Training with noise as a method to increase noise resilience of neural network solution of inverse problems

Inverse problems constitute a special class of problems, which consist in reconstruction of parameters of an object by the data of indirect measurements, which are affected by these parameters. Many inverse problems are ill-posed (incorrect), i.e., characterized by nonuniqueness and/or instability of the solution. Improvement in the stability of the solution of inverse problems is a very topical problem; one of the ways to solve it is the use of artificial neural networks. In the present study, at the example of a model 5-parameter inverse problem it is demonstrated that adding noise to the training set when training neural networks allows one to improve resilience of the neural network solution to noise in input data, with various distribution and intensity of noise.     

A neural-network committee machine approach to the inverse kinematics problem solution of robotic manipulators

In robotics, inverse kinematics problem solution is a fundamental problem in robotics. Many traditional inverse kinematics problem solutions, such as the geometric, iterative, and algebraic approaches, are inadequate for redundant robots. Recently, much attention has been focused on a neural-network-based inverse kinematics problem solution in robotics. However, the result obtained from the neural network requires to be improved for some sensitive tasks. In this paper, a neural-network committee machine (NNCM) was designed to solve the inverse kinematics of a 6-DOF redundant robotic manipulator to improve the precision of the solution. Ten neural networks (NN) were designed to obtain a committee machine to solve the inverse kinematics problem using separately prepared data set since a neural network can give better result than other ones. The data sets for the neural-network training were prepared using prepared simulation software including robot kinematics model. The solution of each neural network was evaluated using direct kinematics equation of the robot to select the best one. As a result, the committee machine implementation increased the performance of the learning.     

Parallel manipulator kinematics learning using holographic neural network models

The forward kinematic problem of parallel manipulators is resolved using a holographic neural paradigm. In a holographic neural model, stimulus–response (input–output) associations are transformed from the domain of real numbers to the domain of complex vectors. An element of information within the holographic neural paradigm has a semantic content represented by phase information and a confidence level assigned in the magnitude of the complex scalar. Networks are trained on a database generated from the closed-form inverse kinematic solutions. After the learning phase, the networks are tested on trajectories which were not part of the training data. The simulation results, given for a planar three-degree-of-freedom parallel manipulator with revolute joints and for a spherical three-degree-of-freedom parallel manipulator, show that holographic neural network models are feasible to solve the forward kinematic problem of parallel manipulators.     

Neural network approach for multicriteria solid transportation problem

In this paper, we propose neural network approach for multicriteria solid transportation problems(STP). First we suggest a neural network architecture to solve single-objective STP according to augmented Lagrange multiplier method. Due to the massive computing unit-neurons and parallel mechanism of neural network approach can solve the large scale problem efficiently and optimal solution can be got. Then we transform the original multicriteria problem into a single objective problem by global criteria method and adopt the neural network approach to solve it. By this way we can get the satisfactory solution of the original problem. The procedure and efficiency of this approach are shown with numerical simulations.     

Kinematic analysis of a novel 3-DOF actuation redundant parallel manipulator using artificial intelligence approach

Kinematic analysis is one of the key issues in the research domain of parallel kinematic manipulators. It includes inverse kinematics and forward kinematics. Contrary to a serial manipulator, the inverse kinematics of a parallel manipulator is usually simple and straightforward. However, forward kinematic mapping of a parallel manipulator involves highly coupled nonlinear equations. Therefore, it is more difficult to solve the forward kinematics problem of parallel robots. In this paper, a novel three degrees-of-freedom (DOFs) actuation redundant parallel manipulator is introduced. Different intelligent approaches, which include the Multilayer Perceptron (MLP) neural network, Radial Basis Functions (RBF) neural network, and Support Vector Machine (SVM), are applied to investigate the forward kinematic problem of the robot. Simulation is conducted and the accuracy of the models set up by the different methods is compared in detail. The advantages and the disadvantages of each method are analyzed. It is concluded that ν-SVM with a linear kernel function has the best performance to estimate the forward kinematic mapping of a parallel manipulator.     

Reliability-based approach to the inverse kinematics solution of robots using Elman's networks

The solution of inverse kinematics problem of redundant manipulators is a fundamental problem in robot control. The inverse kinematics problem in robotics is the determination of joint angles for a desired cartesian position of the end effector. For the solution of this problem, many traditional solutions such as geometric, iterative and algebraic are inadequate if the joint structure of the manipulator is more complex. Furthermore, many neural network approaches have been done to this problem. But the neural network-based solutions are not much reliable due to the error at the end of learning. Therefore, a reliability-based neural network inverse kinematics solution approach has been presented, and applied to a six-degrees of freedom (dof) robot manipulator in this paper. The structure of the proposed method is based on using three networks designed parallel to minimize the error of the whole system. Elman network, which has a profound impact on the learning capability and performance of the network, is chosen and designed according to the proposed solution method. At the end of parallel implementation, the results of each network are evaluated using direct kinematics equations to obtain the network with best result.     

