in unmanned working faces of coal mines in complex geological conditions is difficult. To address this issue, a method that measures the position and attitude of the hydraulic support using binocular vision detection-aided mark points was proposed. First, a combination of binocular vision positioning and a convolutional neural network (CNN) object detection is used to achieve the three-dimensional (3D) location of mark points. Then, the attitude calculation model of the hydraulic support based on the dual quaternion method is established. This method achieves the space attitude detection between multiple hydraulic supports and the straightness detection of hydraulic support group in 3D space. In the laboratory environment, the position and attitude detection test of the hydraulic support is obtained through the working face equipment position detection test bench. This method can adapt to the worse working environment in coal mine production and can provide early data for the automatic control of the straightness of the working face.

Settling-Time Estimation for Finite-Time Stabilization of Fractional-Order Quaternion-Valued Fuzzy NNs

This article solves the problems of finite-time control and settling-time estimation for fractional-order quaternion-valued fuzzy neural networks (FQFNNs) with time delays. A novel fractional differential inequality is established to estimate the settling time of the addressed system, which is more general and less conservative than the existing results. In addition, owing to the noncommutativity of multiplication of quaternions, the decomposition method is usually adopted to discuss the finite-time stabilization (FTS) of quaternion-valued neural networks, which inevitably doubles the dimensionality of the system and brings a great computational burden. To avoid the aforementioned issues, some new properties of the quaternion-valued signum function are presented for exploring the FTS of FQFNNs by the direct quaternion method without any decomposition. Then, 1-norm and 2-norm control strategies are designed to stabilize the addressed system in finite time, and several sufficient criteria are derived to ensure the FTS of FQFNNs. Finally, the validity of the obtained theoretical results and the superiority of the proposed estimation method are illustrated by numerical simulations.

Cooperative control strategy of wheel-legged robot based on attitude balance

AbstractTo integrate the uneven terrain adaptivity of legged robots and the fast capacity of wheeled robots on even terrains, a four wheel-legged robot is addressed and the cooperative control strategy of wheels and legs based on attitude balance is investigated. Firstly, the kinematics of wheel-legged robot is analyzed, which contains the legged and wheeled motion modal. Secondly, the cooperative control strategy of wheel-legged robot based on attitude balance is proposed. The attitude is calculated by using the quaternion method and complementary filtering, and the attitude stability control of the wheel-legged robot is studied. The trajectory planning of leg motion including walk and trot gait is implemented, and the differential control of wheeled motion is deduced. And then, the cooperative motion control of wheels and legs is achieved by keeping the attitude balance of robot body. Finally, a small prototype is set up to validate the feasibility and effectiveness of proposed method. The experimental results show that the established wheel-legged robot can do walk, trot, and wheel-leg compound motion to overcome many complex terrains and environments.

Kinematics analysis and calibration of a 6-degree of freedom light load collaborative robot

Background: In the process of carrying small forgings and other materials, the trajectory error of the 6-degree of freedom light-load collaborative robot will lead to the deviation of forgings placement position. The kinematics analysis and calibration of 6-degree of freedom light load collaborative robot are performed to solve the problem of trajectory error. Methods: The quaternion and cubic spline interpolation methods are adopted to plan the trajectory of the 6-degree of freedom light load collaborative robot. Based on the kinematic error model, the least squares estimation method is adopted to estimate the parameter error of the robot's connecting rod, and the parameter compensation values of each joint are obtained. Results: The kinematic calibration experiment shows that the coordinates of the robot end center are basically consistent with the actual coordinates after compensation, which verifies the rationality of the kinematic model and calibration method. Conclusions: The study lays the theoretical foundation for the trajectory error correction of the light load collaborative robot.

Quaternion Methods and Regular Models of Celestial Mechanics and Space Flight Mechanics: The Use of Euler (Rodrigues–hamilton) Parameters to Describe Orbital (Trajectory) Motion. I: Review and Analysis of Methods and Models and Their Applications

Quaternion Methods and Regular Models of Celestial Mechanics and Space Flight Mechanics: The Use of Euler (Rodrigues–hamilton) Parameters to Describe Orbital (Trajectory) Motion. I: Review and Analysis of Methods and Models and Their Applications

Robust control of uncertain time-delay Markovian jump quaternion-valued neural networks subject to partially known transition probabilities: direct quaternion method.

