Pseudo Inverse Jacobian Matrix Research Articles

An adaptive singularity avoidance method for five-axis toolpath generation with invariant cutter-contact points and bounded tool orientation variation based on the reduction of Jacobian condition number

An adaptive singularity avoidance method for five-axis toolpath generation with invariant cutter-contact points and bounded tool orientation variation based on the reduction of Jacobian condition number

Kinematics decoupling analysis of a hyper-redundant manipulator driven by cables

Abstract. The mapping relationship between the driving space and the workspace is essential for the precise control of a cable-driven hyper-redundant robot. For a hyper-redundant robot driven by cables, the relationships between the driving space and the joint space and between the joint space and the workspace were studied. A joint-decoupling kinematics analysis method was proposed and a kinematic analysis was presented. Based on the analysis of the coupling effect between the cable-driving space and the joint space, a decoupling analysis of the whole cable-driving space and joint space was conducted to eliminate the coupling effect between the joints, and the mapping relationship between the driving cables and the joint angles was obtained. Given the initial and target orientations of the hyper-redundant robot, the variation law for each joint angle was obtained using quintic polynomial trajectory planning and the pseudo-inverse Jacobian matrix, and then the driving cable variation law could be solved. Based on the results, the joint angle changes and the workspace trajectories were solved in turn. By comparing with the initial trajectory, the simulation results verified the appropriateness of the decoupling analysis.

Suboptimal approximations in repeatable inverse kinematics for robot manipulators

Abstract In this paper a repeatable inverse kinematic task was solved via an approximation of a pseudo-inverse Jacobian matrix of a robot manipulator. An entry configuration to the task was optimized and a task-dependent definition of an approximation region, in a configuration space, was utilized. As a side effect, a relationship between manipulability and optimally augmented forward kinematics was established and independence of approximation task solutions on rotations in augmented components of kinematics was proved. A simulation study was performed on planar pendula manipulators. It was demonstrated that selection of an initial configuration to the repeatable inverse kinematic task heavily impacts solvability of the task and its quality. Some remarks on a formulation of the approximation task and its numerical aspects were also provided.

Acquisition of vowel articulation in childhood investigated by acoustic-to-articulatory inversion

While the acoustical features of speech sounds in children have been extensively studied, limited information is available as to their articulation during speech production. Instead of directly measuring articulatory movements, this study used an acoustic-to-articulatory inversion model with scalable vocal tract size to estimate developmental changes in articulatory state during vowel production. Using a pseudo-inverse Jacobian matrix of a model mapping seven articulatory parameters to acoustic ones, the formant frequencies of each vowel produced by three Japanese children over time at ages between 6 and 60 months were transformed into articulatory parameters. We conducted the discriminant analysis to reveal differences in articulatory states for production of each vowel. The analysis suggested that development of vowel production went through gradual functionalization of articulatory parameters. At 6-9 months, the coordination of position of tongue body and lip aperture forms three vowels: front, back, and central. At 10-17 months, recruitments of jaw and tongue apex enable differentiation of these three vowels into five. At 18 months and older, recruitment of tongue shape produces more distinct vowels specific to Japanese. These results suggest that the jaw and tongue apex contributed to speech production by young children regardless of kinds of vowel. Moreover, initial articulatory states for each vowel could be distinguished by the manner of coordination between lip and tongue, and these initial states are differentiated and refined into articulations adjusted to the native language over the course of development.

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 robot's 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 proposedVI-s. The presented method and the LabVIEWVI-s are generally and they can be used in all other robots types and for 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.

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.

Geometric error compensation for multi-axis CNC machines based on differential transformation

As the geometric errors of motion axis can be equivalent to the differential movement, regarded as a differential operator based on its ideal position, a new modeling method for multi-axis CNC machines based on differential transform theory is proposed in this paper. First, the workpiece coordinates is selected to observe the errors of the tool pose. Then, a general geometric error model for multi-axis machines is established. Moreover, the Jacobian matrix is applied to describe the relationship between the tool pose error vector and the compensation error vector. All the elements of the matrix are obtained by computing the differential operators instead of computing the partial derivatives. The compensation errors vector is solved using the pseudo-inverse Jacobian matrix. Finally, an automatic modeling procedure is developed to construct the geometric errors for multi-axis machine tools. An experiment on a five-axis machine tool is conducted to test and verify the proposed method. The results show that the proposed method dramatically improves the overall position accuracy of the test tool path.

