Forward Kinematics Analysis of Parallel Robots Using Global Newton-Raphson Method

In order to obtain direct solutions of parallel manipulator without divergence in real time, a modified global Newton-Raphson (MGNR) algorithm was proposed for forward kinematics analysis of six-degree-of-freedom (DOF) parallel manipulator. Based on geometrical frame of parallel manipulator, the highly nonlinear equations of kinematics were derived using analytical approach. The MGNR algorithm was developed for the nonlinear equations based on Tailor expansion and Newton-Raphson iteration. The procedure of MGNR algorithm was programmed in Matlab/Simulink and compiled to a real-time computer with Microsoft visual studio.NET for implementation. The performance of the MGNR algorithms for 6-DOF parallel manipulator was analyzed and confirmed. Applying the MGNR algorithm, the real generalized pose of moving platform is solved by using the set of given positions of actuators. The theoretical analysis and numerical results indicate that the presented method can achieve the numerical convergent solution in less than 1 ms with high accuracy (1×10−9 m in linear motion and 1×10−9 rad in angular motion), even the initial guess value is far from the root.

In this paper the authors propose a solution in which an intelligent algorithm - genetic algorithm in our case - is used to generate commands for a robot in real time, so that the robot can determine the optimal moves considering several aspects: route tracking and low power consumption. Genetic algorithms are intelligent solutions for multi-criteria optimization and using them to find solutions to the optimization problems containing constrictions. However, they were designed as algorithms running on computer and therefore cannot ensure rapid generation of the solutions. On the other hand, the problem of determining the optimal response to command a robot requires real time response. The paper presents a method for hardware implementation and integration in a FPGA circuit of a genetic algorithm, in order to accelerate the convergence and to generate solutions in real time.

In this paper autonomous formation control for Unmanned Aerial Vehicles (UAVs) has been discussed and a real time solution has been put forward by benefiting General Purpose Graphical Processing Units (GPGPU) accelerated potential field approach while ensuring obstacle and collision avoidance in unknown environment by using real-time sensors. GPGPU accelerated real time formation control for UAVs was designed and the basic model of the approach has been explained in our previous work (Cetin and Yilmaz 2014). As the deficiencies of the previous approach, autonomous real time collision and coordinated obstacle avoidance features in unknown environments are also handled while maintaining formation flight conditions in this work. With these features, improved autonomous formation control approach is discussed as a real time solution. The computation is performed by using Graphical Processing Units (GPUs) as parallel computation architectures by benefiting from Single Instruction Multiple Data (SIMD) type parallel algorithms. Classic binary map conversation, connected component labeling and minimum bounding box algorithms which are commonly used for image processing applications, has been evaluated for real time obstacle detection and avoidance features by developing GPGPU suitable parallel algorithms. Real-time solution has been developed by integrated these parallel algorithms with parallel Artificial Potential Field (APF) computation algorithm. Simulation results are proved that this novel autonomous improved formation control approach is successful and it would be used in real time applications like UAV formation flight missions.

Photolithography is one of the core technologies of micro-nano fabrication. Recently, lithography technology is applied to diverse field of technologies. These technologies include MEMS (micro electro mechanical system) devices, FPD (flat panel display), and semiconductor industry. When it comes to the typical exposure process of lithography technology, photomask costs is occupying large portion of the optical system. So, how to reduce the cost of the mask and employing maskless lithography technology has become an important issue to engineers. Although there being both advantages and disadvantages, maskless lithography is a receiving substantial attention from engineers in the fileds of micro-nano fabrication. With the development of technology, low cost, flexibility, efficiency in the fabrication of device are in high demand in maskless lithography technology. How to generate line/space patterns is gaining considerable attention in terms of maskless lithography exposure process. In order to achieve the accurate alignments of numerous optical heads within a reasonable amount of tack time, installing autonomous position align micro parallel manipulator system in each optical heads required. Applied parallel manipulator that consists of four 2-DOF (degree of freedom) decoupled actuator gives chances to provide 6-DOF independence motion, and has strength in high accuracy. It is thus, this parallel manipulator is suitable for the experiment. This paper covers the follows: First, we reported the DMD (Digital Micro mirror Device)-based makless lithography system to introduce spot array method in maskless digital exposure process. Second, applying a redundant parallel micro manipulator and analyzing kinematic characteristic of the 4-[PP]PS parallel manipulator is described. After that, comparing benefits and drawbacks of 4-[PP]PS parallel and 4-DOF serial manipulator is covered. Third, proposing a suitable error model of the system and applying the genetic algorithm to alignment spot array concerning position correction. Finally, we designed experiment which has vision sensor and align unit to verify positioning algorithm. Simulation and experimental result will be shown with the regard to parallel manipulator can find the optimal solution based on genetic algorithm and carry out the problem of spot array alignment by reducing the position error of the system.

