Spatial Parallel Research Articles

Parallel Hierarchical Control-Based Efficiency Enhancement for Large-Scale Virtual Reality Traffic Simulation

Virtual reality (VR)-based traffic simulation plays an important role in the study of transportation systems, especially in the testing of connected and autonomous vehicles. However, a simulator that provides a large-scale traffic scene with high fidelity is still not available. To address this issue, the parallel hierarchical control method is proposed in this article, which presents a framework that enables the efficient simulation of a VR-based large-scale traffic scene. First, the original data of the basic traffic components are acquired through a modification and generation method. Then, based on the proposed method for spatial parallel slicing, the prepared data and simulation tasks are separated and distributed to subcontrollers considering the connected-vehicle environment. Meanwhile, a fidelity loss-based hierarchical control method is integrated to stratify the separate data into multiple levels. Finally, the experiments are carried out on a virtual driving platform that indicates that the proposed approach effectively ensures the fidelity of the visualized scenes and performs a better allocation of computational resources.

A Novel Geometric Modeling and Calculation Method for Forward Displacement Analysis of 6-3 Stewart Platforms

A novel geometric modeling and calculation method for forward displacement analysis of the 6-3 Stewart platforms is proposed by using the conformal geometric algebra (CGA) framework. Firstly, two formulas between 2-blade and 1-blade are formulated. Secondly, the expressions for two spherical joints of the moving platform are given via CGA operation. Thirdly, a coordinate-invariant geometric constraint equation is deduced. Fourthly, a 16-degree univariate polynomial equation without algebraic elimination by using the Euler angle substitution is presented. Fifthly, the coordinates of three spherical joints on the moving platform are calculated without judging the radical symbols. Finally, two numerical examples are used to verify the method. The highlight of this paper is that a new geometric modeling and calculation method without algebraic elimination is obtained by using the determinant form of the CGA inner product algorithm, which provides a new idea to solve a more complex spatial parallel mechanism in the future.

Identification of geometric parameters of a parallel robot by using a camera calibration technique

This work reports a novel method to estimate the geometrical parameters of a 2-(3-RRPS) parallel robot intended for manufacturing tasks. The method uses camera calibration techniques, and it is based on the concept of vertex space. The advantage of this technique is that the system does not require complex electronic instrumentation, and only uses a CCD camera as a main sensor and planar patterns, which makes it portable, accurate and low cost. To ensure the quality of the measurements, a methodology for characterization of the measurement system is included. The applicability and the advantages of using the proposed method are shown by means of the estimation of the geometrical dimensions of a spatial parallel manipulator with a relatively complex kinematic architecture. Experiments are conducted and show a significant improvement in manipulator accuracy when the parameters estimated with this technique are used.

Adaptive Sliding Mode Neural Network Control and Flexible Vibration Suppression of a Flexible Spatial Parallel Robot

With the goal of creating a flexible spatial parallel robot system in which the elastic deformation of the flexible link causes a rigid moving platform to produce small vibrations, we proposed an adaptive sliding mode control algorithm based on a neural network. To improve the calculation efficiency, the finite element method was used to discretize the flexible spatial link, and then the displacement field of the flexible spatial link was described based on floating frame of reference coordinates, and the dynamic differential equation of the flexible spatial link considering high-frequency vibrations was established through the Lagrange equation. This was combined with the dynamic equation of the rigid link and the dynamic equation considering small displacements of the rigid movable platform due to elastic deformation, and a highly nonlinear and accurate dynamic model with a rigid–flexible coupling effect was obtained. Based on the established accurate multi-body dynamics model, the driving torque with coupling effects was calculated in advance for feedforward compensation, and the adaptive sliding mode controller was used to improve the tracking performance of the system. The nonlinear error was examined to determine the performance of the neural network’s approximation of the nonlinear system. The trajectory errors of the moving platform in the X-, Y-, and Z-directions were reduced by 12.1%, 38.8%, and 50.34%, respectively. The results showed that the designed adaptive sliding mode neural network control met the control accuracy requirements, and suppressed the vibrations generated by the deformation of the flexible spatial link.

