Papers by Keyword: Quaternion

Abstract: In this study, we measured the rolling motion of a spherical six-axis inertial measurement unit (IMU) fabricated via FDM (Fused Deposition Modeling) using wireless communication. When a sphere rolls on a plane, the axis of rotation is undefined, and the amount of rotation is unlimited. Therefore, the conventional Euler angular representation for pose estimation produces singular points (gimbal locks), and a continuous pose representation is not possible. In this paper, we propose an algorithm that incorporates micro-quaternions to achieve continuous posture representation, even at singular points. Subsequently, we discuss its applications.

Abstract: In this study, a novel formulation of phase field model for representing solidification of polycrystalline metals is proposed. A quaternion-based crystal orientation representation is introduced into the KWC-type phase field model. Using this approach, three-dimensional rotation of crystal orientation can be represented by a direct extension of the conventional KWC model. A numerical simulation by the presented model is conducted, and the characteristics and adequacy of the model are discussed.

Abstract: For MEMS (Micro-Electro-Mechanical System) inertial sensor low precision, high noise and the characteristics of the gyroscope error accumulating, this paper designed a kind of yaw angle measuring system based on EKF (Extended Kalman Filter) by STM32 microcontroller and MEMS sensor. The EKF applys the attitude angle quaternion as the filter state variable, the angular rate as the filter time update. And application of the carrier location's gravitational field and geomagnetic data, complete filter measurement update, suppress divergent attitude error, obtain high accuracy and reliability of the attitude angle (pitch angle, roll angle, yaw angle) data. Experimental results show that the practical application of error control heading within ± 1º, with high practical value.

Abstract: J. C. Maxwell applied the quaternion analysis and vector terminology to study the physics properties of electromagnetic field. Nowadays the spaces of electromagnetic and gravitational fields can be chosen as the quaternion spaces, while their coordinates are able to be the complex numbers. The complex quaternion space can be used to describe the physics feature of forces in the electromagnetic and gravitational fields. The paper is capable of writing the terms of force into a single definition, including the inertial force, gravity, electromagnetic force, energy gradient and so on. Further the definition of force can deduce some new but weak terms of force. One of them is the ‘strength gradient force’. The strength gradient force relates only with the gradient and distribution of field strength, and is independent to the electric charge and mass. And this force is able to exert the interaction on neutral and charged particles. As the driving force, the strength gradient force can be used to drive precisely the motion of small mass, and applied to operate the precision machine. By analogy with the optical tweezers and magnetic mirror, the strength gradient force is possible to be applied to devices in the future, including in the precision machine for the focusing, the collimating of the polarization maintaining optical fibers and so forth.

Abstract: This article follows a detailed description of development and validation for the direct kinematic model of six degrees of freedom articulated arm robot - Kawasaki FS10E model. The development of the kinematic model is based on widely used Denavit-Hartenberg notation, but, after the initial parameter identification, the mathematical algorithm itself follows an approach that uses the quaternion number system, taking advantage of their efficiency in describing spatial rotation - providing a convenient mathematical notation for expressing rotations and orientations of objects in three-dimensional space. The proposed algorithm concludes with two quaternion-based relations that express both the position of robot tool center point (TCP) position and end-effector orientation with respect to robot base coordinate system using Denavit-Hartenberg parameters and joint values as input data. Furthermore, the developed direct kinematic model was validated using the programming and offline simulation software Kawasaki PC Roset.

Abstract: Updating attitude precisely in time is the primary task of strapdown inertial navigation system(SINS) algorithms. This paper mainly studied the application of rotation vector in three different methods of data fusion respectively named linear interpolation, gradient descent and complementary filter for attitude-updating, using low-cost MEMS inertial sensors in SINS. Meanwhile, an idea that the quaternion attitude could be updated by constructing micro-rotation quaternion from rotation vector in the sampling interval is proposed. The idea is based on geometric interpretation of space rotation transformation, while the general method is the differential equations of quaternion about rotation vector. Therefore the new method is an approximation method within enough short update interval, but its best superiority is the higher speed of attitude-updating than general method with little loss of accuracy because of no necessary to solve differential equations. The experimental results also show the effectiveness and accuracy of three improved algorithms with the new idea.

Abstract: Micro inertial measurement unit integration storage test system is a typical multi-sensor information fusion system consists of microsensors. The Federated Kalman filter is applied to micro inertial measurement unit integration storage test system. The general structure and characteristics of Federated Kalman filter is expounded. The four-order Runge-Kutta method based on quaternion differential equation was used to dispose the output angular rate data from gyroscope, and the recurrence expressions was established too. The control system based ARM Cortex-M4 master-slave structure is adopted in this paper. The result shown that the dimensionality reduced algorithm significantly reduces implementation complexity of the method and the amount computation. The filtering effect and real-time performance have much increased than traditionally method.

Abstract: This paper proposes a new method of 6-DOF serial robot’s trajectory planning. Ensuring to satisfy the physical constraints of space conditions, the robot’s trajectory is interpolated in the Cartesian coordinate system, and using quaternion interpolation to solve the multiple solution problem in RPY interpolation. Meanwhile, the interpolated position information is transformed into the angular displacement information of the joint coordinate system, and the joint space trajectory planning is achieved using the genetic algorithms integrated velocity, acceleration, jerk and torque and other important kinematic and dynamic constraints. In robot safety and stability, the method is better than the general approach, and it has both the ideal trajectory parameters of the global search ability and performance planning.

Abstract: Singularity problem in attitude estimation of small tail-sitter aircraft with traditional algorithm is researched. According to the flight characteristics of small tail-sitter aircraft, a new algorithm is proposed. Vertical Euler angles whose singularity points are away from standard Euler angles are introduced. Only one set of angles are used in horizontal or near-vertical state to avoid singularity. Simulation results show that attitude angles can vary continuously and have high accuracy under the condition of a large tilting angle.

Abstract: In order to achieve three-dimensional automatic splicing from the multi-angle, the paper presents a new splicing method. The method utilizes the invariance of the spatial characteristics of the characteristic landmarks and then marks the characteristic landmarks by introducing the angle collection between the characteristic landmarks, and match in space for the characteristic landmarks within two perspective regional based on this characteristic collection. This method eliminates the tedious encoding process of the landmarks, so improves the spatial matching rate and ensures the matching accuracy. In addition, in the process of striking the three-dimensional coordinates of the landmarks, this paper strikes image coordinate of the characteristic signs circle center by introducing the regional connectivity feature flag. This method eliminates interference from unwanted areas, and distinguish between the various signs round independence and improves the strike rate of the circle center. At the end rotation matrix R and translation vector T of the coordinate system normalization are solved by the quadruple method. Examples show that the algorithm has strong robustness, can realize quickly, automatic stitching for the visual data, and has the very good practical value.