This paper presents a transformation method to generate the workspace of an n(3RRS) serial–parallel manipulator (S–PM). Firstly, the boundary of the workspace of the 3RRS parallel manipulator (PM) is obtained using the boundary search method and verified by MATLAB/SimMechanics simulation. Secondly, the workspace of the 2(3RRS) S–PM is obtained using the proposed method and verified by MATLAB/SimMechanics simulation. Finally, the workspace of the 3(3RRS) S–PM is obtained using the proposed method. The results indicate that the n(3RRS) S–PM can significantly expand its workspace with the increase in the number of PMs connected in series, and the proposed method can generate the workspaces of n(3RRS) S–PMs efficiently with the advantages of simple operation, high efficiency, and high accuracy. The proposed method is applicable to all S–PMs that are composed of PMs, and it provides a reference for solving the workspaces of other types of redundantly hybrid manipulators.

Zeroing dynamics (ZD), as a powerful method proposed for time-varying problems solving, has found successful applications in motion control of serial manipulators. Compared with serial manipulators, parallel manipulators possess some attractive advantages such as high carrying capacity and high operation accuracy. However, the inherent differences between parallel and serial manipulators set great difficulties on the applications of ZD to the control of parallel manipulators. Making progress along this direction, the first ZD based motion controller of parallel manipulators is proposed and the design procedure of the ZD based scheme is presented. As a typical application, the proposed scheme is utilised to control a Stewart platform for tracking a quatrefoil-shaped path, which illustrates the effectiveness of the ZD based scheme.

Discussion on: “Comparison of Different Multivariable Control Design Methods Applied on Half Car Test Setup”

In this paper, Artificial Intelligence (AI) is developed for studying the Boussinesq Paradigm equation and so called b-equation based on Physics-Informed Cellular Neural Networks (PICNNs). The models studied here come from fluid dynamics. Machine learning through Physics-Informed Neural Networks (PINNs) is a powerful tool for solving complex problems arising in physical laws. By optimization and automatic differentiation, the solutions of the model under consideration can be approximated precisely and can be obtained in real time. In this paper, we shall apply a new algorithm based on Physics-Informed Cellular Neural Networks (PICNNs) for obtaining the interactions between solitons and peakons. The algorithm has many advantages, but the main ones are that it provides the fastest programming and solutions in real time. It is known that Cellular Neural Networks (CNNs) have the ability to approximate, in a very accurate way, nonlinear partial differential equations (PDEs) and to present their solutions in real time. By incorporating the physical laws into the learning process through PICNN we can solve various problems from fluid dynamics, material science, and quantum mechanics.

The industrial robots play an important role in modern industrial manufacturing processes, and their applications are becoming increasingly widespread, greatly improving manufacturing efficiency and significantly enhancing the digitalization level of the manufacturing industry. Therefore, achieving safe control of multi robot collaborative work is of great significance for the stable and efficient operation of robot systems. This article proposes a dual robot safety control technology based on the kinematic model of industrial robots. Firstly, a mathematical model of the kinematic space of the dual robots is constructed using D-H parameters; Then, use recursive traversal algorithm to calculate the minimum distance between each joint arm of the two robots in real time; Finally, the minimum distance between each joint arm will be calculated and compared with the set safety threshold to achieve real-time assessment and control of collision risk during the movement of the dual robots. A dual robot safety control testing platform was built using two KUKA industrial robots, integrated control software was developed, and relevant algorithms were validated. Through experiments, it was verified that this method can evaluate the collision risk of dual robots in real time during motion and effectively control the collision risk during the motion of dual robots.

