Coordinate Transformation Matrix Research Articles

Research on field optimization model of heliostat based on ray tracing

In this paper, the average optical efficiency and output power of the tower solar thermal power station are studied. The ray tracing method is used especially to the calculation process and details of the shadow blocking efficiency and collector truncation efficiency are carefully derived. Combined with intelligent optimization algorithm, the key parameters [1][2] of the mirror field layout are optimized. Then, the main method used in this paper is ray tracing. For the calculation of cosine efficiency and shadow blocking efficiency, the coordinate transformation matrix is established in this paper, which simplifies the coordinate calculation. For the calculation of collector truncation efficiency, based on Monte Carlo simulation, and an accurate collector truncation efficiency model is established by random sampling of large samples. Finally, MATLAB software is used to calculate the efficiency of the heliostat in different coordinate positions. The average optical efficiency (62.71%), cosine efficiency (75.65%), shadow blocking efficiency (94.54%), collector truncation efficiency (98.85%), thermal output power (34.77MW), and average annual thermal output power per unit area mirror (0.5535kW/m2) are obtained. This model not only helps to understand the propagation mode of light in the heliostat field, but also can quantitatively evaluate the loss of light.

Position and Attitude Tracking Controllers Using Lyapunov Transformations for Quadrotors

In this paper, a novel feedback control strategy for quadrotor trajectory tracking is designed and experimentally tested with proof of exponential stability, using the Lyapunov transformations theory. The controller is derived from an inner-outer loop control structure, namely by considering the position system coupled through an interconnection term with the attitude system. For the design of the position controller, the considered dynamics are worked on the body frame, which is uncommon in the literature, and its synthesis derives from theories such as Pontryagin’s maximum principle, Lyapunov theory, and Linear Quadratic Regulator (LQR), which ensure Input-to-state stability, steady-state optimality, and global exponential stability. The attitude system is based on an error quaternion parameterization via a nonlinear coordinate transformation matrix followed by a state input feedback, rendering the system linear and time-invariant. Under a correct transformation, LQR theory ensures almost exponential stability and steady-state optimality for the overall interconnected closed-loop systems. Experimental and simulation results illustrate the performance of the tracking system onboard a quadrotor.

GNSS-Assisted Visual Dynamic Localization Method in Unknown Environments

Autonomous navigation and localization are the foundations of unmanned intelligent systems, therefore, continuous, stable, and reliable position services in unknown environments are especially important for autonomous navigation and localization. Aiming at the problem where GNSS cannot continuously localize in complex environments due to weak signals, poor penetration ability, and susceptibility to interference and that visual navigation and localization are only relative, this paper proposes a GNSS-aided visual dynamic localization method that can provide global localization services in unknown environments. Taking the three frames of images and their corresponding GNSS coordinates as the constraint data, the GNSS coordinate system and world coordinate system transformation matrix are obtained through horn coordinate transformation, and the relative positions of the subsequent image sequences in the world coordinate system are obtained through epipolar geometry constraints, homography matrix transformations, and 2D–3D position and orientation solving, which ultimately yields the global position data of unmanned carriers in GNSS coordinate systems when GNSS is temporarily unavailable. Both the dataset validation and measured data validation showed that the GNSS initial-assisted positioning algorithm could be applied to situations where intermittent GNSS signals exist, and it can provide global positioning coordinates with high positioning accuracy in a short period of time; however, the algorithm would drift when used for a long period of time. We further compared the errors of the GNSS initial-assisted positioning and GNSS continuous-assisted positioning systems, and the results showed that the accuracy of the GNSS continuous-assisted positioning system was two to three times better than that of the GNSS initial-assisted positioning system, which proved that the GNSS continuous-assisted positioning algorithm could maintain positioning accuracy for a long time and it had good reliability and applicability in unknown environments.

