Study on the estimation of Euler angles for Macao Science Satellite-1

The Euler angle estimation is a calibration method for vector data measured by the magnetometer on a satellite.It is used to find the relative rotation between the coordinate system of the magnetometer and the satellite(usually determined by Star Imagers).Before launch of the low-orbit,low-inclination Macao Science Satellite-1(known as MSS-1),we simulated the estimation of Euler angles by using the magnetic measurements of the in-orbit Swarm and China Seismo-Electromagnetic Satellite(noted as CSES),with various data combinations.In this study,11 data sets were designed to analyze the estimation results for the MSS-1 orbit by using a joint estimation method of the geomagnetic field model parameters and Euler angles.For the model results,we found that all the spatial power spectral lines showed behavior consistent with that of the CHAOS-7.8 model at low degrees(corresponding to large-scale magnetic signals).The spectra of models without global data coverage deviated much more(by a maximum of~10^(4) nT^(2))from those of the CHAOS-7.8 model at higher degrees.For models with global data coverage and with various data combinations,the spectral lines were distributed similarly.Moreover,the models with accordant power spectral distributions demonstrated different Euler angle estimations.As more vector data at higher latitudes were included,the estimated Euler angles varied monotonically in all three directions.The models with vector data in the same latitude range showed similar Euler angle results,regardless of whether the poleward scalar data were included.The largest value difference was found between the models using vector data within±40°latitudes and those using vector data within±60°latitudes,which reached to~28″.Therefore,we concluded that the inversion of the spherical harmonic Gauss coefficients in our tests was mainly affected by the spatial coverage range of the data,whereas the estimation of Euler angles largely depended on the latitude range where the vector data could be obtained.These results can be used for future in-flight data testing.We expect the estimation of Euler angles to improve as other methods are adopted.

Realization of orientation interpolation of 6-axis articulated robot using quaternion

In general, the orientation interpolation of industrial robots has been done based on Euler angle system which can result in singular point （so-called Gimbal Lock）. However, quaternion interpolation has the advantage of natural （specifically smooth） orientation interpolation without Gimbal Lock. This work presents the application of quatemion interpolation, specifically Spherical Linear IntERPolation （SLERP）, to the orientation control of the 6-axis articulated robot （RS2） using LabVIEW and RecurDyn. For the comparison of SLERP with linear Euler interpolation in the view of smooth movement （profile） of joint angles （torques）, the two methods are dynamically simulated on RS2 by using both LabVIEW and RecurDyn. Finally, our original work, specifically the implementation of SLERP and linear Euler interpolation on the actual robot, i.e. RS2, is done using LabVIEW motion control tool kit. The SLERP orientation control is shown to be effective in terms of smooth joint motion and torque when compared to a conventional （linear） Euler interpolation.

Attitude control of spacecraft during propulsion of swing thruster

As for orbit transfer vehicle (OTV) with multiple satellites/payloads carried,the release of each payload will bring serious change to the mass center of OTV and the thrust produced by the swing thruster will form a rather large disturbance to the attitude of OTV. Steering the nozzle to track the estimated center of mass (ECM) of OTV can reduce but not remove the disturbance due to the difference between the ECM and the practical mass center (PCM) of OTV. The practical propelling direction will change with the internal motion during the propulsion process and attitude control system should be enabled to guarantee that the propelling direction is collinear with the command. Since the structural parameters have changed,which is due to internal motion and fuel consumption,the dynamic model have to be formulated to determine these time-varying parameters and the required attitude of OTV should be determined as well. Modulating attitude quaternion results in quasi Euler angles. Based on the resulting quasi Euler angles,a novel attitude switching control law is introduced to control the variable-mass OTV. Simulation results show that,even in the case of structural asymmetry,control torque matrix asymmetry,attitude disturbance and strong coupling between the channels,the attitude of OTV can be controlled perfectly,and the proposed attitude control law is effective for the variable-mass OTV with swing thruster.

