Inverse kinematic deriving and actuator control of Delta robot using symbolic computation technology

In order to effectively derive the inverse kinematic solution of the Delta robot and realize actuator control a description of the linear graph principle for automatically generating kinematic equations in a mechanical system as well as the symbolic computation implementation of this procedure is reviewed and projected into the Delta robot. Based on the established linear graph representation the explicit symbolic expression of constraint equations and inverse kinematic solutions are obtained successfully using a symbolic computation engine Maple so that actuator control and trajectory tracking can be directly realized.Two practical motions the circular path and Adept motion are simulated for the validation of symbolic solutions respectively.Results indicate that the simulation satisfies the requirement of the quick motion within an acceptable threshold. Thus the precision of kinematic response can be confirmed and the correctness of inverse solution is verified.

INVERSE KINEMATICS FOR A 6 DOF MANIPULATOR BASED ON NEURAL NETWORK

A methodology is presented whereby a neural network is used to learn the inverse kinematic relationships of the position and orientation of a six joint manipulator. The arm solution for the orientation of a manipulator using a self organizing neural net is studied in this paper. A new training model of the self organizing neural network is proposed by thoroughly studying Martinetz, Ritter and Schulten′s self organizing neural network based on Kohonen′s self organizing mapping algorithm using a Widrow Hoff type error correction rule and closely combining the characters of the inverse kinematic relationship for a robot arm. The computer simulation results for a PUMA 560 robot show that the proposed method has a significant improvement over other methods documented in the references in self organizing capability and precision by training process.

An Analysis of the Inverse Kinematics for a 5-DOF Manipulator

This paper proposes an analytical solution for a 5-DOF manipulator to follow a given trajectory while keeping the orientation of one axis in the end-effector frame. The forward kinematics and inverse kinematics for a 5-DOF manipulator are analyzed systematically. The singular problem is discussed after the forward kinematics is provided. For any given reachable position and orientation of the end-effector, the derived inverse kinematics will provide an accurate solution. In other words, there exists no singular problem for the 5-DOF manipulator, which has wide application areas such as welding, spraying, and painting. Experiment results verify the effectiveness of the methods developed in this paper. Keywords Inverse kinematics - modeling and control - 5-DOF manipulator This work was supported by the National High Technology Research and Development Program of China (No. 2002AA422160), and the National Key Fundamental Research and Development Project of China (973, No.2002CB312200)De Xu graduated from Shandong University of Technology (SUT), China in 1985. He received a Masters degree from SUT in 1990, and a Ph.D. degree from Zhejiang University, China in 2001. He has been with the Institute of Automation, at the Chinese Academy of Sciences (CASIA) since 2001. He is an associate professor with the Laboratory of Complex Systems and Intelligence Science, CASIA. He worked as on academic visitor in the Department of Computer Science, at the University of Essex from May to August 2004. He is a member of the IEEE. His research interests include robotics and automation, especially the control of robots such as visual and intelligent control.Carlos Antonio Acosta Calderon received a B.S. degree in Computer Science Engineering from Pachuca Institute of Technology, Mexico in 2000, and a M.Sc. degree in Computer Science (Robotics and Intelligent Machines) from the University of Essex, UK in 2001. He is currently pursuing a Ph.D degree in Computer Science at the University of Essex, UK. His research interests have focused on mobile robots, in particular, the coordination of multi-robot systems, mobile manipulators, and learning by imitation. He is a member of IEEE.John Q. Gan received a B.Sc. degree in electronic engineering from Northwestern Polytechnic University, China in 1982, a M.Eng. degree in automatic control and a Ph.D degree in biomedical electronics from Southeast University, China in 1985 and 1991, respectively. He is a Senior Lecturer in the Department of Computer Science at the University of Essex, UK. He has co-authored a book, and published over 100 research papers. His research interests are in robotics and intelligent systems, brain-computer interfaces, pattern recognition, signal processing, data fusion, and neurofuzzy computation.Huosheng Hu is a Professor in the Department of Computer Science, at the University of Essex, and head of the Human Centered Robotics Group. His research interests include autonomous mobile robots, human-robot interaction, evolutionary robotics, multi-robot collaboration, embedded systems, pervasive computing, sensor integration, RoboCup, intelligent control, and networked robotics. He has published over 200 papers in journals, books, and conferences, and received two best paper awards. He is a founding member of the IEEE Society of Robotics and Automation Technical Committee of Internet and Online Robots, and a member of the IASTED Technical Committee on “Robotics” for 2001–2004. He was a Conference Chairman for the 1st European Embedded Systems Conference in Paris, 1996, and has been a member of the Program Committees for many international conferences such as IROS (2005–2006), IASTED Robotics and Applications Conferences (2000-present), and RoboCup Symposiums (2000–2004). Dr. Hu is a Chartered Engineer, a senior member of IEEE, and a member of IEE, AAAI, ACM, IASTED and IAS.Min Tan graduated from Tsing Hua University, China in 1986. He received a Ph.D. degree in 1990 from CASIA. He is a professor with the Laboratory of Complex Systems and Intelligence Science, CASIA. He has published over 100 papers in journals, books, and conferences. His research interests include robotics and complex system theory.