This paper addresses the issue of robust stochastic stabilization and control of uncertain time-delay Markovian jump quaternion-valued neural networks (MJQVNNs) subject to partially known transition probabilities. First, the direct quaternion method is proposed to analyse the MJQVNNs, which is different from some conventional methods in that the former is without any decomposition for systems. After that, in order to estimate the upper bound of the derivative of the constructed Lyapunov-Krasovskii functional(LKF) more accurately, the real-valued convex inequality is extended to quaternion domain. Then, by designed the mode-dependent state feedback controllers, the robust stochastic stabilization conditions of MJQVNNs are given for the admissible uncertainties, and reduce the influence of input disturbance on the controlled output to a specified performance level. Lastly, two numerical examples are given to illustrate the effectiveness of the proposed method.

A motion tracking approach to position marine floating structures based on measured acceleration and angular velocity

One of the major challenges arising from dynamic response measurement of floating structures is to effectively track their 6DOF response in harsh environments. Although the combination of GPS and INS techniques has the ability to estimate the positioning of floating structures, it is tedious that the corrections of response measurements have to be carried out at regular intervals due to the low accuracy, instability and various harsh environments. Aiming at achieving long-term stable and efficient measurements of floating structural responses, a motion tracking approach based on the combination of the accelerations and angular velocities has been proposed in this paper. First, a novel displacement reconstruction model has been established to effectively determine the translational displacements of floating structures. Following that, to correct the errors of tilt and coordinate data from the measured accelerometers, the quaternion method has been applied to update the dynamic Euler angle. The major contributions of this research include: (1) the development of a non-integral drift-free method for displacement reconstructions without GPS and (2) the realization of a synchronous tracking system considering dynamic tilt error of accelerometers for floating structures with the motions in 6-DOF. To demonstrate the correctness of the proposed approach, two numerical examples have been examined to track the motion of floating structures. Numerical results have shown that the maximum error of the reconstructed displacement between the proposed approach and Orcaflex is only 0.8096%, indicating their good agreement. Then, a physical experiment of a semi-submersible platform under the action of regular and irregular waves has been conducted to verify the feasibility of the developed tracking approach by comparison of the data from the traditional optical device and camera. The results show that the proposed method has the ability to effectively predict the operation conditions of floating structures and provides a valuable insight into the development of an efficient synchronous tracking system for various engineering applications.

Composite Ski-Resort Registration Method Based on Laser Point Cloud Information

The environment of ski resorts is usually complex and changeable, and there are few characteristic objects in the background, which creates many difficulties for the registration of ski-resort point cloud datasets. However, in the traditional iterative closest point (ICP) algorithm, two points need to have good initial positions, otherwise it is easy to get caught up in local optimizations in registration. Aiming at this problem, according to the topographic features of ski resorts, this paper put forward a ski-resort coarse registration method based on extraction, and matching between feature points is proposed to adjust the initial position of two point clouds. Firstly, the feature points of the common part of the point cloud datasets are extracted based on the SIFT algorithm; secondly, the Euclidean distance between the feature normal vectors is used as the pairing condition to complete the pairing between the feature points in the point cloud datasets; then, the feature point pair is purified by using the included angle of the normal vector; finally, in the process of coarse registration, the rotation matrix and translation vector between point clouds are solved by the unit quaternion method. Experiments demonstrate that the proposed coarse registration method based on the normal vector of feature points is helpful to the smooth completion of the subsequent fine registration process, avoids the phenomenon of falling into local optimization, and effectively completes the ski-resort point cloud registration.