A high‐speed field‐programmable gate array (FPGA) design is proposed to calculate angles and distances for biped robots in real time. A low‐complexity and high‐accuracy hardware‐oriented algorithm based on CORDIC was developed. To reduce hardware cost, a hardware sharing technique was used to realise a CORDIC scaling factor generator and three hardware sharing machines. Moreover, the multipliers and dividers were replaced by cost‐efficiency components, such as adders and shifters to further reduce hardware cost. In addition, the proposed design was implemented with a fully pipelined architecture, which achieved improved operating frequency and throughput efficiency. The proposed design was realised and verified by an FPGA device with a maximum operating frequency of 127 MHz, which achieved the calculation of angles and distances for biped robots in real time. Compared with the previous design, this work not only reduced hardware cost by at least 49.6% and average errors by at least 67.2%, but also improved the average executing performance by 62.7% when calculating ten angles for the biped robots.

Introduction: The position and pose measurement of the rehabilitation robot plays a very important role in patient rehabilitation movement, and the non-contact real-time robot position and pose measurement is of great significance. Rehabilitation training is a relatively complicated process, so it is very important to detect the training process of the rehabilitation robot in real time and accuracy. The method of the deep learning has a very good effect on monitoring the rehabilitation robot state. Methods: The structure sketch and the 3D model of the 3-PRS ankle rehabilitation robot are established, and the mechanism kinematics is analyzed to obtain the relationship between the driving input - the three slider heights - and the position and pose parameters. The whole network of the position and pose measurement is composed of two stages: (1) measuring the slider heights using the CNN based on the robot image and (2) calculating the position and pose parameter using the BPNN based on the measured slider heights from the CNN. According to the characteristics of continuous variation of the slider heights, a regression CNN is proposed and established to measure the robot slider height. Based on the data calculated by using the inverse kinematics of the 3-PRS ankle rehabilitation robot, a BPNN is established to solve the forward kinematics for the position and pose. Results: The experimental results show that the regression CNN outputs the slider height and then the BPNN accurately outputs the corresponding position and pose. Eventually, the position and pose parameters are obtained from the robot image. Compared with the traditional robot position and pose measurement method, the proposed method has significant advantages. Conclusion: The proposed 3-PRS ankle rehabilitation position and pose method can not only shorten the experiment period and cost, but also get excellent timeliness and precision. The proposed approach can help the medical staff to monitor the status of the rehabilitation robot and help the patient rehabilitation in training. Discussion: The goal of the work is to construct a new position and pose detection network based on the combination of the regression convolutional neural network (CNN) and the back propagation neural network (BPNN). The main contribution is to measure the position and pose of the 3-PRS ankle rehabilitation robot in real time, which improves the measurement accuracy and the efficiency of the medical staff work.

This paper addresses the kinematic and dynamic models of a 3-PPR parallel manipulator, which are the foundation of parallel manipulator dynamic control. Then, based on the Udwadia-Kalaba equation, a three-step procedure is exploited to realize the perfect trajectory tracking of 3-PPR parallel manipulator involving the known uncertainty. In addition, when the initial conditions are incompatible and system parameters are uncertain, we adopt the adaptive robust control method to realize approximate trajectory tracking of the planar parallel manipulator. The controller consists of three parts. The first part is the perfect control of dynamic model based on the Udwadia-Kalaba equation. The second part deals with the incompatibility of initial conditions. The third part is the robust control for system uncertainty regulated by adaptive law. Finally, on the basis of theoretical analysis, the adaptive robust control algorithm is demonstrated by simulation.