Kinematic Manipulability of Multi-joint Bio-inspired Extremities

Abstract A linearised navigation control law for multi-legged walking robots is presented. The proposed model is stated in terms of robot's global acceleration, and formulated as an average of the Cartesian speeds of n-extremities of k-DOFs each. The state vector is defined as a general solution scoping three cases of robot's tangential acceleration: uniform, non-uniform, and constant speed. Leg's Cartesian velocities are described by their first order Jacobian, which results in redundant kinematics systems. As particular cases of study, two different biological kinematic configurations were analysed in order to be adapted (DOFs reductions) as potential kinematic functions of the navigation control law. Although, the research interest is centralised on walking systems, the Praying-Mantis raptorial legs, as well as the Smithi ant's legs are analysed. Because of the kinematic redundancy, by using pseudo-inverse numerical methods, the solution near a singularity region is unstable about these values. It was obtained the first-order derivative pseudo-inverse Jacobian matrix using two different numerical methods for multi-joint legs: the right pseudo-inverse, and by singularity properties using the singular value decomposition approach.

Toward Autonomic Computing

Cognitive approach through the neural network “NN” paradigm is a critical discipline that will help bring about autonomic computing “AC.” NN-related research, some involving new ways to apply control theory and control laws, can provide insight into how to run complex systems that optimize to their environments. NN is one kind of AC system that can embody human cog-nitive powers and that can adapt, learn, and take over certain functions previously performed by humans. In recent years, artificial neural networks have received a great deal of attention for their ability to perform nonlinear mappings. In trajectory control of robotic devices, neural networks provide a fast method of autonomously learning the relation between a set of output states and a set of input states. In this article, we apply the cognitive approach to solve position controller problems using an inverse geometrical model. In order to control a robot manipulator in the accomplishment of a task, trajectory planning is required in advance or in real time. The desired trajectory is usually described in Cartesian coordinates and needs to be converted to joint space for the purpose of analyzing and controlling the system behavior. In this article, we use a memory neural network (MNN) to solve the optimization problem concerning the inverse of the direct geometrical model of the redundant manipulator when subject to constraints. Our approach offers substantially better accuracy, avoids the computation of the inverse or pseudo-inverse Jacobian matrix, and does not produce problems such as singularity, redundancy, and considerably increased computational complexity.

Research on embedded MAS based manipulator control

PurposePresents an embedded MAS (Multi‐Agent System) based control method for multi link series manipulators.Design/methodology/approachThe manipulator's completing operation work is based on several agents' cooperation. The entire embedded MAS of a manipulator is implemented in one ARM7 microprocessor. The multi agents and the communications between the agents are constructed depending on the real‐time multitasking capability and the system services of real time operation system, μC/OS‐(tm). An improved distributed inverse kinematics algorithm, which is the foundation the agents' behavior strategies, and the system architecture designing are described in detail.FindingsThis method is very suitable for tele‐operation redundant manipulators' embedded control systems designing, with high reliability.Research limitations/implicationsUsing this paradigm, the embedded system firmware development for a redundant manipulator would be very easy and the code would be reusable. A few amendments should be made for miscellaneous manipulators.Practical implicationsIt is suitable for controlling a high reliability expected tele‐operation manipulator system.Originality/valueThe embedded MAS based manipulator control paradigm has several attractive advantages, led from MAS theory. Basing this method, we do not require computing the traditional inverse (or pseudoinverse) Jacobian matrix to control a redundant manipulator, especially for mobile redundant robot based on a compact embedded control system, expecting high reliability and potential complexity for coping with dynamical environments. The development procedure would be very easy and the code would be reusable. A few amendments should be made for different manipulators.

A Robust Control Strategy of Redundant Manipulator by Workspace Observer

This paper describes a decoupling force control strategy of redundant manipulator by workspace observer. In general, the calculation process of the redundant manipulator becomes complex as the number of degree-offreedom motion increases because the controller includes the pseudo inverse Jacobian matrix. To alleviate this problem, we develop a simplification method of the inverse kinematics solution including null space calculation by using the transposed Jacobian matrix, and the workspace observer. Here the stable condition of the proposed controller is also presented. Its condition is an important index to construct the stable workspace observer.