Attitude Control of Rigid Bodies: An Energy-Optimal Geometric Switching Control Approach

In this article, the attitude control problem for a class of rigid body systems with switching submodes is investigated. To address such issue, an energy-optimal geometric switching control method is proposed for the first time. First, a switching Lie group method and a switching Lie group discrete variational integrator method based on the variational principle are developed. Then, continuous-time and discrete-time attitude switching dynamics models for rigid bodies are globally expressed on a special orthogonal matrix group (i.e., SO(3) group) to avoid the locality, singularity, and ambiguity caused by using the traditional Euler angle method, minimum representation method, or quaternion method. Second, the switching process of rigid bodies from initial attitude and angular velocity to desired attitude and angular velocity within a fixed maneuver time and the minimum energy consumption of rigid bodies with control saturation are solved. Furthermore, by solving the energy-optimal geometric control problem of attitude switching dynamics models, the global optimal geometric switching control and optimal switching time conditions under continuous-time and discrete-time are first derived. The obtained criteria ensure that the intrinsic geometric properties of attitude switching dynamics models will not be lost during the optimization process. Finally, some simulation results are presented to demonstrate the feasibility of the proposed techniques.

Velocity tracking of cardiac vector loops to identify signs of stress-induced ischaemia.

Coronary artery disease (CAD) is among the leading causes of death worldwide. Initial studies require an electrocardiogram stress test often followed by cardiac imaging procedures. However, conventional indices still show insufficient diagnostic performance. We propose quaternion methods to evaluate abnormal alterations during ventricular depolarization and repolarization. Assessment was conducted during a Bruce protocol treadmill stress test and after the end of the exercise. We developed an algorithm to automatically determine the beginning and end of exercise and then, computed the angular and linear velocities. Statistical analysis for feature selection and classification between ischaemic and non-ischaemic patients was used. The most significant markers were maximum linear velocity during ventricular depolarization (p < 5E-9) and maximum angular velocity during the second half of the repolarization loop (p < 5E-16). The latter reached sensitivity / specificity pair of 78 / 92 (AUC 0.89). A linear classifier showed a trend of reduction in cardiac vector velocity in at-risk patients after the end of exercise. The sensitivity / specificity pair reached was 86 / 100. Trajectory deviations of depolarization / repolarization loops that result from ischaemia effects, could be responsible for the observed reduction in dynamic changes during exercise. Further studies could provide non-invasive complementary tools to detect CAD risk. Graphical abstract This data is mandatory, please provide.

A rotary vision system for high-precision measurement over large size

This paper introduced a rotary binocular vision measurement system (RBVMS) consisting of two cameras and two theodolites, with the latter employed as a two-dimensional rotation platform. The camera was driven by mounting it on the theodolite to cover different areas, effectively increasing the measuring range. In the camera calibration stage, virtual 3D points were generated by accurately moving the planar calibration board. A two-order radial and two-order tangential distortion model was considered. The experimental results showed that the intrinsic parameters of the camera had high stability, and the mean reprojection error was about 0.035 pixels. A unit quaternion method was applied to calibrate the transformation matrix between the camera and the theodolite. By solving the transformation matrix between the two theodolites, the measurement data of each position was unified under a fixed coordinate system. At 500 mm in front of the camera, the camera's field of view was about 200 mm. Two targets of different sizes were measured to verify the effectiveness and accuracy of the method. The measurement accuracy of 300 mm and 600 mm targets was about 0.014 mm and 0.027 mm, respectively.

Three-Dimensional Obstacle Avoidance Strategy for Fixed-Wing UAVs Based on Quaternion Method

This work provides a generalization of the three-dimensional velocity obstacle (VO) collision avoidance strategy for nonlinear second-order underactuated systems in three-dimensional dynamic uncertain environments. A hierarchical architecture is exploited to deal with conflicting multiple subtasks, which are defined as several rotations and are parameterized by quaternions. An improved VO method considering the kinodynamic constraints of a class of fixed-wing unmanned aerial vehicles (UAV) is proposed to implement the motion planning. The position error and velocity error can be mapped onto one desired axis so that, only relying on an engine, UAVs can achieve the goal of point tracking without collision. Additionally, the performance of the closed-loop system is demonstrated through a series of simulations performed in a three-dimensional manner.

