Euler Angle Errors Research Articles

Neuro-fuzzy system based proportional derivative gain optimized attitude control of CubeSat under LEO perturbations

Prompt attitude stabilization is more challenging in Nano CubeSat due to its minimal capacity, weight, energy, and volume-constrained architecture. Fixed gain non-adaptive classical proportional integral derivative control methodology is ineffective to provide optimal attitude stability in low earth orbit under significant environmental disturbances. Therefore, an artificial neural network with fuzzy inference design is developed in a simulation environment to control the angular velocity and quaternions of a CubeSat by autonomous gain tuning of the proportional-derivative controller according to space perturbations. It elucidates the dynamics and kinematics of the CubeSat attitude model with reaction wheels and low earth orbit disruptions, i.e., gravity gradient torque, atmospheric torque, solar radiation torque, and residual magnetic torque. The effectiveness of the proposed ANFIS-PD control scheme shows that the CubeSat retained the three-axis attitude controllability based on initial quaternions, the moment of inertia, Euler angle error, attitude angular rate, angular velocity rate as compared to PID, ANN, and RNN methodologies. Outcomes from the simulation indicated that the proposed controller scheme achieved minimum root mean square errors that lead towards rapid stability in roll, pitch, and yaw axis respectively within 20 s of simulation time.

Research on an Adaptive Method for the Angle Calibration of Roadside LiDAR Point Clouds.

Light Detection and Ranging (LiDAR), a laser-based technology for environmental perception, finds extensive applications in intelligent transportation. Deployed on roadsides, it provides real-time global traffic data, supporting road safety and research. To overcome accuracy issues arising from sensor misalignment and to facilitate multi-sensor fusion, this paper proposes an adaptive calibration method. The method defines an ideal coordinate system with the road's forward direction as the X-axis and the intersection line between the vertical plane of the X-axis and the road surface plane as the Y-axis. This method utilizes the Kalman filter (KF) for trajectory smoothing and employs the random sample consensus (RANSAC) algorithm for ground fitting, obtaining the projection of the ideal coordinate system within the LiDAR system coordinate system. By comparing the two coordinate systems and calculating Euler angles, the point cloud is angle-calibrated using rotation matrices. Based on measured data from roadside LiDAR, this paper validates the calibration method. The experimental results demonstrate that the proposed method achieves high precision, with calculated Euler angle errors consistently below 1.7%.

A New Euler Angle Error Model Without Approximation Based on SE(3) for INS

In this paper, a new Euler angle model without approximation based on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SE(3)</i> is proposed to solve the problem that the low common frame performance of conventional Euler angle error model based on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SE(3)</i> for inertial navigation system (INS) when the misalignment angle error is large. Firstly, the Euler angle error is represented by the relationship between Euler angle and the attitude matrix. Then, the left/right error model based on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SE(3)</i> without approximation is rederived, extending the conventional Euler angle error model based on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SE(3)</i> to the application of large misalignment angle error. Finally, the validity of the proposed model is verified by theoretical analysis and field experiments. The results show that the proposed model is more applicable to INS/GPS and INS/DVL, respectively. Especially in the case of large misalignment angle, the convergence and accuracy of the proposed model are higher than the conventional model.

Estimation of Relative Attitude Information of Cooperative Nodes in UAV Cluster

In the collaborative UAV swarm, every node could locate accurately by sharing the accurate navigation information from the leader, through the spatial geometric constraints structured by relative observation. However, the attitude of the followers which only carry cheap navigation sensors can not be optimized through this method. Low-precision attitude system has wide application prospects in military and civil fields such as robots, UUV and UAV, but the existing filtering methods cannot maintain high accuracy of attitude when the carrier move for a long time or maneuvers with high dynamics. This paper provides a method to obtain the relative attitude Euler Angle between the leader and the follower using the visual vector obtained by binocular camera and the target recognition algorithm. In this paper, the simulation and experiment of the proposed method are carried out. The experimental results show that under the good visual conditions, the relative attitude Euler Angle error obtained by identifying distinguishable targets is less than 2 degrees, which meets the demand of attitude determination for cooperative navigation.