Nonlocal weighted sparse unmixing based on global search and parallel optimization

Sparse unmixing (SU) can represent an observed image using pure spectral signatures and corresponding fractional abundance from a large spectral library and is an important technique in hyperspectral unmixing. However, the existing SU algorithms mainly exploit spatial information from a fixed neighborhood system, which is not sufficient. To solve this problem, we propose a nonlocal weighted SU algorithm based on global search (G-NLWSU). By exploring the nonlocal similarity of the hyperspectral image, the weights of pixels are calculated to form a matrix to weight the abundance matrix. Specifically, G-NLWSU first searches for a similar group of each pixel in the global scope then uses singular value decomposition to denoise and finally obtains the weight matrix by considering correlations between similar pixels. To reduce the execution burden of G-NLWSU, we propose a parallel computing version of G-NLWSU, named PG-NLWSU, which integrates compute unified device architecture-based parallel computing into G-NLWSU to accelerate the search for groups of nonlocally similar pixels. Our proposed algorithms shed new light on SU by considering a new exploitation process of spatial information and parallel computing scenario. Experimental results conducted on simulated and real datasets show that PG-NLWSU is superior to comparison algorithms.

A Backdrivable Kinematically Redundant (6+3)-Degree-of-Freedom Hybrid Parallel Robot for Intuitive Sensorless Physical Human–Robot Interaction

A novel backdrivable 3-[ <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</u> ( <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</u> R- <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</u> RR)SR] kinematically redundant (6+3)-degree-of-freedom (DOF) spatial hybrid parallel robot with revolute actuators is proposed for low-impedance physical human–robot interaction. The kinematic model is developed based on the constraint conditions of the robot. It is shown that the type II (parallel) singularities can be completely avoided, thereby yielding a very large translational and orientational workspace. A workspace analysis is presented in order to demonstrate the capabilities of the robot. Mechanisms are then introduced to use the redundant DOF of the robot to operate a gripper with the robot actuators, which are mounted on or close to the base, thus reducing the inertia of the moving parts. The architecture of the robot makes it possible to use direct drive motors, thereby making the robot easily backdrivable and allowing the use of a very simple and effective controller. A prototype of the robot is then designed and built and the large workspace of the robot as well as the effortless physical human–robot interaction are demonstrated. The controller of the robot is then described, including a position control mode and a control mode for physical interaction, which does not require the use of a force/torque sensor or joint torque sensors. Because of its backdrivability and low moving inertia, the robot is particularly well-suited for physical human–robot interaction, as demonstrated in the accompanying videos.

Vanishing Point Detection based on Line Set Optimization

Vanishing point detection plays an important role in camera calibration and 3D scene reconstruction. There are usually a lot of parallel lines in the real scene. Vanishing point is the intersection point of these spatial parallel lines projected onto the image. Commonly used Hough algorithm to detect vanishing points, which has high complexity and low efficiency. This paper proposes a vanishing point detection algorithm based on optimization of line set. Firstly, the LSD algorithm is used to detect the line. Secondly, the extracted line set is optimized to remove the invalid interference line in the image, which improves the accuracy of vanishing point detection. Thirdly, K-means algorithm is used to cluster and group the optimized line set, which improves the overall efficiency of the algorithm. Finally, random sampling fitting algorithm is used to fit the grouped line set to calculate the precise vanishing point. Compared with Hough algorithm, the running speed of this algorithm is improved by 19% in the actual scene. The experimental results show that the algorithm has low complexity and short running time.

Optimal wrench-closure configuration of spatial reconfigurable cable-driven parallel robots

In this paper, a method for computing the optimal actuation of reconfigurable cable-driven parallel robots is presented. By using this method, the imperfect ability in exerting torque and limited orientation workspace of these robots may be improved. In a cable-driven parallel robot with reconfigurability, the attachment points of cables on the base are adjusted with regard to the movement of the end-effector on a trajectory. In such a design the redundant degree-of-freedom of the robot is increased accordingly. For an arbitrary pose of the end-effector, a spherical zone is defined in which the called wrench-closure condition is satisfied for a prescribed range of orientation. Taking the volume of such zone into consideration the optimal configuration of the robot may be determined. This configuration is found by appropriately changing the position of the moving attachment points on the base of the robot. By repeating this computation for a number of points on a specified trajectory, appropriate actuation plans are achieved. The computed optimal actuation guarantees balance of any external wrench by tension force of cables when the end-effector moves close to its trajectory. For a case of spatial reconfigurable cable-driven parallel robot, the optimal actuation is found based on Particle Swarm Optimization and performance of the robot is compared to the one with fixed cable attachment points on base. The result shows significant improvement of the performance of reconfigurable spatial cable-driven parallel robot.