Two optimization algorithms for solving robotics inverse kinematics with redundancy

The kinematic redundancy in a robot leads to an infinite number of solutions for inverse kinematics, which implies the possibility to select a 'best' solution according to an optimization criterion. In this paper, two optimization objective functions are proposed, aiming at either minimizing extra degrees of freedom (DOFs) or minimizing the total potential energy of a multilink redundant robot. Physical constraints of either equality or inequality types are taken into consideration in the objective functions. Since the closed-form solutions do not exist in general for highly nonlinear and constrained optimization problems, we adopt and develop two numerical methods, which are verified to be effective and precise in solving the two optimization problems associated with the redundant inverse kinematics. We first verify that the well established trajectory following method can precisely solve the two optimization problems, but is computation intensive. To reduce the computation time, a sequential approach that combines the sequential quadratic programming and iterative Newton-Raphson algorithm is developed. A 4-DOF Fujitsu Hoap-1 humanoid robot arm is used as a prototype to validate the effectiveness of the proposed optimization solutions.

Wavelet network solution for the inverse kinematics problem in robotic manipulator

Wavelet network, a class of neural network consisting of wavelets, is proposed to solve the inverse kinematics problem in robotic manipulator. A wavelet network suitable for dealing with multi-input and multi-output system is constructed. The network is optimized by reducing the number of wavelets handling large dimension problem according to the sample data. The algorithms for sparseness analysis of input data and fitting wavelets to the output data with orthogonal method are introduced. Then Levenberg-Marquardt algorithm is used to train the network. Simulation results showed that this method is capable of solving the inverse kinematics problem for PUMA560.

Inverse Kinematics Analysis of a 7-DOF Space Manipulator for Trajectory Design

To solve the inverse kinematics problem for redundant degrees of freedom（DOFs）manipulators has been and still continues to be quite challenging in the field of robotics.Aiming at trajectory planning for a 7-DOF space manipulator system,joint rotation trajectories are obtained from predetermined motion trajectories and poses of the end effector in Cartesian space based on the proposed generalized inverse kinematics method.A minimum norm method is employed to choose the best trajectory among available trajectories.Numerical simulations with the7-DOF manipulator show that the proposed method can achieve the planned trajectory and pose under the circumstances of minimum angular velocities.Moreover,trajectory results from the proposed kinematics model and inverse kinematics method has the advantages of simple modelling,low computation cost,easy to solve and plan trajectory conveniently.The smooth and continuous joint rotation functions obtained from the proposed method are suitable for practical engineering applications.

Study on general inverse kinematics of rotating/tilting positioner for robotic arc welding off-line programming

Off line programming provides an essential link between CAD and CAM, whose development will result in greater use of robotic arc welding. An arc welding system with a robot and a rotating/tilting positioner is one of the most typical workcells. The inverse kinematics of robot and positioner is the foundation of the off line programming system. The previous researchers only focused on a special solution of the positioner inverse kinematics, which is the solution at down hand welding position. In this paper, we introduce a method for representing welding position. Then a general algorithm of rotating/tilting positioner inverse kinematics is presented, and an approach to find the unique solution of the inverse kinematics is discussed. The simulation experiment results show that the general algorithm can improve the ability of robotic arc welding off line programming system to program all types of welding positions.