A study of teeth generation for arbitrary-shaped sprockets

ABSTRACT In the noncircular sprocket designing process, drawing the teeth cannot be automatically performed using any function in the drawing software, and it needs complicated manual operations and adjustments. The accuracy and time waste are big problems here. This paper proposes a procedure to automatically generate a complete 3D sprocket design from a set of sprocket pitch coordinates. Japanese standard tooth profile (JIS B 1801) is used as an example model in the procedure development. First, the tooth profile equation is derived using the theory of gearing in a particular coordinate system. Subsequently, the coordinate transformation matrix is built to attach the tooth profile on every sprocket pitch coordinate in the correct direction, remove some coordinates surpassing the outer diameter limit, and build the complete 3D sprocket profile. The proposed procedure can be implemented into programming languages with the sprocket pitch coordinate file as the input and the set of sprocket teeth coordinate as the output. With the proposed procedure, a 3D design of any shape sprocket can be generated quickly and accurately.

A dual-loop feedback trajectory tracking control for rock drilling hydraulically driven manipulator

This paper is devoted to proposing a feedback trajectory tracking control method for hydraulically driven rock drilling robotic manipulators. The rock drilling robot has a large-scale long boom and multiple joints (6R-2P), so the deformation of the arm may not be neglected. A kinematic model with the flexible deformation of the boom is developed by adding a modified coordinate transformation matrix to the general model. Each joint motion is determined by solving the inverse kinematic model in an optimization algorithm, which aims at minimizing the positional error and smoothing the motion. A dual-loop feedback controller is proposed to track the end-effector’s position and orientation. Based on the model predictive control (MPC) method, the inner-loop controller controls the cylinder motion by controlling the cylinder motion. The outer-loop controller uses the fuzzy-PID control to correct the position error which is caused by the inner-loop controller. Several reference trajectories are designed to validate the effectiveness of the proposed dual-loop control strategy, which demonstrates it has higher accuracy and lower control fluctuation than single-loop and other dual-loop controllers.

The six-degrees-of-freedom attitude measurement instrument for the large aperture mirror using the prepressing sensors and flexible supporting.

To achieve precise measurement of a large aperture mirror, a six-degrees-of-freedom (6-DOF) measurement instrument is designed to monitor and calculate the real-time attitude of the mirror. Magnetoelectric displacement sensors are prepressed, and a flexible sensor supporting is designed to achieve high-accuracy measurement. The relationship between 6-DOF displacements of the mirror and the six sensor values can be obtained using the coordinate system transformation and Jacobian matrix. The Newton's iteration method is used to decouple the strong coupling measurement system, and 6-DOF displacements are obtained. The displacements directly measured by using laser sensors are compared with the calculated values in the experiments, the minimum average error of the measured displacement is 1.87%, and the mean difference of the displacement is 0.43 µm.

Finite Element Analysis of Curved Beam Elements Employing Trigonometric Displacement Distribution Patterns

A finite element analysis (FEA) model was developed for Euler and Timoshenko curved beam elements by incorporating trigonometric displacement distribution patterns. Local polar coordinate stiffness matrices were derived based on force-displacement relations and static equilibrium conditions. By employing the kinetic energy theorem and triangular displacement functions, an expression for the consistent mass matrix of a curved beam element was obtained. A coordinate transformation matrix for the curved beam element was established by relating the local polar coordinate system to the global polar coordinate system. Calculation programs were implemented in the Fortran language to evaluate the static–dynamic performance and natural frequency characteristics of curved beam bridges. The obtained results were then compared with those obtained using ANSYS solid models and “replace curve with straight” beam element models. The comparison demonstrated a strong agreement between the results of the Euler and Timoshenko curved beam element models and those of the ANSYS solid models. However, discrepancies were observed when comparing with the results of the “replace curve with straight” beam element model, particularly in terms of lateral static displacement. This discrepancy suggests that the characteristic matrix derived in this study accurately represents the stiffness and mass distribution of the curved beam, making it suitable for mechanical performance analysis of curved beam bridges. It should be noted that the “replace curve with straight” method overlooks the initial curvature and the bending–torsion coupling effects of a curved beam, resulting in calculation deviations. On the other hand, the use of curved beam elements in numerical analysis provides a simple and practical approach, which facilitates further research in areas such as vehicle–bridge coupling vibrations and seismic analysis of curved beam bridges.

