Homogeneous Coordinate Transformation Research Articles

Analysis and Design of Infrared Search and Track System with Afocal Zoom Telescope

The infrared search and track system (IRST) is a type of special electrical optical (EO) system that can be used in various scenarios to fulfill situation awareness, reconnaissance, and tracking of targets. We proposed a homogeneous coordinate transformation method to analyze the residual image wandering induced by the rotation of the scanning platform and the compensation fast steering mirror and help with the commonly trivial selection of the telescope magnification and the objective focal length. The analysis and simulation are carried out with specified IRST optics, which adopt a 640 × 512 array and 15 μm pitch detector, in a focal range of 60 mm~360 mm, and a scan speed of 360°/s to 60 °/s at 50 fps, and optical specifications are determined further. The presented optical system, with only three kinds of common infrared materials, works at 3.7 μm~4.8 μm, demonstrates good image performance and tolerance characteristics, and shows potential in manufacturing. Also, the resulting image wandering of 8 μm, less than a 0.6-pixel size, at an integral time of 16 ms, proves the correctness of the method and makes the scheme of considerable interest for electrical optical systems.

Action recognition for sports combined training based on wearable sensor technology and SVM prediction

In the field of sports, coaches have mainly relied on observing the performance of athletes on the spot to formulate suitable training plans for athletes, which has extremely high requirements for the professionalism of coaches. Based on the above requirements, this paper designs a sports action recognition system for sports enthusiasts based on the SVM algorithm optimization model, and for the purpose of verifying the applicability of the system to different sports fields, experiments are carried out on basketball actions and race walking actions. The system uses wearable sensors to capture the motion data of the user, and then analyzes and identifies the user's actions through the SVM algorithm optimization model. By standardizing the user's sports combination training under the system algorithm, the user can improve their training efficiency and reduce the risk of injury. To establish the human body motion model, this paper divides the human skeleton model into five motion branches. The rotation freedom constraints and joint rotation angle range limits are added to the model to ensure the accuracy of the motion analysis. Combining the forward kinematics of the robot and the homogeneous coordinate transformation, the human body joint rotation motion model and the human bone position and posture model are established. In the end, the user can standardize the sports combination training under the system algorithm. In this paper, through the research of wearable sensor technology and sports combined training action recognition, and apply it to practical life, it aims to promote its development and application.

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.

Kinematic Analysis of 5-axis CNC Laser Processing Machine Based on GSN Control Card

The five axis CNC laser machining machine is widely used in the processing industry with high efficiency and precision and other advantages. Based on the basic principle of kinematics theory on the multi-body system, this paper describes the homogeneous coordinate transformation law of the five-axis laser machining machine tool based on GSN control card, and analyzes the solution of the motion trajectory and converts it into the incremental data of the position of each axis in the coordinate system of the machine tool, which solves the correctness, universality and automation of the numerical control system. It provides a powerful help for the five axis CNC laser machining machine based on GSN control card.

Performance analysis of object detection algorithms for robotic welding applications in planar environment

ABSTRACT Weld seam detection and tracking using intelligent techniques is a common task in robotic welding. In this study, vision-based robotic welding is implemented using a 2D Camera to reduce the experimental cost in a planar environment. Firstly, different multi-class object recognition algorithms namely Faster Region-Based Convolutional Neural Network (Faster R-CNN), Single Shot Detector (SSD) and You Look Only Once (YOLOv3) are trained with 1530 manually labeled images. To recognize the weld seam under different brightness levels addressing arc light and splash, Contrast-Limited Adaptive Histogram Equalization (CLAHE) method has been used. Further, an extensive experimental study is conducted to find the optimal hyperparameters among three deep learning models. The performance metrics like Accuracy, Root Mean Square Error, Precision, Recall, Mean Average Precision and F1-score are calculated for different test cases. Finally, homogeneous coordinate transformation is implemented to obtain robot coordinates from weld seam pixel coordinates. The analysis is also extended to detect the bad welding conditions for improper shapes and track the weld seam for good welding shapes using TAL BRABO manipulator. It was found that the weld shapes were accurately detected and tracked precisely with 99.9% accuracy using YOLOv3 than Faster R-CNN and SSD.