Collision detection for multiple robot manipulatyors by using orthogonal neural networks

This article discusses the application of orthogonal neural networks to detect collisions between multiple robot manipulators that work in an overlapped space. By applying an expansion/shrinkage algorithm, the problem of collision detection between arms is transformed into that among cylinders (or rectangular solids) and line segments. This mapping simplifies the collision detection problem and thus neural networks can be applied to solve it. The property of parallel processing enables neural networks to detect collisions rapidly. A single-layer orthogonal neural network is developed to avert the problems of conventional multilayer feedforward neural networks such as initial weights and the number of layers and processing elements. This orthogonal neural network can approximate various functions and is used to calculate forward solution and to detect collisions. An efficient neural network system for collision detection is also developed. © 1995 John Wiley & Sons, Inc.     

基于广义投影神经网络优化的模型预测控制*

为降低模型预测控制优化问题的计算复杂度,以时滞系统的模型预测控制问题作为研究对象,利用神经网络动态平衡点与优化问题解相对应的特点,提出一种基于广义投影神经网络的模型预测控制优化算法。首先,将模型预测控制优化问题描述为一个带约束的二次规划问题,进一步,通过广义投影神经网络模型进行在线优化。该方法充分发挥了神经网络并行、结构简单的优点,通过具体实例仿真,验证了本文算法的有效性与优越性。     

Design of the Inverse Function Delayed Neural Network for Solving Combinatorial Optimization Problems

We have already proposed the inverse function delayed (ID) model as a novel neuron model. The ID model has a negative resistance similar to Bonhoeffer–van der Pol (BVP) model and the network has an energy function similar to Hopfield model. The neural network having an energy can converge on a solution of the combinatorial optimization problem and the computation is in parallel and hence fast. However, the existence of local minima is a serious problem. The negative resistance of the ID model can make the network state free from such local minima by selective destabilization. Hence, we expect that it has a potential to overcome the local minimum problems. In computer simulations, we have already shown that the ID network can be free from local minima and that it converges on the optimal solutions. However, the theoretical analysis has not been presented yet. In this paper, we redefine three types of constraints for the particular problems, then we analytically estimate the appropriate network parameters giving the global minimum states only. Moreover, we demonstrate the validity of estimated network parameters by computer simulations.      

Application of artificial neural networks to solve problems of identification and determination of concentration of salts in multi-component water solutions by Raman spectra

In this paper, the results of elaboration and comparative analysis of approaches concerned with application of neural network algorithms for effective solution of problem of pattern recognition (inverse problem with discrete output) along with inverse problem with continuous output are presented. Consideration is carried out at the example of problem of identification and determination of concentrations of inorganic salts in multi-component water solutions by Raman spectra. The studied approach is concerned with solution of both problems (classification and determination of concentrations) using a single neural network trained on experimental or quasi-model data.     

An offset error compensation method for improving ANN accuracy when used for position control of precision machinery

Artificial Neural Networks (ANNs) have recently become the focus of considerable attention in many disciplines, including robot control, where they can be used as a general class of nonlinear models to solve highly nonlinear control problems. Feedforward neural networks have been widely applied for modelling and control purposes. One of the ANN applications in robot control is for the solution of the inverse kinematic problem, which is important in path planning of robot manipulators. This paper proposes an iterative approach and an offset error compensation method to improve the accuracy of the inverse kinematic solutions by using an ANN and a forward kinematic model of a robot. The offset error compensation method offers potential to generate accurately the inverse solution for a class of problems which have an easily obtained forward model and a complicated solution.Now Lecturing in Taiwan.     

Neural network technique for fuzzy multiobjective linear programming

Neural Network(NN) is well-known as one of powerful computing tools to solve optimization problems. Due to the massive computing unit-neurons and parallel mechanism of neural network approach we can solve the large-scale problem efficiently and optimal solution can be gotten. In this paper, we intoroduce improvement of the two-phase approach for solving fuzzy multiobjectve linear programming problem with both fuzzy objectives and constraints and we propose a new neural network technique for solving fuzzy multiobjective linear programming problems. The procedure and efficiency of this approach are shown with numerical simulations.     

基于Elman神经网络的Stewart平台位姿正解

Stewart平台广泛应用于运动模拟器、光学、精密定位等领域,然而由于复杂的多元非线性使得位姿正解难以准确得到.针对Stewart平台的位姿正解问题,常规的方法比如迭代法和数值法存在初始值难以选取、计算速度较慢等问题,提出了基于Elman神经网络的位姿正解方法.首先建立Stewart平台支腿长度与平台位姿的运动学模型,然后利用Elman神经网络来实现位姿正解的求解并实验验证.该方法具有良好的动态特性,精度高,能够快速准确的实现Stewart平台位姿正解的求解.实验证明了该方法的有效性.     

