Serban Olaru

Proper Assisted Research Method Solving of the Robots Inverse Kinematics Problem

Finding the better solution of the inverse kinematics problem, with the minimum of the trajectory errors, is very difficult because there are many variable parameters and many redundant solutions. The presented paper show the assisted solving of the inverse kinematics with the goal to minimize the final end-effector trajectory errors, by optimizing the distance between the and-effector final position and the target. All obtained results were been verified by applying the proper forward kinematics virtual LabVIEW instrumentation. The paper tries to answer at the inverse kinematics problem for one known mathematical trajectory and identifying the cinematic errors after the establishing and applying the proper assisted solving method using the Cycle Coordinate Descent Method coupled to the proper Neural Network Sigmoid Bipolar Hyperbolic Tangent (CCDM-SBHTNN). We were shown one complete study case to obtain one circle space trajectory using one arm type robot fixed on the ceiling. The presented method is general and can be used in all other robots types and in all other conventional and unconventional space curves.

Assisted Research of the Neural Network

In the optimization of the trajectory or of the guidance of mobile robots one of the more important things is to assure one small difference between the output data of the system and the target. This paper show how on-line will be possible to establish one convergence way to the target without any influences of the input data or initial conditions of the weights or biases. The paper show the general components and the mathematical model of some more important neurons and one numerical simulation of the linear neural network. In the paper was used the least mean square (LMS) error algorithm for adjusting the weights and biases and incremental training by different training rate, finally to obtain one minimum error to the target.

Assisted Research and Optimization of the Proper Neural Network Solving the Inverse Kinematics Problem

Finding the better solution of the neural network design to solve the inverse kinematics problem with the minimum of the trajectory errors is very difficult, because there are many variable parameters and many redundant solutions. The presented paper show the assisted research of the influences of some more important parameters to the final end-effector trajectory errors of the proposed neural network model solving the inverse kinematics problem. We were been studied the number of neurons in each layers, the sensitive function for the first and second layer, the magnifier coefficient of the trajectory error, the variable step of the time delay and the position of this block, the different cases of target data and the case when the hidden target data were adjusted. All obtained results were been verified by applying the proper direct kinematics virtual LabVIEW instrumentation. Finally we were obtained one optimal Sigmoid Bipolar Hyperbolic Tangent Neural Network with Time Delay and Recurrent Links (SBHTNN(TDRL)) type, what can be used to solve the inverse kinematics problem with maximum 4% of trajectory errors.

Assisted Research of the Neural Network with LabVIEW Instrumentation

The paper open the way to the assisted choose of the optimal neural network. There are shown some important neurons type, transfer functions, weights and biases of neurons, and some complex layers with different type of neurons in a static and dynamic networks. By using the proper virtual LabVIEW instrumentation were established some influences of the network parameters to the number of iterations till canceled the mean square error to the target. Were presented the simulation of some different neural network types like linear, sigmoid, sigmoid bipolar and radial. For some of more important, were presented the complex mathematical models and numerical simulation using the proper teaching law.

Increase the Space Trajectory Precision by Using the Proper Assisted Research Method for Inverse Kinematics Problem

Inverse kinematics model of the industrial robot is used in the control of the end-effecter trajectory. The solution of the inverse kinematics problem is very difficult to find, when the degree of freedom increase and in many cases this is impossible. In these cases is used the numerical approximation or other method with diffuse logic. The paper showed one new method for optimization of the inverse cinematic solution by applying the proper assisted Iterative Pseudo Inverse Jacobian Matrix Method coupled with proper Sigmoid Bipolar Hyperbolic Tangent Neural Network with Time Delay and Recurrent Links Method (IPIJMM-SBHTNN-TDRLM). In the paper was shown one case study to obtain one space circle curve by using one arm type robot and the proposed method. The errors of the space coordinates of the circle, after applying the proposed method, was less than 0.001. The study has contained the determining the internal coordinates corresponding to the external coordinates of the circle space curve, by solving the inverse kinematics with the proposed method and after that, by applying the forward kinematics to this coordinates, were obtained the external coordinates, what were compared with the theoretical one. The presented method is general and it can be used in all other robots types and for all other conventional and unconventional space curves.

Modeling and Simulation of the Multiple Robot’s Applications

This paper explains and demonstrates how can designed one multi robots application with many tasks and some different type of modular collaborative robots. Was described the general mathematical model for the direct and inverse kinematics to controlling the robots and how can solve the inverse kinematics of multiple tasks by using the priority of tasks or serial tasks composed by sum of the weighted several tasks. Some collaborative multi robots applications with parallel, serial or composed robots configurations were shown. The general mathematical matrix model of the robot application point with three translations and three rotations to the world Cartesian coordinates of the application map was defined. The designed method, the animation programs and the used LabVIEW proper virtual instruments open the way to easily define the multi robots application map, establish the constraints of the used robots and of the environment to avoid the singular points and tests the manipulation programs for collaborative application.