Modeling of CNC machine tools’ spatial geometric error based on two-dimensional angle error

A modeling method of CNC machine tools’ spatial geometric error is proposed based on two-dimensional angle error in this paper. Different from traditional modeling method, this method takes into account the effect of additional angle errors because the machine tool’s angle errors in the system of the lower guide rail will be passed on to slip board structure to the upper guide rail system. Firstly, after analyzing the principle of two-dimensional angle error, an optimized error compensation model of CNC machine tools’ spatial geometric error contains two-dimensional angle error is established through the traditional homogeneous coordinate transformation matrix method (HTM). Further, by applying the experiment, the compensation effect of the model is verified through comparing the body diagonal errors of CNC machine tools before and after compensation. Experiment results show that the body-diagonal accuracy after compensation based on the optimized model is 87.73% higher than that before compensation, and 54.82% higher than that of the traditional model after compensation.Article HighlightsThe highlight of the study reported here is threefold: Firstly, the principle of two-dimensional angle error is analyzed. Secondly, an optimized spatial geometric error compensation model of CNC machine tool is established based on the principle of two-dimensional angle error. Thirdly, the compensation effect of the optimized compensation model is verified by comparing the bodies diagonal precision of the machine tool.

Iterative weighted algorithm for 9-dof pose solution and its application

Nine-axis motion parameters need to be calculated according to the relative pose to be simulated when the precision calibration test of rendezvous and docking optical imaging sensor is carried out with nine-degree of freedom motion simulator. Based on the structural characteristics of the system and the principle of homogeneous coordinate transformation, the inverse kinematics equations are established in this paper, in order to improve the test efficiency and ensure the accuracy of pose simulation, the iterative algorithm with fixed degrees of freedom was adopted to approximate the solution results, at last, the nine-axis weighting algorithm was used to judge the end of iteration and obtain the solution results of relative pose optimization.

QPSO-MPC based tracking algorithm for cable-driven continuum robots.

Cable-driven continuum robots (CDCRs) can flexibly travel through narrow space for complex workspace tasks. However, it is challenging to design the trajectory tracking algorithm for CDCRs due to their nonlinear dynamic behaviors and cable hysteresis characteristics. In this contribution, a model predictive control (MPC) tracking algorithm based on quantum particle swarm optimization (QPSO) is designed for CDCRs to realize effective trajectory tracking under constraints. In order to make kinematic analysis of a CDCR, the forward and inverse mapping among actuation space, joint space and work space is analyzed by using the piecewise constant curvature method and the homogeneous coordinate transformation. To improve the performance of conventional MPC for complex tracking tasks, QPSO is adopted in the rolling optimization of MPC for its global optimization performance, robustness and fast convergence. Both simulation and operational experiment results demonstrate that the designed QPSO-MPC presents high control stability and trajectory tracking precision. Compared with MPC and particle swarm optimization (PSO) based MPC, the tracking error of QPSO-MPC is reduced by at least 43 and 24%, respectively.

Optimal Design Method for Static Precision of Heavy-Duty Vertical Machining Center Based on Gravity Deformation Error Modelling

Due to the large size and large span of heavy-duty machine tools, the structural deformation errors caused by gravity account for a large proportion of the static errors, and the influence of gravity deformation must thus be considered in the machine tool precision design. This paper proposes a precision design method for heavy-duty vertical machining centers based on gravity deformation error modelling. By abstracting the machine tool into a multibody system topology, the static error model of the machine tool is established based on the multibody system theory and a homogeneous coordinate transformation. Assuming that the static error of each motion axis is composed of two parts, i.e., the manufacturing-induced geometric error and the gravity deformation error, the machine tool stiffness model of the relationship between gravity and deformation error is developed using the spatial beam elements. In the modelling process, the stiffness coefficients and volume coefficients of the components are introduced to fully consider the influences of structural parameters on machine tool precision. Taking the machine tool static precision, the component stiffness coefficients and the volume coefficients as the design variables, based on the use of the worst condition method, error sensitivity analysis and global optimization algorithm, the optimal allocation of the static error budget of the machine tool and the structural design requirements of each component are determined, providing a valuable guide for the detailed structure design and manufacture processing of the machine tool components.

Thermal-optical characteristics analysis of an aerial camera optical system.