The Global Navigation Satellite System (GNSS) precise point positioning (PPP) technology is currently used to process GNSS water vapor observations in real time or near real time. Further developments are required to improve the accuracy and real-time performance of processing tropospheric delays from which the water vapor observations are extracted. In real-time BDS/GPS precise clock correction estimation with square-root information filtering and PPP solution with Kalman filtering, a fixed variance is often assigned for the process noise of the troposphere dynamics model. However, this fixed value may deviate from reality as the weather conditions change, especially for extreme weather. In this paper, a new adaptive Kalman filter is proposed for tropospheric delay processing, in which the variance of the process noise for the zenith tropospheric delay (ZTD) dynamics model is tuned in real time using the least-squares variance component estimation technique. MGEX/IGS data of 15 consecutive days were processed in a stepwise manner. Namely: Real-time BDS/GPS precise clock corrections were estimated firstly, followed by comparison among ZTD solutions of four schemes based on these real-time clocks of first step and GFZ multi-GNSS precise clock (GBM) final clocks: (1) real-time solution of ZTD (G(GPS), GC(GPS and BDS)) without VCE; (2) real-time solution of ZTD (G, GC) with VCE; (3) final solution of ZTD (G, GC, GR (GPS and GLONASS), GE (GPS and GALILEO), GRC (GPS, GLONASS and BDS), GREC (GPS, GLONASS, GALILEO and BDS) without VCE; and (4) final solution of ZTD (G, GC, GR, GE, GRC, GREC) with VCE. The performance of the ZTD and positioning solution was analyzed. Results showed that the accuracy of estimated real-time satellite clock correction was 0.27, 1.31, 0.29, and 0.21 ns for GPS, BDS/GEO, BDS/IGSO, and BDS/MEO, respectively. For the ZTD solutions, the results of schemes 1 and 2 were 12.8 mm (GC) and 10.1 mm (GC) in terms of mean root-mean-square (RMS) values and 2.1 mm (GC) and 1.6 mm (GC) in terms of minimum RMS values, respectively, thereby showing an improvement for scheme 2 of 1.8–81.4% over scheme 1 with average increasing rates of 20.7% (GC) and 20.2% (G). The results for schemes 3 and 4 were 7.6 mm (G) and 6.3 mm (GRC) in terms of mean RMS values and 2.1 mm (G) and 1.9 mm (GRCE) in terms of minimum RMS values, respectively, thereby showing an improvement in scheme 4 over scheme 3 by 1.3–85.6% with average increasing rates of 22.1% (GRCE), 21.9% (GRC), 18.4% (GR), 15.9% (GC), 15.2% (GE), and 12.1% (G). Similar results can be observed for the positioning solution, especially in the height component. These findings clearly show the advantage of the proposed method, which is consistent with the theoretical analysis. Notably, the advantage of the adaptive VCE becomes significant with the inclusion of additional satellite systems.

Decontamination and Dismantling (D&D) activities within the U.S. Department of Energy (DOE) require a long reach manipulator with a large load capacity. Variable Geometry Trusses (VGTs) are a unique class of mechanical structures which allow the advantages of truss structures for large scale applications to be applied to large robotic manipulators. Individual VGT units may be assembled to create a modular, long-reach, truss-type manipulator. Each module of such a manipulator system is either a static truss section or one of several possible VGT geometries. While many potential applications exist for this technology, the present work is largely motivated by the need for generic robotic systems for remote manipulation. A manipulator system based on VGT modules provides several advantages. The reconfigurable nature of the manipulator system allows it to be adapted on site to unforeseen conditions. The kinematic redundancy of the manipulator enables it to work effectively even in a highly obstructed workspace. The parallel structure of the truss modules enables the manipulator to be withdrawn in the event of a structural failure. Finally, the open framework of the modules provides a clear, protected passageway for control and power cabling, waste conveyance, or other services required at the end effector. As is implied in a truss structure, all primary members of a VGT are ideally loaded in pure tension or compression. This results in an extremely stiff and strong manipulator system with minimal overall weight. Careful design of the joints of a VGT is very important to the overall stiffness and accuracy of the structure, as several links (as many as six) are joined together at each joint. The greatest disadvantage to this approach to manipulator design has traditionally been that the kinematics of VGT structures are complex and poorly understood. This report specifically addresses the kinematics of several possible geometries for the individual VGT units. Equations and solution techniques are developed for solving the "forward" or "direct" and "inverse" kinematic problems for these geometries. The" forward" kinematic problem is that of finding the position and orientation of the distal end of the VGT relative to the proximal end, given the specific displacements of the (linear) actuators. This problem is rarely solvable in closed form. However, powerful iterative algorithms capable of solution in real time on typical modern robot control hardware are presented. The "inverse" kinematic problem is that of finding the required actuator displacements given the position and orientation of the distal end of the VGT relative to the proximal end. For specific VGT geometries, closed-form solutions are presented. For the more general problem, iterative algorithms capable of solution in real time are again derived and presented.

Robot formation control greatly relies on the accuracy and real-time performance associated with acquiring the information of the leader robot. The traditional communication and vision-based methods lead to a large delay and lack robustness to noise. In order to satisfy both requirements, we propose a cascaded multitask convolutional network to jointly address target detection and key point detection. In order to achieve high flexibility, we perform experiments using different model hyper parameters and explore the trade-off between accuracy and real-time performance. The experimental results demonstrate the effectiveness of our method for acquiring the information of the leader robot in real time with high accuracy. Furthermore, our method can be easily adapted to other vision-based tasks, laying foundation for the design of vision-based controllers for robots.