During the Industry 4.0 era, the open source-based robotic arms control applications have been developed, in which the control algorithms apply for movement precision in the trajectory tracking paths based on direct or reverse kinematics. Therefore, small errors in the joint positions can summarize in large position errors of the end-effector in the industrial activities. Besides the change of the end-effector position for a given variation of the set-point in manipulator joint positions depends on the manipulator configuration. This research proposes a control based on Proportional Derivative (PD) Control with gravity compensation to show the robustness of this control scheme in the robotic arm’s industrial applications. The control algorithm is developed using a low-cost board like Raspberry Pi (RPI) where the Robot Operating System (ROS) is installed. The novelty of this approach is the development of new functions in ROS to make the PD control with gravity compensation in low-cost systems. This platform brings a fast exchange of information between the Kuka™ youBot robotic arm and a graphical user’s interface that allows a transparent interaction between them.

Low-Cost Automation for Gravity Compensation of Robotic Arm

Review of the performance optimization of parallel manipulators

Gravity and flexibility will cause fluctuations of the rotation angle in the servo system for flexible manipulators. The fluctuation will seriously affect the motion accuracy of end-effectors. Therefore, this paper adopts a control method combining the RBF (Radial Basis Function) neural network and pole placement strategy to suppress the rotation angle fluctuations. The RBF neural network is used to identify uncertain items caused by the manipulator’s flexibility and the time-varying characteristics of dynamic parameters. Besides, the pole placement strategy is used to optimize the PD (Proportional Differential) controller’s parameters to improve the response speed and stability. Firstly, a dynamic model of flexible manipulators considering gravity is established based on the assumed mode method and Lagrange’s principle. Then, the system’s control characteristics are analyzed, and the pole placement strategy optimizes the parameters of the PD controllers. Next, the control method based on the RBF neural network is proposed, and the Lyapunov stability theory demonstrates stability. Finally, numerical analysis and control experiments prove the effectiveness of the control method proposed in this paper. The means and standard deviations of rotation angle error are reduced by the control method. The results show that the control method can effectively reduce the rotation angle error and improve motion accuracy.

Control Method of Flexible Manipulator Servo System Based on a Combination of RBF Neural Network and Pole Placement Strategy

https://backend.orbit.dtu.dk/ws/files/140259309/Active_Tilting_Pad_Journal_Bearings_Supporting_Part_2.pdf

Active tilting-pad journal bearings supporting flexible rotors: Part II–The model-based feedback-controlled lubrication

A complete analytical solution for the dimensional synthesis of 3-DOF delta parallel robot for a prescribed workspace

. This extensive review paper, which involves 204 papers,
discusses comprehensively a number of performance indices that are
instrumental in the design of parallel kinematics manipulators. These
indices measure the workspace as well as its quality including the distance
to singularity, dexterity, manipulability, force transmission, accuracy,
stiffness, and dynamic performance. After being classified, the indices are
discussed in terms of some important aspects including definition, physical
meaning soundness, dependency, consistency, scope of applicability, and
computation cost. For the sake of completeness, some key mathematical
expressions of the indices are provided.

/pdf/review-article-performance-measures-of-parallel-kinematics-3wcest16eb.pdf

Review article: Performance measures of parallel kinematics manipulators

This paper proposes a special non-symmetric topology of a 3PRR planar parallel kinematics mechanism, which naturally avoids singularity within the workspace and can be utilized for hybrid kinematics machine tools. Subsequently, single-objective and multi-objective optimizations are conducted to improve the performance. The workspace area and minimum eigenvalue, as well as the condition number of the homogenized Cartesian stiffness matrix across the workspace, have been chosen as the objectives in the optimization based on their relevance to the machining application. The single-objective optimization is conducted by using a single-objective genetic algorithm and a hybrid algorithm, whereas the multi-objective optimization is conducted by using a multi-objective genetic algorithm, a weighted sum single-objective genetic algorithm, and a weighted sum hybrid algorithm. It is shown that the single-objective optimization gives superior value in the optimized objective, while sacrificing the other objectives, whereas the multi-objective optimization compromises the improvement of all objectives by providing non-dominated values. In terms of the algorithms, it is shown that a hybrid algorithm can either verify or refine the optimal value obtained by a genetic algorithm.