Global Mittag-Leffler stability for fractional-order quaternion-valued neural networks with piecewise constant arguments and impulses

This paper is devoted to analysing the global Mittag-Leffler stability of fractional-order quaternion-valued neural networks with piecewise constant arguments and impulses. The quaternion direct method is adopted to address the considered model avoiding any decomposition. By utilising the matrix inequality technique and Lyapunov direct method, some sufficient conditions to guarantee the global Mittag-Leffler stability of equilibrium point for the considered model are obtained in the form of quaternion-valued linear matrix inequalities (LMIs). To certify the validity of the derived result, a numerical example is presented.

Quaternion methods and models of regular celestial mechanics and astrodynamics

This paper is a review, which focuses on our work, while including an analysis of many works of other researchers in the field of quaternionic regularization. The regular quaternion models of celestial mechanics and astrodynamics in the Kustaanheimo-Stiefel (KS) variables and Euler (Rodrigues-Hamilton) parameters are analyzed. These models are derived by the quaternion methods of mechanics and are based on the differential equations of the perturbed spatial two-body problem and the perturbed spatial central motion of a point particle. This paper also covers some applications of these models. Stiefel and Scheifele are known to have doubted that quaternions and quaternion matrices can be used efficiently to regularize the equations of celestial mechanics. However, the author of this paper and other researchers refuted this point of view and showed that the quaternion approach actually leads to efficient solutions for regularizing the equations of celestial mechanics and astrodynamics.This paper presents convenient geometric and kinematic interpretations of the KS transformation and the KS bilinear relation proposed by the present author. More general (compared with the KS equations) quaternion regular equations of the perturbed spatial two-body problem in the KS variables are presented. These equations are derived with the assumption that the KS bilinear relation was not satisfied. The main stages of the quaternion theory of regularizing the vector differential equation of the perturbed central motion of a point particle are presented, together with regular equations in the KS variables and Euler parameters, derived by the aforementioned theory. We also present the derivation of regular quaternion equations of the perturbed spatial two-body problem in the Levi-Civita variables and the Euler parameters, developed by the ideal rectangular Hansen coordinates and the orientation quaternion of the ideal coordinate frame.This paper also gives new results using quaternionic methods in the perturbed spatial restricted three-body problem.

Research on QPSO algorithm for trajectory planning of FFSR general kinematics modeling

Aiming at the optimal trajectory planning problem faced by free floating space robot (FFSR) in capturing non cooperative target (NCT) with unknown dynamic parameters, firstly, based on the unique intrinsic characteristics of FFSR in microgravity environment, a general FFSR kinematic model based on generalized velocity variables and an NCT dynamic model based on quaternion method are established. Secondly, the optimal criterion of FFSR trajectory planning and the parametric modeling method of FFSR manipulator joint trajectory based on sinusoidal function are studied; Finally, a QPSO algorithm for FFSR trajectory planning based on the optimal comprehensive index is proposed

Discrete Element Simulations of Ice Load and Mooring Force on Moored Structure in Level Ice

Moored structures are suitable for operations in ice-covered regions owing to their security and efficiency. This paper aims to present a new method for simulating the ice load and mooring force on the moored structure during ice-structure interaction with a spherical discrete element method (DEM). In this method, the level ice and mooring lines consist of bonded sphere elements arranged in different patterns. The level ice model has been widely validated in simulation of the ice load of fixed structures. In the mooring line simulation, a string of spherical elements was jointed with the parallel bond model to simulate the chains or cable structure. The accuracy of the mooring line model was proved by comparing the numerical results with the nonlinear FEM results and model towing experiment results. The motion of the structure was calculated in the quaternion method, considering the ice load, mooring force, and hydrodynamic force. The hydrodynamic force comprised wave-making damping, current drag, and buoyancy force. Based on the proposed model, the interaction of a semi-submersible structure with level ice was simulated, and the effect of ice thickness on the ice load was analyzed. The numerical results show that the DEM method is suitable to simulate the ice load and mooring force on moored floating structures.