Mass spectral database for TOF-SIMS of stable isotopes of Sr and Zr

Nuclear accidents (e.g., at the Chernobyl and Fukushima Daiichi nuclear power plants) release considerable amounts of radioactive pollutants into the environment. Radioactive particles in dust and soil can range from a few micrometers to several micrometers in size. Detection of these micrometer-sized particles requires a fast and effective analytical method. Because time-of-flight secondary ion mass spectrometry (TOF-SIMS) exhibits high spatial resolution and parallel detection capability, it is suitable for analyzing micrometer-sized radioactive particles. However, due to isobaric interferences, TOF-SIMS cannot effectively distinguish between isobaric elements such as 90Sr and 90Zr. Resonant ionization sputtered neutral mass spectrometry (R-SNMS) eliminates isobaric interferences and enables the measurement of isotope ratios of isotopes approaching the detection limit. However, R-SNMS cannot be performed independently because its results are based on the TOF-SIMS spectra. This study provides a database of reference spectra for Sr and Zr stable isotopes, which can act as important reference for further analysis of radioactive particles in environmental samples.

Effects of Spherical Clearance Joint on Dynamics of Redundant Driving Spatial Parallel Mechanism

SUMMARYThis paper proposes a dynamic modeling method of redundant drive spatial parallel mechanism, dynamics of 4-UPS-RPU redundant driving spatial parallel mechanism considering spherical joint clearance are analyzed. The dynamic equation of spherical joint clearance with Lagrange multiplier is built. The influences of single clearance and multiple clearances on dynamic responses of redundant drive spatial parallel mechanisms are analyzed under different clearance values. The results show that the dynamic characteristics of the mechanism with single clearance are basically consistent with the ideal situation, and the dynamic characteristics of the mechanism with multi-clearance are significantly different from the ideal situation.

A novel modified analytical method and finite element method for vibration analysis of cable-driven parallel robots

Cable-driven parallel robots (CDPRs) are vulnerable to vibration due to the inevitable flexible properties of the cables. Thus, vibration analysis is critical for CDPR’s operation in which highly accurate motion is required. However, most of the current methods related to vibration analysis of CDPRs rely on simple spring models which have limitations in their performance and complexity that are not general to analyze the vibration of various CDPRs. Hence, accurate, simple and general approaches for vibration analysis in CDPRs are need. To solve this problem, this paper presents the finite element method (FEM) and the modified analytical method to analyze the vibration of CDPRs. To validate these methods, free vibration analysis was conducted using the proposed methods for the planar and spatial cable-driven parallel robots. The natural frequencies of these two CDPRs were computed by the proposed two methods and compared with those of the commercial software, SAP2000. The solutions obtained by the FEM and the modified analytical models turned out to be close to SAP2000’s results, thereby verifying the validity of the proposed methods.

Spatial Management of Distributed Social Systems

The paper describes the use of invented, developed, and tested in different countries of the high-level spatial grasp model and technology capable of solving important problems in large social systems, which may be represented as dynamic, self-evolving and distributed social networks. The approach allows us to find important solutions on a holistic level by spatial navigation and parallel pattern matching of social networks with active self-propagating scenarios represented in a special recursive language. This approach effectively hides inside the distributed and networked language implementation traditional system management routines, often providing hundreds of times shorter and simpler high-level solution code. The paper highlights the demands to efficient simulation of social systems, briefs the technology used, and provides some programming examples for solutions of practical problems.

The Invariance of the Diffusion Coefficient with Iterative Operations of the Charged Particle Transport Equation

Abstract The spatial parallel diffusion coefficient (SPDC) is one of the important quantities describing energetic charged particle transport. There are three different definitions for the SPDC: the displacement variance definition , the Fick’s law definition with , and the Taylor–Green–Kubo (TGK) formula definition . For a constant mean magnetic field, the three different definitions of the SPDC give the same result. However, for a focusing field, it is demonstrated that the results of the different definitions are not the same. In this paper, from the Fokker–Planck equation, we find that different methods, e.g., the general Fourier expansion and iteration method, can give different equations of the isotropic distribution function (EIDFs). But it is shown that one EIDF can be transformed into another by some derivative iterative operations (DIOs). If one definition of the SPDC is invariant for the DIOs, it is clear that the definition is also invariant for different EIDFs; therefore, it is an invariant quantity for the different derivation methods of the EIDF. For the focusing field, we suggest that the TGK definition is only an approximate formula, and the Fick’s law definition is not invariant to some DIOs. However, at least for the special condition, in this paper we show that the definition is an invariant quantity to the DIOs. Therefore, for a spatially varying field, the displacement variance definition , rather than the Fick’s law definition and TGK formula definition , is the most appropriate definition of the SPDCs.

