Trajectory Planning of Robot Manipulator Based on RBF Neural Network

Robot manipulator trajectory planning is one of the core robot technologies, and the design of controllers can improve the trajectory accuracy of manipulators. However, most of the controllers designed at this stage have not been able to effectively solve the nonlinearity and uncertainty problems of the high degree of freedom manipulators. In order to overcome these problems and improve the trajectory performance of the high degree of freedom manipulators, a manipulator trajectory planning method based on a radial basis function (RBF) neural network is proposed in this work. Firstly, a 6-DOF robot experimental platform was designed and built. Secondly, the overall manipulator trajectory planning framework was designed, which included manipulator kinematics and dynamics and a quintic polynomial interpolation algorithm. Then, an adaptive robust controller based on an RBF neural network was designed to deal with the nonlinearity and uncertainty problems, and Lyapunov theory was used to ensure the stability of the manipulator control system and the convergence of the tracking error. Finally, to test the method, a simulation and experiment were carried out. The simulation results showed that the proposed method improved the response and tracking performance to a certain extent, reduced the adjustment time and chattering, and ensured the smooth operation of the manipulator in the course of trajectory planning. The experimental results verified the effectiveness and feasibility of the method proposed in this paper.     

最优组合预测模型的构建及其应用研究

由于证券价格是随机游走的,在证券定价研究中RBF神经网络模型、灰色GM（1,1）模型、ARIMA模型不具备时效性,通过对上述三个模型进行综合分析,结合三者中有用的信息集合,构建一个最优组合预测模型．在此基础上选取了深发展A在2007年全年的收盘价作为研究样本对这四个模型进行实证研究,研究结果发现,最优组合预测方法对证券价格进行预测具有很好的预测精度和很高的可靠性．     

基于模糊神经网络的MVP评价模型及实证分析

利用模糊数学和神经网络方法建立对运动员进行评价的模糊网络模型,采用NBA流行的各评价指标作为其输入,模糊综合评价结果作为输出。样本数据采用2003~2004赛季NBA各单项50强的常规赛数据,分别用BP网络和RBF网络,建立分析系统,比较结果证明RBF网络仿真效果最好,完全可以实用,该模型也可以用在其它综合评价系统中。     

A robust regression approach for spectrophotometric signal analysis

The effectiveness of a regression method strongly depends on the characteristics of the considered regression problem. As a consequence, this makes it difficult to choose a priori the most appropriate algorithm for a given dataset. This issue is faced in this work through a novel regression approach based on the fusion of an ensemble of different regressors. In order to implement the proposed robust multiple system (RMS), four different fusion strategies are explored. In this context, we propose a novel fusion strategy named selection‐based strategy (SBS) that provides as output the estimate obtained by the regression algorithm (included in the ensemble) characterized by the highest expected accuracy in the region of the feature space associated with the considered model. The SBS is based not on a direct combination of the estimates yielded by all the regressors but on a selection mechanism that identifies the expected best available estimate. For such purpose, it exploits the accuracies of the regressors included in the ensemble in different portions of the input feature space. The experimental assessment of the RMS was carried out on three different datasets: a wine, an orange juice, and an apple datasets. The obtained experimental results suggest that, in general, the fusion of an ensemble of different regression algorithms leads to a regression process that is more robust and sometimes also more accurate than traditional regression methods. In particular, the proposed SBS method represents an effective solution to carry out the fusion process. Copyright © 2012 John Wiley & Sons, Ltd.     

A linear system‐free Gaussian RBF method for the Gross‐Pitaevskii equation on unbounded domains

Gaussian radial basis function (RBF) interpolation methods are theoretically spectrally accurate. However, in applications this accuracy is seldom realized due to the necessity of solving a very poorly conditioned linear system to evaluate the methods. Recently, by using approximate cardinal functions and restricting the method to a uniformly spaced grid (or a smooth mapping thereof), it has been shown that the Gaussian RBF method can be formulated in a matrix free framework that does not involve solving a linear system [ 1 ]. In this work, we differentiate the linear system‐free Gaussian (LSFG) method and use it to solve partial differential equations on unbounded domains that have solutions that decay rapidly and that are negligible at the ends of the grid. As an application, we use the LSFG collocation method to numerically simulate Bose‐Einstein condensates. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 389–401, 2012     

RBF‐ENO/WENO schemes with Lax–Wendroff type time discretizations for Hamilton–Jacobi equations

In this research, a class of radial basis functions (RBFs) ENO/WENO schemes with a Lax–Wendroff time discretization procedure, named as RENO/RWENO‐LW, for solving Hamilton–Jacobi (H–J) equations is designed. Particularly the multi‐quadratic RBFs are used. These schemes enhance the local accuracy and convergence by locally optimizing the shape parameters. Comparing with the original WENO with Lax–Wendroff time discretization schemes of Qiu for HJ equations, the new schemes provide more accurate reconstructions and sharper solution profiles near strong discontinuous derivative. Also, the RENO/RWENO‐LW schemes are easy to implement in the existing original ENO/WENO code. Extensive numerical experiments are considered to verify the capability of the new schemes.     

RBFNN结合自适应边界的机器人手臂轨迹跟踪控制系统设计

针对机器人手臂动态模型中存在动态不确定性问题,提出一种结合径向基函数神经网络(RBFNN)和自适应边界控制的机械臂轨迹跟踪方法。利用RBF神经网络在线学习系统中现有的结构化和非结构化不确定性,近似补偿未知动态部分;利用自适应边界来估计非结构化不确定性上的未知边界和神经网络重建误差;通过加权矩阵产生的李雅普诺夫函数证明了该系统具有渐进稳定性。利用三自由度机械臂进行实验,结果表明,相比其他几种较为先进的控制器,本文设计的控制器具有最优的控制精度。     

Adaptive meshless refinement schemes for RBF-PUM collocation

In this paper we present an adaptive discretization technique for solving elliptic partial differential equations via a collocation radial basis function partition of unity method. In particular, we propose a new adaptive scheme based on the construction of an error indicator and a refinement algorithm, which used together turn out to be ad-hoc strategies within this framework. The performance of the adaptive meshless refinement scheme is assessed by numerical tests.     

基于季节性RBF神经网络的月度市场需求预测研究

本文提出一种季节性神经网络预测模型,对具有季节性变化的产品月度市场需求进行预测.在Matlab语言环境下,用傅立叶周期分析法得到时间序列的周期长度;借鉴嵌入理论,提出了确定季节性神经网络输入维数的策略;利用计算机程序搜索,确定最优参数;通过合理插值,重构样本集.仿真实验表明,该模型的预测精度明显高于其他几个常用的季节预测模型.     

基于RN和GN的两种RBF神经网络的工程造价预测模型

建立了调用NEWRB函数的正规化网络RN和基于K-means聚类的广义网络GN的两种RBF‘神经网络的工程造价预测模型,以55个厦门市工程造价案例进行实证分析.结果表明:当调用NEWRB函数构建RBF模型时,其性能主要取决于分布宽度,而基于K-means聚类的RBF神经网络主要取决于重叠系数和隐含层节点数;基于广义网络GN的RBF神经网络模型的训练效果较差,但学习速度更快、预测精度更高.