Optimization of the Neural Network by Using the LabVIEW Instrumentation

The paper shown one assisted method to construct simple and complex neural network and to simulate on-line them. By on-line simulation of some more important neural simple and complex network is possible to know what will be the influences of all network parameters like the input data, weight, biases matrix, sensitive functions, closed loops and delay of time. There are shown some important neurons type, transfer functions, weights and biases of neurons, and some complex layers with different type of neurons. By using the proper virtual LabVIEW instrumentation in on-line using, were established some influences of the network parameters to the number of iterations before canceled the mean square error to the target. Numerical simulation used the proper teaching law and proper virtual instrumentation. In the optimization step of the research on used the minimization of the error function between the output and the target.

Assisted Optimisation of the Robot Dynamic Behavior with Magnetorheological Damper

The paper showed the assisted research of one magnetorheological damper and the influences to the dynamic behavior of the industrial robots. The research contents the assisted theoretical simulation of the new mathematical model, the parameterization of the known characteristics of the magnetorheological damper and the assisted establish of the influences of the model coefficients to the characteristics parameters. In the assisted experimental research was established the values of all coefficients of the proper mathematical model to assure the concordance between the experimental and the theoretical characteristics. By knowing the real mathematical model of the damper was possible to develop the new matrix -vector form of the force- moment and the research of the global dynamic behavior of the industrial robot with proper smart damper system.

Optimization of the Robot's Position Base Point by Using the Proper Algorithm and Iterative Pseudo Inverse Jacobian Neural Network Matrix Method

In the robotized production one of the more important think is to choose the optimal solution to use the robots with respect an objective function which represents, for example, minimum time of motion during a application, or minimum consumption of energy, or maximum precision, or combination of these. Some objective functions could results from the specificity of the application like is the case of casting of forging, where the minimum of the accumulation of heat could be one of the optimization criteria. In the controlling of the space movement of the end effecter and the robot’s joints of the all robots from the applications, one of the most important think is to know, with the extreme precision, the joints relative displacements of all robots. One of the most precise method to solve the inverse kinematics problem in the robots with redundant chain is the complex coupled method of the neural network with Iterative Pseudo Inverse Jacobian Matrix Method. In this paper was used the proper coupled method Iterative Pseudo Inverse Jacobian Matrix Method (IPIJMM) with Sigmoid Bipolar Hyperbolic Tangent Neural Network with Time Delay and Recurrent Links (SBHTNN-TDRL) to establish the optimal position of the application point of the robots base with respect simultaneously two objective functions: the extreme precision and the minimum of the movements time. The paper shown how can be changed the multi robots application in to one application with parallel robot structure with three independent robots, all of them with optimal location point with respect the obiective function. The presented method and the virtual instrumentations (VI) are generally and they can be used in all other robots application and for all other conventional and unconventional space curves.

Controlling of the 3D Space Trajectory of the Multi Robots Applications by Using the Proper Iterative Pseudo Inverse Jacobian Neural Network Matrix Method

In many applications we used the multi robots with the central coordination of the 3D space trajectory. In the controlling of the space movement of the end effecter of the all robots from this type of applications and the robot’s joints one of the most important problem is to solve the forward and inverse kinematics, that is different from the single robot application. It is important to know with the extreme precision the joints relative displacements of all robots. One of the most precise method to solve the inverse kinematics problem in the robots with redundant chain is the complex coupled method of the neural network with Iterative Jacobian Pseudo Inverse method. In this paper was proposed and used the proper coupled method Iterative Pseudo Inverse Jacobian Matrix Method (IPIJMM) with Sigmoid Bipolar Hyperbolic Tangent Neural Network with Time Delay and Recurrent Links (SBHTNN-TDRL). The paper contents the mathematical matrix model of the forward kinematics of multiple robots applications, mathematical model of the proper iterative algorithm and all proper virtual LabVIEW instrumentation, to obtain the space conventional and unconventional curves in different Euller planes for one case study of three simultaneously robots movement with extreme precision of the end-effecter less than 0.001mm. The paper shown how can be changed the multi robots application in to one application with parallel robot structure with three independent robots. The presented method and the virtual instrumentations (VI) are generally and they can be used in all other robots application and for all other conventional and unconventional space curves.