A generalized method for three-dimensional dynamic analysis of a full-vehicle model

Dynamic performances of the vehicle are significantly influenced by the suspension mechanisms. An understanding of the effects of the suspension kinematics and statics (or, briefly, kinestatics) is crucial to improve the dynamic performances of a vehicle. However, the suspension kinestatics is often neglected in the dynamic analysis. This paper presents a generalized full-vehicle model for the three-dimensional dynamic analysis, which consists of two pairs of the front and rear spatial suspension mechanisms. Each suspension is represented by a corresponding instantaneous screw joint supporting the vehicle body at any instant. The full-vehicle model is viewed to be a 6-degree-of-freedom spatial parallel mechanism. As the spatial parallel mechanism, the kinematics and statics of the full-vehicle model are analysed using the theory of screws. Taking the suspension kinestatics and tyre dynamics into consideration, the dynamic equations of the full-vehicle model are formulated in terms of the Lagrangian equations. As immediate applications, the dynamic behaviours of a vehicle are simulated and evaluated under two different road disturbances, respectively. By comparing with the simulation results from two other widely used methods, it confirms the validity of the theoretical method.

A geometrically accurate deformable-body approach for the analysis of robotic and parallel-mechanism systems

Strength and durability investigations of parallel-mechanism (PM) and robotic systems, used as integral part in modern manufacturing, are necessary at the virtual design stage. Nonetheless, because of the limitations of existing finite element (FE) approaches, flexible-link geometries are often simplified or distorted when converting solid models to FE analysis meshes. This article introduces and demonstrates the use of a new unified geometry/analysis approach for the small-deformation analysis of robotic and parallel mechanism (RPM) systems with flexible links. The approach used in this investigation integrates the geometrically accurate absolute nodal coordinates formulation (ANCF) with the computationally efficient floating frame of reference (FFR) formulation that allows for systematic elimination of high-frequency and insignificant deformation modes. The proposed ANCF/FFR approach allows modeling accurately the stress-free reference configuration geometry, captures the dynamic coupling between the rigid-body and elastic displacements, is based on a unified geometry/analysis mesh that eliminates the need for geometry/analysis model conversion or coordinate transformation, and allows for efficient and accurate solution of the nonlinear dynamic equations that govern the RPM motion. The formulation of the spatial ANCF/FFR equations of motion including the elastic (stress) forces using a general continuum-mechanics approach is presented, and use of the strain split method (SSM) as an FE locking-alleviation technique is discussed. A frequency-convergence analysis of flexible links with tapered geometry is performed and the obtained numerical results are compared with solutions obtained using commercial FE software. The application of the new procedure in the nonlinear dynamics simulations of RPM systems is demonstrated using a spatial parallel mechanism that includes flexible links and prismatic, revolute, and spherical joints.

Kinematic calibration of the 3-degree-of-freedom redundantly actuated spatial parallel module of a five-axis hybrid machine

As a new type of manufacturing equipment, redundant hybrid machines have the theoretical advantage over the traditional serial machines in efficiently processing large structural parts with high material removal ratio and complex parts with curved surfaces. In order to solve the accuracy problem of the redundantly actuated spatial parallel module of a five-axis hybrid machine, an improved kinematic calibration method is proposed in this article. First, different from error modeling for the corresponding non-redundant parallel module, the geometric error model of the redundantly actuated spatial parallel module considers the deformations at active joints caused by actuation redundancy as an error source. Then, the applicable error model is developed using projection technique to remove the need of active joints’ stiffness measurement or modeling. Later, the practical error model is derived from model reduction method to avoid using additional sensors or gratings. Finally, three forms of relative measurement and step identification are adopted for the calibration work, and the bilinear interpolation compensation function is introduced to ensure the calibration effect. On this basis, the kinematic calibration of the redundantly actuated spatial parallel module is conducted. The max position errors are reduced from original −0.192 to 0.075 mm after RM1 and SI1, and then further reduced to 0.014 mm after bilinear interpolation compensation, while the max orientation errors are reduced from −0.017° and 0.249° to −0.005° and −0.007° after RM2 and SI2, and RM3 and SI3, respectively. A contrasting experiment is also carried out with the previous method for the corresponding non-redundant parallel module. As a result, the proposed method shows better convergence value and speed in identifying error parameters, and therefore the effectiveness and efficiency of the proposed method for the redundantly actuated spatial parallel module are validated.