Neural network modeling of vector multivariable functions in ill-posed approximation problems

A neural network solution of the ill-posed inverse approximation problem of a multivariable vector function based on of a committee of multilayer perceptrons is proposed. A nonlinear adaptive decision-making rule by the committee is developed that improves the accuracy compared with other neural network solutions of the inverse problem. Using a model example, the accuracy characteristics of the method are shown. An applied engineering problem is considered and the results of its solution by the proposed method are presented.     

A study of neural network based inverse kinematics solution for a three-joint robot

A neural network based inverse kinematics solution of a robotic manipulator is presented in this paper. Inverse kinematics problem is generally more complex for robotic manipulators. Many traditional solutions such as geometric, iterative and algebraic are inadequate if the joint structure of the manipulator is more complex. In this study, a three-joint robotic manipulator simulation software, developed in our previous studies, is used. Firstly, we have generated many initial and final points in the work volume of the robotic manipulator by using cubic trajectory planning. Then, all of the angles according to the real-world coordinates (x, y, z) are recorded in a file named as training set of neural network. Lastly, we have used a designed neural network to solve the inverse kinematics problem. The designed neural network has given the correct angles according to the given (x, y, z) cartesian coordinates. The online working feature of neural network makes it very successful and popular in this solution.     

基于神经网络的冗余度TT-VGT机器人的运动学求解

应用BP神经网络对冗余度TT-VGT机器人的位姿正解进行训练学习,进而求解机器人 的位姿反解问题．根据网络模型求得机器人的一、二阶影响系数,应用神经网络求解雅可比 矩阵的伪逆．并对七重四面体的变几何桁架机器人进行了仿真计算．     

Design and analysis of maximum Hopfield networks

Since McCulloch and Pitts presented a simplified neuron model (1943), several neuron models have been proposed. Among them, the binary maximum neuron model was introduced by Takefuji et al. and successfully applied to some combinatorial optimization problems. Takefuji et al. also presented a proof for the local minimum convergence of the maximum neural network. In this paper we discuss this convergence analysis and show that this model does not guarantee the descent of a large class of energy functions. We also propose a new maximum neuron model, the optimal competitive Hopfield model (OCHOM), that always guarantees and maximizes the decrease of any Lyapunov energy function. Funabiki et al. (1997, 1998) applied the maximum neural network for the n-queens problem and showed that this model presented the best overall performance among the existing neural networks for this problem. Lee et al. (1992) applied the maximum neural network for the bipartite subgraph problem showing that the solution quality was superior to that of the best existing algorithm. However, simulation results in the n-queens problem and in the bipartite subgraph problem show that the OCHOM is much superior to the maximum neural network in terms of the solution quality and the computation time.     

Solving general convex nonlinear optimization problems by an efficient neurodynamic model

In this paper, a neural network model is constructed on the basis of the duality theory, optimization theory, convex analysis theory, Lyapunov stability theory and LaSalle invariance principle to solve general convex nonlinear programming (GCNLP) problems. Based on the Saddle point theorem, the equilibrium point of the proposed neural network is proved to be equivalent to the optimal solution of the GCNLP problem. By employing Lyapunov function approach, it is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the original problem. The simulation results also show that the proposed neural network is feasible and efficient.     

利用有限差分法计算真实头模型脑电正问题

脑电研究领域的两个关键问题是脑电正问题和脑电逆问题,脑电正问题是脑电逆问题的基础.由于复杂、非规则真实头模型中的脑电正问题不存在解析解,因此脑电源分析依赖于正问题数值算法的精度和效率.文章首先详细推导了有限差分算法求解三维各向同性脑电正问题的数学模型,然后在三层同心球模型上通过与解析解比较验证了该算法的精度和效率,最后将该算法应用于真实头模型.仿真结果表明,有限差分法可以有效地处理任意形状几何体的电位场分布问题,是模拟计算真实头模型中脑电正问题的有力工具.     

Dynamics of a six degrees-of-freedom parallel robot actuated by three two-wheel carts

This paper deals with a new, six degrees-of-freedom parallel manipulator comprising a platform, three links and three two-wheel carts supporting the links. The wheels are independently driven, allowing the manipulator a workspace which is limited only by the lengths of the links and the size of the plane on which the carts move. The direct and inverse dynamic problems of the manipulator are solved. It is shown that the Jacobian associated with the direct problem becomes identically singular when used to solve the inverse problem, and hence must be redefined; and that once redefined, it losses its standard structure and cannot be used to solve the direct problem. Three solution methods to the inverse problem are presented and are shown to lead to indistinguishable results.