Study on Initial Alignment Under Large Misalignment Angle

Misalignment angle error model describing the SINS mathematical platform error is presented in this paper following the idea of small misalignment angle error model and large azimuth misalignment angle error model.It can be considered that the three misalignment angles are independent of the rotational sequence in the misalignment error model,but not suitable in the large misalignment error model.The error angle of Euler platform is used to represent the three misalignment angles from theoretical navigation coordinate system to computational navigation coordinate system.The Euler platform error angle is utilized to represent the mathematical platform error and its physical meaning is very clear.The SINS nonlinear error model is deduced by using the error angle of Euler platform and is simplified under the condition of large azimuth error and small error.The simplified results are more comprehensive and accurate than the large azimuth misalignment error model.The damping SINS algorithm and its error model are proposed to change the structure of the strapdown inertial navigation algorithm by using the external damping information.The accuracy of SINS error model of large Euler platform error angle is simulated,and has strong practicability in initial alignment and is conducive to reducing the amount of calculation.

A novel orientation measurement using optical sensor for spherical motor

The measurement of spherical rotor orientation is crucial to the close-loop control of spherical motors. This paper presents a novel method for the measuring of three-degree-of-freedom (DOF) rotor orientation of spherical motors using optical sensors. The spatial orientation of spherical rotor is output in the form of ZXZ Euler angles. Firstly, the structure of the measuring system composed of optical sensors and the patterns on the rotor surface are presented, and the operational principle of recognizing intersection points between the optical ring detectors and the latitude/longitude on the rotor surface is illustrated. The analytical model of input-output characteristic is established for the measuring system of three-DOF rotor orientation. Afterwards, the effect of parameters of the optical ring detectors on the linearity, sensitivity, resolving power and measuring range of the measuring system is analyzed using the analytical model. Finally, the feasibility of the measurement is validated through experiments of prototype measuring system. The analysis is expected to be a basis for the design parameter optimization of the orientation measuring system of a PM spherical motor.

Modeling and Stability Analysis of a Flexible Rotor Based on the Timoshenko Beam Theory

Based on the Timoshenko beam theory,a novel mathematical model of a rotating shaft with centrifugal terms is developed by using Hamilton^principle and Euler angles.The associated conventional model is provided for comparison purpose.The features of the proposed mathematical model are discussed based on some selected coordinate systems.The frequencies and modes are investigated to show the influences of centrifugal terms on the stability of the gyroscopic systems.The results show that the novel model proposed may lose stability due to the centrifugal terms.It is also found that the backward precession mode can be changed into a forward one beyond the critical rotating velocity.

Detecting the filamentary structure of 3D point clouds:Proposal of a wavelet-based method

The analysis of the filamentary structure of the cosmo as well as that of the internal structure of the polar ice suggests the development of models based on three-dimensional(3D)point processes.A point process,regarded as a random measure,can be expressed as a sum of Delta Dirac measures concentrated at some random points.The integration with respect to the point process leads the continuous wavelet transform of the process itself.As possible mother wavelets,we propose the application of the Mexican hat and the Morlet wavelet in order to implement the scale-angle energy density of the process,depending on the dilation parameter and on the three angles which define the direction in the Euclidean space.Such indicator proves to be a sensitive detector of any variation in the direction and it can be successfully implemented to study the isotropy or the filamentary structure in 3D point patterns.

Multiscale analysis of composite material reinforced by randomly-dispersed particles

A multiscale analysis method is presented in which detailed information on the microscopic level is incorporated into macroscopic models capable of simulating damage evolution and ultimate failure.The composite considered is reinforced by randomly-dispersed particles,which reflects the statistical characteristics of real materials,such as cement-based materials.Specifically,a three-dimensional material body is decomposed into many unit cells.Each unit cell is reinforced by a cylindrical particle,the orientation of which is characterized by three Euler angles generated by the random number generator.Based on a detailed finite element analysis,the material properties of the representative volume element are obtained.As verification,the properties of the cylindrical particles are set equal to those of the matrix and the computed‘composite’properties reduce exactly to those of the‘isotropic’material,as expected.Through coordinate transformation,the effective material properties of each unit cell are calculated.The assembly of stiffness matrices of all unit cells leads to the stiffness matrix of the whole specimen.Under the simple tension loading condition,the initial damaged unit cell can be identified according to the vonMises yield criterion.The stiffness of the damaged unit cell will then be reduced to zero and it will cause stress redistribution and trigger further damage.It was found that the reinforcement is effective to mitigate and arrest the damage propagation,and therefore prolongs the material’s lifetime.These results suggest that the hierarchical coupling approaches used here may be useful for material design and failure protection in composites.