Relative Pose Estimation of Non-Cooperative Space Targets Using a TOF Camera

It is difficult to determine the accurate pose of non-cooperative space targets in on-orbit servicing (OOS). The visual camera is easily affected by the extreme light environment in space, and the scanning lidar will have motion distortion when the target moves at high speed. Therefore, we proposed a non-cooperative target pose-estimation system combining a registration and a mapping algorithm using a TOF camera. We first introduce the projection model of the TOF camera and proposed a new calibration method. Then, we introduce the three modules of the proposed method: the TOF data preprocessing module, the registration module and the model mapping module. We assembled the experimental platform to conduct semi-physical experiments; the results showed that the proposed method has the smallest translation error 8 mm and Euler angle error 1° compared with other classical methods. The total time consumption is about 100 ms, and the pose tracking frequency can reach 10 Hz. We can conclude that the proposed pose-estimation scheme can achieve the high-precision pose estimation of non-cooperative targets and meet the requirements necessary for aerospace applications.

Motion error analysis of a shield machine tool-changing robot based on a screw-vector method

Industrial robots are widely used in various industrial fields, such as handling and welding, due to their good repeat positioning accuracy. The motion error determines the absolute accuracy. For robot design, dimensional parameter errors and drive parameter errors, a mathematical model of a kinematic exponential product with error screws was proposed. The influence of different rod lengths and transmission errors on the accuracy of the end motion was analysed. A composite analysis method based on screw theory and vector method is proposed for the spatial deflection error of robot rotating joints with clearance. By using screw theory, a mathematical error model of the axial movement and spatial deflection of the joint gap was established. A mathematical model of joint space radial movement was established by using the three-dimensional vector method. Through numerical simulation, the position distribution law of the random error of the robot terminal in the workspace and the distribution of the plane projection density were obtained. By solving the attitude matrix, the distribution of each Euler angle error was obtained. A simulation test was carried out to verify the model's correctness. The calculation showed that the method is simple and correct, and the obtained error distribution characteristics are of great significance to improving robotic kinematic calibration accuracy and optimising the spatial position error distribution.

A General Calibration Method for Dual-PTZ Cameras Based on Feedback Parameters

With the increasing application of dual-PTZ (Pan-Tilt-Zoom) cameras in intelligent unmanned systems, research regarding their calibration methods is becoming more and more important. The intrinsic and extrinsic parameters of dual-PTZ cameras continuously change during rotation and zoom, resulting in difficulties in obtaining precise calibration. Here, we propose a general calibration method for dual-PTZ cameras with variable focal length and posture under the following conditions: the optical center of the camera does not coincide with the horizontal and pitch rotation axes, and the horizontal and pitch rotation axes are not perpendicular to each other. We establish a relationship between the intrinsic and extrinsic parameters and the feedback parameters (pan, tilt, zoom value) of dual-PTZ cameras by fitting and calculating previous calibration results acquired at specific angles and zoom values using Zhang’s calibration method. Subsequently, we derive the intrinsic and extrinsic parameter calculation formula at arbitrary focal length and posture based on the camera’s feedback parameters. The experimental results show that intrinsic and extrinsic parameters computed using the proposed method can better meet precision requirements compared with the ground truth calibrated using Zhang’s method. The average focal length error is less than 4%, the cosine similarity of the rotation matrix between the left and right cameras is more than 99.8%, the translation vector error is less than 1%, and the recalculated Euler angle errors are less than 1 degree. Our work can quickly and accurately obtain intrinsic and extrinsic parameters during the use of the dual-PTZ camera.

RETRACTED ARTICLE: On-orbit calibration of sun sensor’s central point error for triad

ABSTRACT In this paper, a novel sun sensor which has been applied on orbit since 2018 is introduced. The remote data transmitted from the satellite is analyzed to show its performance. In the lighting area, the sun sensor can give the sun vector which used for the attitude determination. From the data, the center point error is found to be the most significant factor that affects the accuracy of the sun sensor. In the “Sun pointing” work mode, the real output of the sun sensor is different from the theoretical output. The data from the star sensor is used for compensating the center point error based on ellipse fitting. The triad algorithm is affected by the center point error of the sun sensor. The simulation only considers this kind of error. And the result shows that it can decrease the Euler angle errors, so that improves the accuracy of triad algorithm.