Inverse kinematics of a heavy duty manipulator with 6-DOF based on dual quaternion

An iterative method is introduced successfully to solve the inverse kinematics of a 6-DOF manipulator of a tunnel drilling rig based on dual quaternion, which is difficult to get the solution by Denavit-Hartenberg(D-H) based methods. By the intuitive expression of dual quaternion to the orientation of rigid body, the coordinate frames assigned to each joint are established all in the same orientation, which does not need to use the D-H procedure. The compact and simple form of kinematic equations, consisting of position equations and orientation equations, is also the consequence of dual quaternion calculations. The iterative process is basically of two steps which are related to solving the position equations and orientation equations correspondingly. First, assume an initial value of the iterative variable; then, the position equations can be solved because of the reduced number of unknown variables in the position equations and the orientation equations can be solved by applying the solution from the position equations, which obtains an updated value for the iterative variable; finally, repeat the procedure by using the updated iterative variable to the position equations till the prescribed accuracy is obtained. The method proposed has a clear geometric meaning, and the algorithm is simple and direct. Simulation for 100 poses of the end frame shows that the average running time of inverse kinematics calculation for each demanded pose of end-effector is 7.2 ms on an ordinary laptop, which is good enough for practical use. The iteration counts 2-4 cycles generally, which is a quick convergence. The method proposed here has been successfully used in the project of automating a hydraulic rig.

Implementation and Kinematic Control of a Hyper-redundant Mobile Manipulator System

Redundant or hyper-redundant mobile manipulator can give lots of assistance to astronauts in space station. The design and implementation of a hyper-redundant mobile manipulator system are described, which is composed of an 8 DOF module robot and a 1 DOF motorized rail. Inverse kinematic resolution of the system is discussed and one simplified control method based on joint limit avoidance and configuration optimization is proposed. Simulation and experimental results are presented.

Kinematics of a Trinal-Branch Space Robotic Manipulator with Redundancy

This paper presents a trinal-branch space robotic manipulator with redundancy, due to hash application environments, such as in the station. One end-effector of the manipulator can be attached to the base, and other two be controlled to accomplish tasks. The manipulator permits operation of science payload, during periods when astronauts may not be present. In order to provide theoretic basis for kinematics optimization, dynamics optimization and fault-tolerant control, its inverse kinematics is analyzed by using screw theory, and its unified formulation is established. Base on closed-form resolution of spherical wrist, a simplified inverse kinematics is proposed. Computer simulation results demonstrate the validity of the proposed inverse kinematics.

Inverse Kinematics Analysis of Weld Inspection Manipulator at Pipe Joint in Nuclear Industry

A redundant manipulator that can online clamp pipe was developed to track along a cylinder intersection curve. With an ultrasonic transducer mounted on its end-effector, the manipulator can perform welding seam inspection at pipe joint in nuclear industry. An inverse kinematics solution expressed in joint space was solved based on the combination of geometric method and D-H matrix transformation. Expression about joints variables was obtained based on the scanning parameters of pipeline. The analysis method and results can be widely applied for online trajectory planning of intersection curve scanning manipulators.

Inverse kinematics and welding experiments of the intersecting pipe welding robot

A robot used for multi-pass welding of the piping branch junctions and nozzle attachments to main pressure vessels is 4-DOF serial mechanism, two mobile joints and two rotary joints are adopted in design. The kinematic model was established with DH parameters, the inverse kinematics was solved. According to the forward and inverse kinematics equations, the robot kinematics was simulated in Matlab, the simulations indicate that the solution for inverse kinematics can satisfy the welding requirements well. As there are size errors, processing errors and welding deformation, the path of welding is forecasted according to the previous welding situation, and then, the path is taught at desired via-points, which plays an important role in submerged-arc welding. The submerged-arc welding experiments indicate that the robot and the welding methods are preferable to ensure welding quality.

An Inverse Kinematic Analysis Modeling on a 6-PSS Compliant Parallel Platform for Optoelectronic Packaging

Multiple degree of freedom motion platform is always one of the important components in optoelectronic packaging systems,its characteristics have a vital impact on the performances of optoelectronic packaging.This paper presents a 6-Prismatic-Spherical-Spherical compliant parallel platform for optoelectronic packaging.This platform is a kind of parallel layout structure,which uses the piezoelectric motors as active joints and the large-stroke flexure hinges are employed as passive joints.An inverse kinematic modeling based on elastokinematic analysis is analyzed and deduced.The elastokinematic analysis considers the elastic deformation of the large-stroke flexure hinges in movement process,and improves the positioning accuracy of the compliant parallel platform in applications.The finite element analysis model and the prototype of the compliant parallel platform are developed,and the validity of the proposed method is finally verified.This paper provides a theoretical reference and experimental data for the inverse kinematic analysis of six degrees of freedom motion compliant parallel platforms with large-stroke flexure hinges.