The Influence of Coordinate Systems on the Stability Analysis of Lateral–Torsional Coupled Vibration

Stability analysis of lateral–torsional coupled vibration is obligatory for rotating machinery, such as aero-engines. However, the state-of-the-art method may lead to stability misjudgment under different coordinate systems. The cause of this misjudgment has not yet been well explored. The purpose of this paper is to clarify the error source of the stability analysis in a more comprehensive manner. A vertical Jeffcott rotor model including torsion vibration is built, and the Lagrange approach is applied to establish the motion equations. The coordinate transformation matrix is used to transfer the motion equations into the rotating coordinate system, making the coefficients of the motion equation constants. The differences in the unstable speed regions in the two coordinate systems are captured. The limitations of the Floquet theory and Hill’s determinant analysis in the stability estimation of the lateral–torsional coupled vibration are explained. It is found that, for Hill’s method, increasing the number of the harmonic truncation cannot correct the misjudgment, and the matrix truncation is the fundamental error source. The above research provides more accurate theoretical support for the analysis of the lateral–torsional coupling instability of rotors.

High-Precision Calibration of a Monocular-Vision-Guided Handheld Line-Structured-Light Measurement System.

Due to the advantages of simple construction, easy application and good environmental suitability, handheld structured-light measurement systems have broad application prospects in 3D measurements. Here, a monocular-vision-guided line-structured-light measurement system is developed, and the posture of the handheld device can be obtained via a specifically designed target attached to it. No more marker points need to be adhered onto the object under inspection. The key for the system calibration is to obtain the coordinate transformation matrix from the sensor to the featured target coordinate system. The mathematical model of the system is first established. Then, an improved multi-view calibration method is proposed, where a selection process for the image pairs is conducted for accuracy improvement. With this method, the maximum relative error of the measured stair heights can be reduced from 0.48% to 0.16%. The measurement results for the specific parts further verified the effectiveness of the proposed system and the calibration method.

Feature-constrained real-time simultaneous monitoring of monocular vision odometry for bridge bearing displacement and rotation

The displacement and rotation are critical indicators of bridge's health, especially for the key components of the bridge such as bridge bearings. This study presents a real-time simultaneous measurement method of bridge bearing displacement and rotation to realize round-the-clock structure monitoring. The main contributions include: (1) A displacement and rotation simultaneous measurement algorithm and system is developed based on feature-constrained monocular visual odometry (VO), which uses image sequences of infrared array lamp targets with multiple feature constraints as visual input to construct the mathematical relationship between displacement and rotation and coordinate system transformation matrix. (2) A two-step parameter optimization strategy is proposed based on adaptive multi-window centroid array tracking and transformation matrix purification and refinement, effectively improving displacement and rotation measurement accuracy and robustness. The effectiveness of the proposed method is verified in the laboratory experiment and the actual bridge bearing monitoring of the Huangpu Pearl River Bridge.

Design, integration, and evaluation of a robotic peach packaging system based on deep learning

Fruit packaging is one of the most time-consuming and labor-intensive tasks during postharvest commercialization. With the aging of the global population, it is necessary to apply robot to replace the manual manipulation. However, robotic packaging for fragile fruit is more complicated and difficult, compared with other postharvest processes, such as quality detection and grading. In this study, for better positioning accuracy and grasping robustness, we developed a prototype for peach packaging robot based on deep learning. First, the dataset for peach object detection was built, and YOLO v5 models with different width and depth were trained in an end-to-end manner on this dataset. Considering the requirements on both accuracy and real-time performance in fruit postharvest processing, YOLO v5 - S was finally adopted as the peach detection model for robotic manipulation, which can achieve mAP-50 = 0.996 on validation set and runs at 142.86 fps on RTX 3060. Next, the “Eye-on-Base” hand eye calibration method was used to solve the coordinate transformation matrix from the camera coordinate system to the robot base coordinate system. The results on landmark positioning experiment showed that the positioning error along X and Y axes was 4.87 mm and 5.00 mm on average, respectively. The positioning error alone Z direction was 18.47 mm on average, which was caused mainly by the depth perception error of the RGB-D camera. In the grasping experiment, the influence of the depth perception accuracy was explored, the grasping success rate for small, medium, and large size of peaches was 100 %, 97 %, and 97 %, respectively. Besides, the entire pipeline proposed in this study took 252.81 ms on average for depth perception, object detection, coordinate transformation, and grasping path planning. Finally, the early stage bruise of the peaches was also evaluated through SFDI technology. In general, this research provided a feasible and reliable scheme for the fruit packaging robot, which is potential to be deployed in postharvest commercialization.