A Double-Step Unscented Kalman Filter and HMM-Based Zero-Velocity Update for Pedestrian Dead Reckoning Using MEMS Sensors

In this paper, we propose a novel method for pedestrian dead reckoning (PDR) using microelectromechanical system magnetic, angular rate, and gravity sensors, which includes a double-step unscented Kalman filter (DUKF) and hidden Markov model (HMM)-based zero-velocity-update (ZVU) algorithm. The DUKF divides the measurement updates of the gravity vector and the magnetic field vector into two steps in order to avoid the unwanted correction for the Euler angle error. The HMM-based ZVU algorithm is developed to recognize the ZVU efficiently. Thus, the proposed PDR method can reduce the position drift caused by the heading error and fault zero-velocity measurement. Experimental results demonstrate that the proposed method achieves better yaw estimate, as well as zero-velocity measurement, and obtains more accurate dead-reckoning position than other methods in the literature.

Design of Attitude Control Servomechanisms with Fluid Ring and CMG for Rigid Satellite

Satellites cover a wide range of space missions as remote sensing. Accomplishment of the mission depends on satellite’s stability maintenance and direction. The main task of the attitude control system is to provide stability to the satellite against external disturbances. Such perturbations are caused due to aerodynamic drag, solar radiation and magnetic field. The attitude dynamics model and the development of a controller to stabilize the three degrees of freedom rotational angles are quite important steps in the design of satellites. Although there are several actuators to provide attitude determination and control, a novel type is considered in this paper. This new actuator is the fluid contained inside one or more rings and fluid flow supplied by pump. The required torque control made by change of angular velocity of fluid. In this paper, the satellite is considered rigid and nonlinear dynamics equations were written. Because of the importance of satellite mission, the failure of the pyramid-shaped satellite with an additional ring fluid will be discussed. Satellite attitude control is carried out with an Euler angle errors control law. The performance of this actuator is compared with moment control gyro and their advantages on to each other have been described.

An attitude determination method based on convected Euler angle error model for SINS/CNS integrated system

The attitude determination method plays an important role in SINS/CNS integrated system for spacecraft. Since the misalignment angels are indirect measurements, the misalignment angle model used in the existing attitude determination method can cause transformation errors. To solve the problem, an attitude determination method based on convected Euler angle error model for SINS/CNS integrated system is proposed. The attitude error propagation is analyzed, and the convected Euler angle error model is derived. Furthermore, the state equation of SINS/CNS integrated system is established. The Kalman filter estimates and compensates the Euler angle errors. Finally, simulation results verified that the proposed method can improve the attitude accuracy compared to the conventional misalignment angle method.

ROBUST POSITIONING OF DRONES FOR LAND USE MONITORING IN STRONG TERRAIN RELIEF USING VISION-BASED NAVIGATION

For land use monitoring, the main problems are robust positioning in urban canyons and strong terrain reliefs with the use of GPS system only. Indeed, satellite signal reflection and shielding in urban canyons and strong terrain relief results in problems with correct positioning. Using GNSS-RTK does not solve the problem completely because in some complex situations the whole satellite's system works incorrectly. We transform the weakness (urban canyons and strong terrain relief) to an advantage. It is a vision-based navigation using a map of the terrain relief. We investigate and demonstrate the effectiveness of this technology in Chinese region Xiaoshan. The accuracy of the vision-based navigation system corresponds to the expected for these conditions. . It was concluded that the maximum position error based on vision-based navigation is 20 m and the maximum angle Euler error based on vision-based navigation is 0.83 degree. In case of camera movement, the maximum position error based on vision-based navigation is 30m and the maximum Euler angle error based on vision-based navigation is 2.2 degrees.

A General Euler Angle Error Model of Strapdown Inertial Navigation Systems

Attitude error models play an important role in analyzing the characteristics of navigation error propagation for the design and operation of strapdown inertial navigation systems (SINS). However, the majority of existing attitude error models focus on misalignment, rather than Euler angle errors. Misalignment cannot directly describe attitude error propagation, which is an indirect measurement. To solve the problem, a general Euler angle error model of SINS is proposed. Based on Euler angle error propagation analysis, relative Euler angle errors, and convected Euler angle errors are introduced to compose the general Euler angle error model. Simulation experiments are carried out to verify the proposed model.

Fast Fine Initial Self-alignment of INS in Erecting Process on Stationary Base

Fine initial alignment is vital to the Inertial Navigation System (INS) before the launching of a missile. The existing initial alignment methods are mainly performed on a stationary base after the missile has been erected to the vertical state. However, these methods consume extra alignment time and some state variables have poor degrees of observability, thus losing the rapidity of alignment. In order to solve the problem, a fast fine initial self-alignment method of a missile-borne INS is proposed, which is performed during the erecting process on a stationary base. The convected Euler angle error is modelled to optimise the erecting manoeuvre which can prevent large Euler angle errors and improve the system observability. The fine initial alignment model is established to estimate and correct the initial misalignment. Several experiments verify that the proposed method is effective for improving the rapidity of the fine initial alignment for a missile-borne INS.

