Niculae Mihai

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.

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 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.

Proper LabVIEW Instrumentation of the Robot’s Kinematics and Dynamics Behavior

The most important in the study of the robots is the kinematic and dynamic analyze. Many researchers studied the kinematics or dynamics without simulation and assisted analyze that it is very heavy to understand the behavior and to show some characteristics. The paper shows one assisted method by using the virtual proper LabVIEW instrumentation (VI). For the forward kinematics (FK) and for direct dynamics (DD) was used one recurrent matrix method which was developed with quaternion algebra, that will be possible to use in many different other types of robots, only by initial settings of the type of joints, the movement axis, the home position, the dimension of each robot’s body, the application point in the working space of the manufacturing cells and the internal coordinates in each joint. For the inverse kinematics (IK) we used the Iterative Pseudo Inverse Jacobian Matrix Method (IPIJMM) coupled with the proper Sigmoid Bipolar Hyperbolic Tangent Neural Network with Time Delay and Recurrent Links (SBHTNN-TDRL). The paper describe all steps in one case study to obtain the space curve in different Euller planes by using one arm type robot and the proposed VI-s. The presented method and the LabVIEW VI-s are generally and they can be used in all other robots types and for all other conventional and unconventional space curves.

Proper Smart Method of the Inverse Kinematic Problem

One of the most precise method solving the inverse kinematics problem in the redundant cases of the robots is the coupled method. The proposed method use the Iterative Pseudo Inverse Jacobian Matrix Method (IPIJMM) coupled with the proper Sigmoid Bipolar Hyperbolic Tangent Neural Network with Time Delay and Recurrent Links (SBHTNN-TDRL). One precise solution of the inverse kinematics problem is very difficult to find, when the degree of freedom increase and in many cases this is impossible because the redundant solutions. In all these cases must be used the numerical iterative approximation, like the proposed method, with artificial intelligence algorithm. The paper describe all the steps in one case study to obtain the space circle curve in different planes by using one arm type robot and the proposed method. The errors of the space movement of the robot end-effecter, after applying the proposed method, was less than 0,01. The presented method is general and it can be used in all other robots types and for all other conventional and unconventional space curves.