Research on Target Tracking Algorithm of Micro-UAV Based on Monocular Vision

Aiming at the problem of limited payload and endurance of micro-UAV, the target tracking algorithm based on monocular vision is proposed. Since monocular vision cannot directly measure distance between the UAV and the target, triangulation and triangle similarity are used to calculate the distance information. Then, a target tracking method based on Kalman filter and KCF is designed. The tracking result of KCF is modified by Kalman filter to solve the problem of target occlusion. Finally, the position of the target in the world coordinate system is calculated through the coordinate transformation matrix, which is used to control the UAV for tracking the moving target. In order to verify the feasibility of the algorithm, target size estimation and target tracking algorithms are carried out. The experimental results show that the proposed algorithm can track the moving target effectively under the condition of short-term occlusion.

Design, modeling and solar tracking control for a novel parabolic dish solar concentrator

AbstractA novel parabolic dish solar concentrator based on the improved 3-RPS parallel manipulator to drive the reflective mirror facet is proposed and designed, which can not only automatically adjust the position and orientation of the reflective mirror facet but also have the advantages of independent drive, high stiffness and no cumulative error. Then, using the coordinate transformation matrixes of the novel parabolic dish solar tracking platform, the kinematics models of the 3-RPS parallel manipulators associated with the solar altitude and azimuth angles are established. The altitude and azimuth angles of the solar movement at the installation location are calculated according to the calculation formula of solar position. To solve the problem of too many telescopic rods of the 3-RPS parallel manipulator, a genetic algorithm is used to optimize the height of the concentrator’s center of mass. Then the ideal trajectory and attitude of each telescopic rod of the 3-RPS parallel manipulators at different times of the day can be obtained with the inverse kinematics. The particle swarm optimization (PSO)-proportional-integral-derivative (PID) controller, which uses PSO algorithm to tune PID parameters, is proposed for solar trajectory tracking of the novel parabolic dish solar concentrator. The visual simulation model of the parabolic dish system is established in Simscape Multibody, and the trajectory tracking control experiment is carried out. The experimental results show that the trajectory tracking error of the novel dish solar tracking platform can be within 2.6 mm by using the PSO-PID controller.

A unified vibration modeling of open cylindrical shell-rectangular plate coupling structures based on the dynamic stiffness method

This paper presents a unified vibration modeling for free and forced vibration analysis of coupled open cylindrical shell-plate structures (COSPS). In the model, the coupled structure is first split into several open cylindrical shells and rectangular plates, and then based on Kirchoff's thin plate theory and Flügge's thin shell theory, the dynamic stiffness (DS) matrix of each substructure is separately established by applying the generalized superposition method and the projection method. Subsequently, according to the continuity and equilibrium conditions of the coupled boundary, the coordinate transformation matrix of each substructure is derived. After obtaining fundamental DS matrices and their coordinate transformation matrices, global DS matrices of various COSPS are assembled using a strategy similar to the finite element method (FEM) without repeating the theoretical derivation. To verify the convergence and reliability of the current formulation, free vibration and forced vibration analysis of three types of coupled structures are carried out, and the results are compared with those from published works and FEM solutions. In addition, an experimental model of a coupled structure is established and an experimental test is performed. The comparison results show that the proposed model is reliable and effective, and its modeling process is more direct and convenient. This work not only greatly expands the application scope of the DSM but also provides a new idea for the vibration analysis of COSPS.