Neural Network Inversion for Multilayer Quaternion Neural Networks

Recently, solutions to inverse problems have been required in various engineering fields. The neural network inversion method has been studied as one of the neural network-based solutions. On the other hand, the extension of the neural network to a higher-dimensional domain, e.g., complex-value or quaternion, has been proposed, and a number of higher-dimensional neural network models have been proposed. Using the quatemion, we have the advantage of expressing 3D （three-dimensional） object attitudes easily. In the quaternion domain, we can define inverse problems where the cause and the result are expressed by the quaternion. In this paper, we extend the neural network inversion method to the quatemion domain. Further, we provide the results of the computer experiments to demonstrate the process and effectiveness of our method.

Simulation of proton–neutron collisions in inverse kinematics and its possible application

Neutrons have played a vital role in many nuclear physics fields.In some cases,the inverse kinematics of neutrons colliding with other nuclei are also worth studying.In this study,the inverse kinematics of thermal neutrons colliding with high-energy protons is simulated by using the Monte Carlo method.Thermal neutrons are taken as target particles,whereas protons are incident particles.The simulation implies that,after collision,the energy of the output neutron at 0°equals the energy of the incident proton.A possible application of the result is proposed that might yield single-energy neutrons.Some key parameters of the conceptual design were evaluated,demonstrating that the design may reach high-neutron-energy resolution.

Inverse kinematics analysis of tubular joint welding robot

A rail type mobile robot introduced in this paper is used to carry out automatic welding on the T, Y and K-joints in offshore platform jackets. This robotic system is composed of a mobile platform and a serial manipulator. The structure of manipulator was designed according to the mathematical modeling of single brace tubular joint ; some improvements of the robot mechanism were considered to improve the flexibility＂ of manipulator and increase the workspace. The inverse kinematics analysis was solved through two steps calculation. The collision avoidance strategy used in the K-joint automatic welding was discussed. Moreover, the simulation results were presented to demonstrate the feasibility of the robot mechanism used in tubular joint welding and the validity of the joint value calculation method.

Robot inverse kinematics based on FCM and fuzzy-neural network

Presents a fast and effective method proposed by combining the fuzzy C means (FCM) and the fuzzy neural network for solving robot inverse kinematics, and its successful application to the robot inverse kinematics and concludes from simulation results that this new method not only has high efficiency and accuracy, but also good generalization, and it also overcomes the "dimension disaster" of fuzzy set in a fuzzy neural network fairly well.

Inverse kinematics of redundant robot based on VC++

：This paper uses a 7-degree-of-freedom （7-DOF） manipulator end-effector to research inverse kinematics solution, Three methods are used and compared, including fixing an angle method, the iteration method and the neutral network method. By comparison, the iteration method is much better because of its high accuracy, fast speed and stabilization, and it does not require calculation of the pseudoinverse of the 2acobian. Thus, this control scheme is well suited for real-time im- plementation, which is essential if the end-effector trajectory is continuously modified based on sensor＇s feedback. Finally, using VC ＋ ＋ and Microsoft foundation classes （MFC） to achieve the main machine interface. Through verification, the precision meets the requirements of general control system in real-time implementation.

Inverse Kinematics Analysis of a Five Jointed Revolute Arm Mechanism

This paper presents some initial solutions to the problem of accuracy and repeatability of the arm position placement in applied kinematics by solving the inverse kinematics problem of a serial jointed manipulator whose forward kinematics solution was earlier presented to solve the position placement problem of a mobile manipulator for Lunar Oxygen production. The problem herein is that of identifying a combination of joint angles to effectively position the end-effecter at a specified location in space. The reverse solution as presented in this paper is predicated on DH＇s （Denavit-Hartenberg＇s） technique for robot arm position analysis. The generalized solution for the 5-degrees of freedom DOF （degree of freedom） revolute joint variables which comprises 2-1inks and a spade-like 3-DOF end-effecter was obtained by solving a set of algebraic equations emerging from series of transformation matrices. The proposed solution herein has a high degree of accuracy and repeatability for workspace reachable domains where joint combination is analytic.

Kinematic Model Extraction for Serial Manipulators Which Have in Different Topologies in Vpython Environment

In this study, we aim at obtaining inverse kinematic model of a serial manipulator using spatial operator algebra. For testing the inverse kinematic algorithm, the Vpython software program which has simultaneous view and software working, is used. The aim is to measure the inverse kinematics modeling work on different serial manipulator mechanisms with spatial vector algebra. The algorithm is used with the same reference inputs on the recursive, exact and nonrecursive manipulators. During the tests, the permitted error tolerance is 0.01 cm. The graph plots show that the algorithm is fit for the error tolerance.