Error analysis of analytical coarse alignment formulations for stationary SINS

This paper presents a comprehensive error analysis of coarse alignment formulations for stationary strapdown inertial navigation systems (SINS). Analytical expressions for the residual normality, orthogonality, alignment, and Euler angle errors are systematically derived, allowing us to establish comparisons in terms of rapidity, accuracy, and autonomy requirements. For the purpose of the error analysis, geographic latitude and local gravity acceleration uncertainties are considered, in addition to the inertial sensor uncertainties. As the main contribution of this paper, an improved coarse alignment method is proposed, which is based on orthonormality constraints existing between the Euler angles and the attitude matrix. In contrast to the traditional methods, the proposed formulation does not imply normality and orthogonality errors, besides producing time-independent alignment and Euler angle errors. The latter is seen to be particularly interesting for situations wherein, due to time constraints, posterior fine alignment and orthonormalization procedures cannot be implemented. The superiority of the proposed formulation is validated through simulated and experimental tests, regardless of the SINS initial orientation. The accuracy degradation produced by each alignment formulation in the navigation stage is used as the performance index.

Optimizing the Satellite Control Gains with Nonlinear Motion Equations using SQP Method

functions of control system are attitude maneuver and attitude stability. The capability to attitude-maneuver a satellite is based on using control torques. In this paper, the torques generated by Euler angle errors and quaternion error vector for small attitude commands are compared and then the same is done for large attitude commands. It's founded that Euler angle errors characterized by a fixed control do not produce the desirable response. The SQP optimization method also used to optimize calculated control gains. This SQP optimization method with the following provisions such as maximum settling time, maximum rise time, maximum overshoot and maximum steady state error causes that the Euler angles error method provides an appropriate responses.

EULER ANGLE ERROR COMPUTATION AND THRUST VECTOR CONTROL SCHEME FOR INITIAL TURNING PHASE OF A VERTICAL LAUNCH SURFACE TO AIR MISSILE

A vertical launch missile requires to be turned towards the Predicted Interception Point (PIP) with the target within few seconds from the launch. The autopilot used for the same requires the error in Euler Angles between the missile and the target to be supplied, which is generally computed using Error Quaternions approach [1]. For some kinds of engagement scenarios, say a Near Boundary Low Altitude target, the turn angle required in the pitch plane during the initial phase can become more than 90 degrees. In such cases, the conventional 3-2-1 frame transformation method fails to compute the Euler Angle errors correctly. As an alternative approach the Euler Angle error computation using 2-3-1 frame transformation is proposed in this paper. After computing the Euler Angle Errors, the desired turning is achieved by Thrust Vector Control [2] using jet vanes or thrusters. The initial turning using Aerodynamic control is not desirable because of low dynamic pressure, where as the usage of jet vanes brings more hardware complications for small tactical missiles. The possibility of using thrusters for initial turning phase in a short range tactical missile is studied in this paper with the help of simulation results.

A Novel Method to Integrate IMU and Magnetometers in Attitude and Heading Reference Systems

Modern attitude and heading reference systems (AHRS) generally use Kalman filters to integrate gyros with some other augmenting sensors, such as accelerometers and magnetometers, to provide a long term stable orientation solution. The construction of the Kalman filter for the AHRS is flexible, while the general options are the methods based on quaternion, Euler angles, or Euler angle errors. But the quaternion and Euler angle based methods need to model system angular motions, and, meanwhile, all these three methods suffer from nonlinear problems which will increase the system complexities and the computational difficulties. This paper proposes a novel implementation method for the AHRS integrating IMU and magnetometer sensors. In the proposed method, the Kalman filtering is implemented to use the Euler angle errors to express the local level frame (lframe) errors, rather than express the body frame (bframe) errors as the customary methods do. A linear system error model based on the Euler angles errors expressing thelframe errors for the AHRS has been developed and the corresponding system observation model has been derived. This proposed method for AHRS does not need to model system angular motions and also avoids the nonlinear problem which is inherent in the commonly used methods. The experimental results show that the proposed method is a promising alternative for the AHRS.