Simple AR Method for Rehabilitation Support System Based on 3D Pose Estimation

Studies have been conducted on the application of Augmented Reality to support rehabilitation of motor function recovery. The goal of these studies is to facilitate functional recovery training through patient interaction with virtual objects generated by AR. Many of them use special devices such as depth sensors to superimpose virtual objects at appropriate positions in images, but a simple method that does not require such a device is desired. In order to realize superimposition using only a personal computer (PC) with a camera, this study utilizes a deep neural network that estimates the 3-dimensional (3D) coordinates of keypoints, such as human joints, from camera images. Specifically, a coordinate transformation matrix for superimposition is calculated from the 3D coordinates of keypoints. In order to clarify the effectiveness of this method, we conducted an experiment to evaluate the superimposition accuracy. The results show that the accuracy was highest in the space near the keypoints that had been used to compute the coordinate transformation matrix, and the accuracy was even higher when the number of keypoints was small. This indicates that this method is more suitable for localized training such as hand rehabilitation than for whole-body training. Since this method can be used only with a PC with a camera, it is expected to be widely used for rehabilitation support.

A real-time shaft alignment monitoring method adapting to ship hull deformation for marine propulsion system

Shaft alignment states are strictly stipulated in the marine propulsion system. However, there are relatively limited studies on shaft alignment monitoring and control considering the effects of ship hull deformation (SHD). SHD can be caused by wave load, loading, depth, speed, etc., and leads to various relative displacements at different shaft supporting points between the ship foundation and the support bearings of the propulsion system. It leads to shaft misalignment, increases shaft vibration and noise, and even endangers the safety of shaft system during the operation stages. To overcome this problem, a real-time shaft alignment monitoring method based on laser displacement sensors (SAMM/LDS) is proposed. Firstly, the defects of a present shaft alignment monitoring method based on eddy current displacement sensors (SAMM/ECDS) are analyzed when considering the effects of SHD. The structure and working principle of a shaft alignment monitoring system adapted to SHD (SAMS/SHD) are proposed. It consists of three sub-systems: the shaft alignment monitoring sub-system adapting to SHD (SAMSS/SHD), the present shaft alignment monitoring sub-system (SAMSS/P), and the shaft alignment correcting sub-system (SACSS). Based on SHD data-driven, SAMS/SHD can not only take advantage of SAMSS/P for long-time operations but also reflect SHD by exploiting the advantages of SAMSS/SHD. Secondly, SAMM/LDS is deduced. Two laser displacement sensors (LDS) are placed on the driving shaft and the driven shaft to reflect the spatial relative displacement and attitude information affected by SHD. Therefore, two reference coordinate systems are fixed at the center of LDS, and the coordinate expressions of their imaging points are derived using a 4 × 4 homogeneous coordinate transformation matrix. For reducing computing complexity in engineering applications, a simplified monitoring model is proposed for very small rigid-body rotational angularities. Finally, the effectiveness and testing accuracy of the SAMM/LDS is verified on a five-DOF platform which can simulate the effects of SHD. The SAMM/LDS can be used to realize real-time and high-precision shaft alignment monitoring for marine propulsion system which can adapt to the effects of SHD and so on. Based on the foundation of this research, compensation control algorithms to solve the misalignment effects deduced by SHD will be studied for marine propulsion system with resilient mounts in the next few years.

Neural network-based robot nonlinear output feedback control method

In order to improve the accuracy of robot terminal pose tracking and the anti-interference performance of robot nonlinear motion path control, a nonlinear output feedback control method based on neural network is proposed. Construct the coordinate transformation matrix of the connecting rod, calculate the linear and angular velocity of the nonlinear motion of the robot, then calculate the sum of the kinetic energy of each connecting rod of the robot, and establish the motion equation of the robot. The structure of BP neural network is analyzed, and the motion equation is solved by BP neural network. Finally, a Fractional Order PID controller is designed and BP neural network is constructed to control the nonlinear motion equation of the robot to complete the output feedback control of the robot. The experimental results show that the end attitude tracking error of this method is the smallest, and it best fits the actual nonlinear trajectory of the robot. It shows that this method can accurately track the end posture of the robot, and can still effectively control the trajectory of the robot in the interference environment.