Ambient temperature is one of the important factors affecting the imaging quality of the optical system. Therefore, it is necessary to analyze the thermal-optical characteristics of the optical system when studying the imaging quality of the optical system. Taking the self-made aerial camera optical system as an example, this paper reports the use of the finite element software ANSYS to analyze the thermal stress of the aerial camera optical system, the use of the homogeneous coordinate transformation method to remove the rigid body displacement caused by the mirror surface, and the performance of a Zernike polynomial simulation on the processed surface data. Together, the Zernike coefficients obtained after the fitting are substituted into the ZEMAX optical software to express the surface shape obtained after deformation to analyze the changes in optical imaging quality under thermal environmental conditions. The results of the experiment show that when the working environmental temperature is 50°C, the (MTF) decreases from 0.371 to 0.315 and, when the working environmental temperature is -40∘C, the MTF decreases from 0.371 to 0.285. The comparison results of the experiment and simulation show that the environmental temperature is heating up or, under the condition of cooling, the imaging quality of the aerial camera will be reduced. The thermal-optical analysis method can be used to simulate the actual use conditions of the aerial camera optical system and predict the imaging quality change trend of the optical system. The method of thermo-optical analysis has important guiding significance for the design of an optical-mechanical system.

Kinematics and dynamics analysis of a six-degree of freedom parallel manipulator

Modeling and analysis of inverse kinematics and dynamics for a novel parallel manipulator are established in this article. The manipulator is a spatial mechanism, which consists of six identical kinematic chains connecting to the moving platform. Firstly, screw theory is applied to compute the degree of freedom of this manipulator. Then the inverse position is achieved based on the homogeneous coordinate transformation principle while motion law of the moving platform is given. Furthermore, the first-order influence coefficient method is employed to obtain the Jacobian matrices of the considered manipulator and the links, so do the velocities. Afterward, the rigid-body dynamics model is derived from the Lagrange formulation. To obtain the integrated inverse dynamics model, an approach for simplified flexible dynamics analysis is proposed. Finally, simulations are conducted to compute the position and driving force of this considered manipulator, which validate the new method simultaneously.

The Wearable Lower Limb Rehabilitation Exoskeleton Kinematic Analysis and Simulation.

In recent years, due to the increase in the incidence of traffic accidents, the number of people with limb injuries has also increased. At the same time, among the aging population, neurological diseases or cardiovascular and cerebrovascular diseases have caused many people to have limb hemiplegia. It has been clinically proven that the use of rehabilitation equipment can help patients with limb injuries to restore limb motor function. This paper takes wearable lower limb rehabilitation exoskeleton as the research object, and its main contents are mechanical structure design, kinematics analysis, gait planning, virtual prototype simulation, and experimental verification and analysis. Based on the physiological characteristics of human body and the principle of comfortable and reliable wearing, this paper designs wearable exoskeleton for lower limb rehabilitation. Firstly, the physiological structure characteristics and movement mechanism of human lower limbs were studied and analyzed. By referring to the rotation range and height and size of each joint of human lower limbs, the overall scheme of wearable lower limb rehabilitation exoskeleton was designed and the degree of freedom was allocated. At the same time, Solidworks was used to establish a three-dimensional model. On the basis of a 3D model, a kinematics model was established, and the forward kinematics solution was obtained by using homogeneous coordinate transformation. Since the inverse kinematics solution was relatively complicated, the inverse kinematics solution was conducted in this paper according to the geometric relations of the joints of the lower limbs. Kinematics analysis of the exoskeleton structure of wearable lower limb rehabilitation was carried out to lay a theoretical foundation for gait planning. The off-line gait planning was carried out by using the method based on ZMP stability criterion, and the gait planning was divided into five stages: squat, start, middle step, stop and rise, and the motion trajectory of the center of mass and ankle joint was planned. Based on the inverse kinematics formula, the function of the change of joint angle with time in walking process is derived. The virtual prototype is established in ADAMS, and the simulation of virtual prototype is carried out by using the function of gait planning's joint angle and time. The correctness of structural design and gait planning was verified by measuring the trajectories of the centroid and ankle joints in each gait stage and the functional relationship between the rotation angle of each joint and time. Then, using a 3D dynamic capture system to capture the human lower limb motion trajectory of each joint, each joint trajectory data output, using the MATLAB software to output data, gets the joint trajectory change over time function curve and is used to verify feasibility and applicability of human gait planning. Through the research and analysis of the joints of the lower limbs of the human body, it can be concluded that the hip joint and the knee joint have 3 degrees of freedom, respectively, and the knee joint has 1 degree of freedom.