Genetic and hybrid algorithms for optimization of non-singular 3PRR planar parallel kinematics mechanism for machining application

The need of rotating machines to operate at higher speeds requires better techniques of vibration control. This paper presents how optimal control is applied to rotor-bearing-support systems in which the rotor finite element models have relatively large degrees of freedom (DOF). To conduct the control design for such rotor finite element models with large DOF is challenging and expensive. At this point, the order reduction of the model has its role. In this work, two types of rotor-bearing-support system were used: one with tilting pad journal bearings and the other one with plain full journal bearings which is typically less stable. For cost consideration, the large DOF rotor was reduced into smaller DOF. The quality of the model reduction was evaluated by comparing some first natural frequencies, modal damping ratios, critical speeds, and response of both the full system and the reduced system, along the frequency range of interest. To control vibration, linear quadratic regulator (LQR) control technique was used. From the closed-loop responses, it is shown that the LQR controller suppresses the resonance quite well. In this case, two different pairs of weighting matrices were used. It is shown that the first pair is better at lower speeds, whereas the second pair is better at higher speeds.

Optimal control of reduced-order finite element models of rotor-bearing-support systems

Rotating discs with variable thickness and nonhomogeneous material properties are frequently used in industrial applications. The nonhomogenity of material properties is often caused by temperature change throughout the disc. The governing differential equation presenting this problem contains many variable coefficients so that no possible analytical closed form solution for this problem. Many numerical approaches have been proposed to obtain the solution. However, in this study the Finite Element Method (FEM), which presents a powerful tool for solving such a problem, is used. Thus, a turbine disc modeled by using ax symmetric finite elements was analyzed. But, in order to avoid inaccuracy of the stress calculation quite fine meshing is implemented. The analysis showed that maximum displacement occurs at the boundary of the disc, either at the outer or inner boundary, depending on the loadings. The maximum radial stress occurs at an area in the middle of the disc which has the smallest thickness. In this study, rotational blade load was shown to give the largest contribution to the total displacement and stress. Also, the radial displacement and stress in a disc with variable thickness are found to be affected by the contour of the thickness variation. In general, the results obtained show excellent agreement with the published works.

Stress Analysis of Nonhomogeneous Rotating Disc with Arbitrarily Variable Thickness Using Finite Element Method

This paper presents the implementation of nonlinear least squares and iterative linear least squares algorithms for external kinematic calibration of a hybrid kinematics machine composed of two 3PRR planar parallel kinematics mechanisms by utilizing a laser tracker. First the hand-eye and robot-world transformations were obtained by a separable closed-form solution and refined by the nonlinear least squares. Subsequently, the geometric parameters of the machine’s mechanisms were estimated using the two algorithms. Due to the rank deficiency, we implemented the nonlinear least squares algorithm through a subset selection approach in which we performed the estimation in two steps. We iterated the closed-form solution of the linear least squares until the solution converges to the actual values. We have shown that the nonlinear least squares algorithm successfully refined the hand-eye and robot-world transformations and outperformed the iterative linear squares algorithm in the estimation of the geometric parameters of the mechanisms.

/pdf/external-kinematic-calibration-of-hybrid-kinematics-machine-2ug3b47bzy.pdf

Abdur Rosyid

Papers

Review article: Performance measures of parallel kinematics manipulators

Genetic and hybrid algorithms for optimization of non-singular 3PRR planar parallel kinematics mechanism for machining application

Optimal control of reduced-order finite element models of rotor-bearing-support systems

Stress Analysis of Nonhomogeneous Rotating Disc with Arbitrarily Variable Thickness Using Finite Element Method

External Kinematic Calibration of Hybrid Kinematics Machine Utilizing Lower-DOF Planar Parallel Kinematics Mechanisms