Large-Scale Aircraft Pose Estimation System Based on Depth Cameras

In the fields of wind tunnel measurement and aerospace, the real-time pose information of aircraft is an important index. In this paper, we propose a large-scale aircraft pose estimation system, in which depth cameras are used to scan the entire aircraft model in multiple directions. Using a principal component analysis (PCA) featuring vectors as the target coordinate system through a coordinate transformation matrix for the point cloud calibration of aircraft, we merge the complete aircraft model with the point cloud. An intrinsic shape signature (ISS) key point extraction and a signature of histograms of orientations (SHOT) feature description are used to form feature descriptors. The scale of the point clouds is reduced, and coarse registration of the point clouds is performed by feature matching and random sample consensus (RANSAC) mismatching. The robustness of the algorithm is improved, and the initial pose estimation is achieved for the precise registration of point clouds. The experimental results demonstrate that the proposed system can achieve an angle measurement accuracy of 0.05°.

A method for dynamic analysis and design of joined conical-cylindrical shells based on the model condensation

In the vibration analysis of joined conical-cylindrical shells, mode methods are widely used. However, from the practical results, boundary conditions affect significantly on the vibration behaviors of these structures. Therefore, the assumed modes may not obtain accurate results, which is terrible for structural design or vibration control. Finite element method (FEM) can be used to solve such problems, whereas the time and hardware costs are unacceptable, especially for the structural design and vibration control. The Craig-Bampton (C-B) method takes into account the advantages of both FEM and mode theory, and is very suitable for the dynamic analysis. This paper studies the advantages and feasibility of the C-B method in vibration analysis of joined conical-cylindrical shells. Using the eight-node super-parametric shell element and Hamilton's principle, the finite element equation of motion for the joined conical-cylindrical shell is established. The reduced FE model of the structure is obtained by using the C-B method. A process for efficient structural dynamic design is proposed. The correctness of the model reduction based on C-B method is verified through modal measurement experiments. In addition, some examples are given to illustrate the advantages of the C-B method in the optimization design and dynamic analysis of joined conical-cylindrical shell structures. Finally, a solution idea of coordinate transformation matrix is proposed when there are much more interfaces between substructures.

Framework for Geometric Information Extraction and Digital Modeling from LiDAR Data of Road Scenarios

Road geometric information and a digital model based on light detection and ranging (LiDAR) can perform accurate geometric inventories and three-dimensional (3D) descriptions for as-built roads and infrastructures. However, unorganized point clouds and complex road scenarios would reduce the accuracy of geometric information extraction and digital modeling. There is a standardization need for information extraction and 3D model construction that integrates point cloud processing and digital modeling. This paper develops a framework from semantic segmentation to geometric information extraction and digital modeling based on LiDAR data. A semantic segmentation network is improved for the purpose of dividing the road surface and infrastructure. The road boundary and centerline are extracted by the alpha-shape and Voronoi diagram methods based on the semantic segmentation results. The road geometric information is obtained by a coordinate transformation matrix and the least square method. Subsequently, adaptive road components are constructed using Revit software. Thereafter, the road route, road entity model, and various infrastructure components are generated by the extracted geometric information through Dynamo and Revit software. Finally, a detailed digital model of the road scenario is developed. The Toronto-3D and Semantic3D datasets are utilized for analysis through training and testing. The overall accuracy (OA) of the proposed net for the two datasets is 95.3 and 95.0%, whereas the IoU of segmented road surfaces is 95.7 and 97.9%. This indicates that the proposed net could accomplish superior performance for semantic segmentation of point clouds. The mean absolute errors between the extracted and manually measured geometric information are marginal. This demonstrates the effectiveness and accuracy of the proposed extraction methods. Thus, the proposed framework could provide a reference for accurate extraction and modeling from LiDAR data.