A three-dimensional PWR-core pin-by-pin analysis code NECP-Bamboo2.0

A PWR-core pin-by-pin fuel management calculation code system named NECP-Bamboo2.0 has been developed, including the two-dimensional lattice calculation code Bamboo-Lattice2.0 and the three-dimensional steady-state whole-core pin-by-pin calculation code Bamboo-Core2.0. Pin-cell homogenized few-group constants are handled in an optimized least-square fitting form. A tightly coupled calculation strategy is employed for multi-physics coupling iterative process. A three-dimensional whole-core spatial parallel algorithm based on the unified domain decomposition is established to decrease both computing time and storage. (1) Compared with the traditional two-step method, the pin-by-pin calculation can ensure the accuracy of reactor reactivity, can reduce the average error of pin-power calculation from 2% to 1% for large commercial PWR core, can reduce the error of pin-power from 11% to 3% for the small PWR core. (2) NECP-Bamboo2.0 can directly provide pin-resolved distributions, including coolant temperature, fuel temperature, burnup and so on. The corresponding accuracy is comparable with one-step high-fidelity results.

Jacobian approach to the kinestatic analysis of a full vehicle model with application to cornering motion analysis

The Jacobian approach to the kinestatic analysis of a planar suspension mechanism has been previously presented. In this paper, the theory is extended to three-dimensional kinestatic analysis by developing a full kinematic model and viewing it as a spatial parallel mechanism. The full kinematic model consists of two pairs of the front (double wishbone) and rear (multi-link) suspension mechanisms together with a newly developed ground-wheel contact model. The motion of each wheel of four suspension mechanisms is represented by the corresponding instantaneous screw at any instant. A vehicle is considered to be a 6-degrees-of-freedom spatial parallel mechanism whose vehicle body is supported by four serial kinematic chains. Each kinematic chain consists of a virtual instantaneous screw joint and a kinematic pair representing ground-wheel contact model. The kinestatic equation of the 6-degrees-of-freedom spatial parallel mechanism is derived in terms of the Jacobian. As an important application, a cornering motion of a vehicle is analysed under the assumption of steady-state cornering. A numerical example is presented to illustrate how to determine the optimal locations of strut springs for the least roll angle in cornering motion using the proposed method.

WORKSPACE ANALYSIS AND OPTIMIZATION OF THE PARALLEL ROBOTS BASED ON COMPUTER-AIDED DESIGN APPROACH

This paper provides workspace determination and analysis based on the graphical technique of both spatial and planar parallel manipulators. The computation and analysis of workspaces will be carried out using the parameterization and three-dimensional representation of the workspace. This technique is implemented in CAD (Computer Aided Design) Software CATIA workbenches. In order to determine the workspace of the proposed manipulators, the reachable region by each kinematic chain is created as a volume/area; afterwards, the full reachable workspace is obtained by the application of a Boolean intersection function on the previously generated volumes/areas. Finally, the relations between the total workspace and the design parameters are simulated, and the Product Engineering Optimizer workbench is used to optimize the design variables in order to obtain a maximized workspace volume. Simulated annealing (SA) and Conjugate Gradient (CG) are considered in this study as optimization tools.

An Anatomical-Based Subject-Specific Model of In-Vivo Knee Joint 3D Kinematics From Medical Imaging

Biomechanical models of the knee joint allow the development of accurate procedures as well as novel devices to restore the joint natural motion. They are also used within musculoskeletal models to perform clinical gait analysis on patients. Among relevant knee models in the literature, the anatomy-based spatial parallel mechanisms represent the joint motion using rigid links for the ligaments’ isometric fibres and point contacts for the articular surfaces. To customize analyses, therapies and devices, there is the need to define subject-specific models, but relevant procedures and their accuracy are still questioned. A procedure is here proposed and validated to define a customized knee model based on a spatial parallel mechanism. Computed tomography, magnetic resonance and 3D-video-fluoroscopy were performed on a healthy volunteer to define the personalized model geometry. The model was then validated by comparing the measured and the replicated joint motion. The model showed mean absolute difference and standard deviations in translations and rotations, respectively of 0.98 ± 0.40 mm and 0.68 ± 0.29 ° for the tibia–femur motion, and of 0.77 ± 0.15 mm and 2.09 ± 0.69 ° for the patella–femur motion. These results show that accurate personalized spatial models of knee kinematics can be obtained from in-vivo imaging.