Influence Analysis of Geometric Error and Compensation Method for Four-Axis Machining Tools with Two Rotary Axes

Four-axis machine tools with two rotary axes are widely used in the machining of complex parts. However, due to an irregular kinematic relationship and non-linear kinematic function with geometric error, it is difficult to analyze the influence the geometry error of each axis has and to compensate for such a geometry error. In this study, an influence analysis method of geometric error based on the homogeneous coordinate transformation matrix and a compensation method was developed, using the Newton iterative method. Geometric errors are characterized by a homogeneous coordinate transformation matrix in the proposed method, and an error matrix is integrated into the kinematic model of the four-axis machine tool as a means of studying the influence the geometric error of each axis has on the tool path. Based on the kinematic model of the four-axis machine tool considering the geometric error, a comprehensive geometric error compensation calculation model based on the Newton iteration was then constructed for calculating the tool path as a means of compensating for the geometric error. Ultimately, the four-axis machine tool with a curve tool path for an off-axis optical lens was chosen for verification of the proposed method. The results showed that the proposed method can significantly improve the machining accuracy.

Design and characterization of innovative optical prism for four-degree-of-freedom fast steering mirror active laser compensation system.

In this study, an innovative four-degree-of-freedom (4-DOF) compensation prism is designed for fast steering mirror active laser compensation systems. In addition to improving the disadvantages of the commercially available compensation systems, such as a larger number of components and longer optical paths, the proposed system has further enhanced the shortcoming of high sensitivity to the laser by using double Porro prisms as 4-DOF compensation prisms proposed in a previous study. The prism proposed in this study reduces the sensitivity to the laser while maintaining two translations and two rotations in 4-DOF control characteristic for laser, thereby improving the resolution of the system to control the laser. First, Zemax was used to build the overall system and evaluate the system characteristics. Then, the skew-ray tracing method and homogeneous coordinate transformation matrix were used to build the mathematical model of the compensation prism and analyze the sensitivity of the proposed prism to the laser. Finally, the closed-loop algorithm was established and the system was completely built on the optical table for experiments to compare the results between the laser before and after compensation by the proposed prism. In addition, the resolution of the proposed prism is compared with the double Porro prisms.

Influences of the workpiece pose errors on gear skiving accuracy

This paper investigates the influence of the workpiece pose errors on gear skiving accuracy. First, based on the theory of homogeneous coordinate transformation, the mapping relationship between the tooth flank of the workpiece and the skiving tool is established according to the principle of gear skiving. Second, the workpiece pose errors are defined, and the relationship between each workpiece pose error and cutting depth is analyzed. According to the kinematic chain of the machine tool, a method for measuring the workpiece pose errors based on the actual inverse kinematic model is proposed. Third, the tooth deviations caused by individual workpiece pose errors and the coupling workpiece pose errors are studied. Then, the sensitive errors are obtained by numerical simulation. Finally, the numerical analysis is verified by gear skiving experiments, and the proposed method can be used to identify the possible workpiece pose errors. Furthermore, the particle swarm optimization algorithm is introduced to guide the workpiece setting pose errors in the gear skiving process.

Motion-Planning Algorithm for a Hyper-Redundant Manipulator in Narrow Spaces

In this study, a hyper-redundant manipulator was designed for detection and searching in narrow spaces for aerospace and earthquake rescue applications. A forward kinematics equation for the hyper-redundant manipulator was derived using the homogeneous coordinate transformation method. Based on the modal function backbone curve method and the known path, an improved modal method for the backbone curves was proposed. First, the configuration of the backbone curve for the hyper-redundant manipulator was divided into two parts: a mode function curve segment of the mode function and a known path segment. By changing the discrete points along the known path, the backbone curve for the manipulator when it reached a specified path point was dynamically obtained, and then the joint positions of the manipulator were fitted to the main curve by dichotomy. Combined with engineering examples, simulation experiments were performed using the new algorithm to extract mathematical models for external narrow space environments. The experimental results showed that when using the new algorithm, the hyper-redundant manipulator could complete the tasks of passing through curved pipes and moving into narrow workspaces. The effectiveness of the algorithm was also proven by these experiments.

English

As crops have different agricultural requirements in pot seedling and the parameters of the planting mechanism need to be repeatedly designed, this paper proposed a reverse design method for the classic gear five-bar planting mechanism based on the agronomic requirements for pot seedling planting. The mathematical model of the planting trajectory of the geared fivebar planting mechanism was constructed through homogeneous coordinate transformation method,; the conditions for the geared five-bar planting mechanism to achieve zero-speed planting were: the gear ratio of the gear pair is -2, and the difference in length between the planetary gear rod and the sun gear rod is equal to the ratio of the planting distance to 2π. Based on the agronomic parameters of pot seedlings (planting depth, planting distance), the parameters of the geared five-bar mechanism were reversed to realize the reverse design of the geared five-bar planting mechanism. Field test results: the average planting depth of tomato pot seedlings is 47mm, the planting distance is 203mm, and the uprightness of pot seedlings is 97.5%, which meets the agronomic requirements of planting tomato pot seedlings. Therefore, the proposed reverse design method of geared five-bar planting mechanism based on agronomic requirements can solve the problem of repeated design of planting mechanism due to different agricultural parameters of most crops, which can greatly reduce the workload of designing various crop planting mechanisms