Observer-Based Local Torque Optimization in Redundant Manipulator.

In this paper, a local torque optimization strategy for a redundant manipulator based on observer is proposed. The calculation of the torque-optimizing controller becomes more complicated as the number of degrees-of-freedom increases because a pseudo inverse Jacobian matrix is generally used and the controller needs to calculate dynamical torque. To resolve this problem, the disturbance observer is applied to the redundant manipulator to simplify the controller calculation. Then, the torque-optimizing controller is realized without much effort required for calculating the null space term and dynamical effects. Furthermore, we find that the good performance of the workspace position response is obtained in the proposed controller. The validity of the proposed method is confirmed by the numerical and experimental results in the 3-link planar redundant manipulator.

A Robust Control Strategy of Redundant Manipulator by Workspace Observer.

This paper describes a decoupling force control strategy of redundant manipulator by workspace observer. In general, the calculation process of the redundant manipulator becomes complicated as the number of degree-of-freedom motion increases since the controller includes the pseudo inverse Jacobian matrix. To improve this issue, we develop a simplification method of the inverse kinematics solution including null space calculation by using the transposed Jacobian matrix, and the workspace observer. Here the stable condition of the proposed controller is also shown. Its condition is an important index to construct the stable workspace observer.The validity of the proposed method is confirmed by the numerical and experimental results in the 3link planar redundant manipulator.

冗長ロボットアームのためのコンプライアンス制御の一手法

A method of compliance control for a redundant robotic arm was proposed. The method is constructed by combining two different compliance control scheme ; the fundamental compliance control in the joint space and the adjusting compliance control in operational space. One of the features of the proposed method is to achieve both the desired compliance condition in the operational space and the unique determination of the redundant manipulator configuration. Another feature of it is that the inverse kinematic solution of the redundant manipulator was obtained according only to fundamental compliance parameters. -Also, how to control the trajectory of the end-effector was intro-duced. The inverse kinematics solution is similar to be obtained from the pseudo-inverse Jacobian matrix with a weight matrix. However, it has a different benefit benefit from the pseud-inverse approach, because it provides a function of adjusting the end-effector compliance as well as the inverse kinematics solution. Through experiments using a manufactured four d. o. f. robotic arm with redundancy, the effectiveness of the method was confirmed.

A Method for Solving Inverse Kinematics of Variable Structure Truss Arm with High Redundancy

A method of solving the inverse kinematic problem for highly redundant degrees of freedom truss arm is proposed. The method is based on the compliance control technique. One special feature of the method is that it can provide an analytical formula tion of the inverse kinematic solution. The other is that it enables the control of end- effector compliance as well as the position and the orientation control. The pseudo-inverse Jacobian matrix with a weight matrix which is popularly used to solve the inverse kine matics with redundancy also provides the equivalent result to the proposed methods. The difference between them is that the pseudo-inverse approach provides a solution only for the position control and has no extension to the compliance control. In the paper, first, the forward kinematics will be formulated. Secondly, the inverse kinematic solution will be derived based on the compliance control technique. Thirdly, the end-effector compliance control and the arm configuration control will be addressed. Finally, the effectiveness of the method is confirmed through simulation experiments.

ROBOSIM: a CAD-based off-line programming and analysis system for robotic manipulators

In order for a robotic manipulator to perform useful work, it must be programmed to accomplish the desired task or motion cycle. There are many methods available for interfacing the human user with the industrial robot This article concentrates on the off-line programming, analysis and interactive computer simulation of a general five-axis revolute robotic manipulator. An off-line programming system, called ROBOSIM (ROBOtic SIMulation), was developed for this task. The software that was produced included three-dimensional wire-frame graphics demonstrated on a commercially available CAD package. The off-line system solves the inverse kinematics at each point in the trajectory plan and determines the actual path of the end effector, using either joint-interpolated motion and/or straight-line motion. Velocity calculations and singularity checks are performed using the pseudo–inverse Jacobian matrix. A language translation module was also written for automatic code generation for the five-axis Microbot TeachMover. The developed off-line program has the ability to simulate any general five-axis robot of similar design and allows for easy updates to the system modules.