Error-free measurement method for 6-DOF systems via matrix decomposition approach

A six-degree-of-freedom measurement system possessing a pure algebraic and error-free calculation algorithm is proposed based on the rotation/translation matrix decomposition approach. Generally, such complicated mathematical models are simplified through linearization. However, this inevitably leads to calculation errors. Accordingly, in the method proposed in this study, the object motion behavior in three-dimensional space is described instead using a pose-change homogeneous coordinate transformation matrix consisting of two separate matrices, namely a rotation matrix which describes the nonlinear component of the object motion and a translation matrix which describes the linear component. In the solution process, the image-orientation-change method is first used to determine the rotation matrix. The translation matrix is then obtained using the singular-value-decomposition least-squares method. Finally, the two matrices are multiplied together to obtain the desired pose-change matrix. The validity of the proposed approach is demonstrated by means of an illustrative numerical example and a simple experimental trial. It is shown that, since the calculation algorithm is a purely analytical and algebraic method and involves no approximations or omissions (i.e., the relevant equations are not simplified through linearization and thus retain their original nonlinear integrity), the derived solutions are error-free if the errors introduced by the measurement technology are ignored.

An adaptive laser focus auto-positioning method for non-datum complex components based on 3D vision

For the advantages of high single-pulse energy and non-contact processing, laser is used to process easily deformable, high-hardness, and high-brittle materials. For some rough, easily deformed, and no-datum workpieces, it is difficult to locate the laser focus on the machining datum, resulting in processing deviation. This paper aims to solve the problem of automatic positioning of the laser focus on complex workpieces without positioning datum in three-dimensional laser processing. A calibration method of 3D scanner and five-axis laser machine tool is proposed, which combines the laser-processed circular hole, calibration ball and the virtual geometric features formed by the high-precision movement of the machine tool as the calibration objects. Based on the calibration results and the principle of homogeneous coordinate transformation, the kinematic model of five-axis laser machine tool is established dynamically. Then, according to the geometric information of the key points obtained by visual measurement, the automatic positioning of the laser focus on non-datum complex components is realized. Finally, the method proposed in this paper is verified by using planar ceramic components and non-datum complex ceramic components as positioning objects respectively. The results show that the method provided in this paper can effectively realize the automatic positioning of laser focus for non-datum complex components. And the positioning error is less than 45µm. The method proposed in this paper has been applied in the actual ceramic core trimming.

Freeform surface topography model for ultraprecision turning under the influence of various errors

This work establishes an accurate freeform surface topography model considering geometric errors, tracking errors, and cutting forces. Regarding geometric errors, based on the theory of multibody systems and homogeneous coordinate transformation, the transfer relationship between various geometric errors and the tool error in the workpiece coordinate system is described. Using the continuous acceleration Position-Velocity-Time (PVT) interpolation method, the offset discrete points caused by geometric errors are interpolated and rediscretized, and the accurate mathematical model between the tool errors (position and posture) in the workpiece coordinate system and the topography of the freeform surface is established. Based on the model, the influence of geometric errors on the contour errors of freeform surfaces is accurately calculated, and the contribution and similarity of the effects of various geometric errors on the contour errors of freeform surfaces are analyzed. For dynamic-dependent factors, a second-order system with two degrees of freedom on the X or Z axis is established. According to the simplified result of the equivalent system, the contour error of the freeform surface caused by the tracking error and cutting force is analyzed. For the tracking error, under the condition of constant rotation velocity of the spindle, the change of the slope of the freeform surface along the circumferential direction causes the change in the velocity and acceleration of the motion axis; thus, the corresponding area of the surface has a larger contour error. For cutting force, the change of the slope of the freeform surface along the circumferential direction changes the tool working rake angle, the tool working clearance angle, and the shearing angle, resulting in a change in the cutting force. Moreover, the change of cutting speed is accompanied by the change of cutting force. An experiment verifies the effectiveness of the proposed modeling method. In addition, the modeling method provides an effective solution for the calculation of the contribution rate of different error sources to the contour error of the freeform surface.