Neuro-fuzzy technique for navigation of multiple mobile robots

In this paper, navigation techniques for several mobile robots are investigated in a totally unknown environment. In the beginning, Fuzzy logic controllers (FLC) using different membership functions are developed and used to navigate mobile robots. First a fuzzy controller has been used with four types of input members, two types of output members and three parameters each. Next two types of fuzzy controllers have been developed having same input members and output members with five parameters each. Each robot has an array of sensors for measuring the distances of obstacles around it and an image sensor for detecting the bearing of the target. It is found that the FLC having Gaussian membership function is best suitable for navigation of multiple mobile robots. Then a hybrid neuro-fuzzy technique has been designed for the same problem. The neuro-fuzzy technique being used here comprises a neural network, which is acting as a pre processor for a fuzzy controller. The neural network considered for neuro-fuzzy technique is a multi-layer perceptron, with two hidden layers. These techniques have been demonstrated in simulation mode, which depicts that the robots are able to avoid obstacles and reach the targets efficiently. Amongst the techniques developed neuro-fuzzy technique is found to be most efficient for mobile robots navigation. Experimental verifications have been done with the simulation results to prove the authenticity of the developed neuro-fuzzy technique.     

模糊集在手写数字识别中的应用

为提高识别速度，本文提出先对文字图象进行直（折）线段、圆的ＬＭＳＥ近似并用Ｆｕｚｚｙ定义算法进行描述，以得到对书写工整的部分数字的快速识别，其速度提高近两倍（达到３７５个／秒），约有２０％的字在这一过程中就可以被识别。本文叙述的算法已经用在我们进行的无限制手写数字识别系统的实验中；反复使用表明：本文提出的方法既快又准确。     

The fuzzy entropy concept and its application

The fuzzy entropy is applied to the seal impression problem to measure the subjective value of information under the condition of uncertainty.Two methods, successive and direct segmentation, are introduced in recognizing the pattern to find out which method is more cost-effective. For the equal entropy, the comparative elements sought in association with the cost information on the successive and direct segmentation methods are 441 and 1024, respectively. Thus, the effectiveness of the former method is 2.32 times higher than that of the latter method, provided that the cost of information is equal.A parametric analysis among the membership function, fuzzy entropy, and threshold level is made and a summary graph shown.     

Analytic center of spherical shells and its application to analytic center machine

The two-case pattern recognition problem aims to find the best way of linearly separate two different classes of data points with a good generalization performance. In the context of learning machines proposed to solve the pattern recognition problem, the analytic center machine (ACM) uses the analytic center cutting plane method restricted to spherical shells. In this work we prove existence and uniqueness of the analytic center of a spherical surface, which guarantees the well definedness of ACM problem. We also propose and analyze new primal, dual and primal-dual formulations based on interior point methods for the analytic center machine. Further, we provide a complexity bound on the number of iterations for the primal approach. F.M.P. Raupp was partially supported by CNPq Grant 475647/2006-8 and FAPERJ/CNPq through PRONEX-Computational Modeling. B.F. Svaiter was partially supported by CNPq Grants 300755/2005-8, 475647/2006-8 and by FAPERJ/CNPq through PRONEX-Optimization.     

Competitive on-line coverage of grid environments by a mobile robot

We describe in this paper two on-line algorithms for covering planar areas by a square-shaped tool attached to a mobile robot. Let D be the tool size. The algorithms, called Spanning Tree Covering (STC) algorithms, incrementally subdivide the planar area into a grid of D-size cells, while following a spanning tree of a grid graph whose nodes are 2D-size cells. The two STC algorithms cover general planar grids. The first, Spiral-STC, employs uniform weights on the grid-graph edges and generates spiral-like covering patterns. The second, Scan-STC, assigns lower weights to edges aligned with a particular direction and generates scan-like covering patterns along this direction. Both algorithms cover any planar grid using a path whose length is at most (n+m)D, where n is the total number of D-size cells and mn is the number of boundary cells, defined as cells that share at least one point with the grid boundary. We also demonstrate that any on-line coverage algorithm generates a covering path whose length is at least (2−)l_opt in worst case, where l_opt is the length of the optimal off-line covering path. Since (n+m)D2l_opt, the bound is tight and the STC algorithms are worst-case optimal. Moreover, in practical environments mn, and the STC algorithms generate close-to-optimal covering paths in such environments.     

Controlling of a mobile robot with a trailer and its nilpotent approximation

This work studies a number of approaches to solving the motion planning problem for a mobile robot with a trailer. Different control models of car-like robots are considered from the differential-geometric point of view. The same models can also be used for controlling a mobile robot with a trailer. However, in cases where the position of the trailer is of importance, i.e., when it is moving backward, a more complex approach should be applied. At the end of the article, such an approach, based on recent works in sub-Riemannian geometry, is described. It is applied to the problem of reparking a trailer and implemented in the algorithm for parking a mobile robot with a trailer.     

Development of fuzzy state controller and its application to a hydraulic position servo

By combining control theory and fuzzy set theory, a new kind of state controller is proposed. Full order feedback and membership functions, which utilize the experience of experts, are used in the design of the state controller which we call a fuzzy state controller. Hydraulic position servos with a nonsymmetrical cylinder are commonly used in industry. This kind of system is nonlinear in nature and generally difficult to control. For different ending position, moving direction, strokes, and load the system dynamics is totally different. Once the above-mentioned parameters of the system are known, it is relatively straightforward to tune the gains of state controller to obtain good dynamic response. But when these parameters change, especially in case of the load, using the same gains will cause overshoot or even loss of system stability. Adaptive control is not applicable in this case due to the complexity of the algorithm, its rate of convergence, and the fast response characteristic of the system. The fuzzy state controller has been successfully applied to a hydraulic position servo. The system shows excellent robustness against variations of system parameters.     

Directional fuzzy clustering and its application to fuzzy modelling

The paradigm of clustering (unsupervised learning) viewed as a fundamental tool for data analysis has been found useful in fuzzy modelling. While the objective functions guiding the clustering mechanisms are by and large direction-free (namely, they do not distinguish between independent (input) and dependent (output) variables, for most of the models this discrimination becomes of vital importance. The method of directional clustering takes the directionality requirement into account by incorporating the nature of the functional relationships into the objective function guiding the formation of the clusters. The complete clustering algorithm is presented. The role of this method in a two-phase fuzzy identification scheme is also revealed in detail.     

Fixed-time synchronization of a reaction-diffusion BAM neural network with distributed delay and its application to image encryption

In this paper, the fixed-time synchronization of reaction-diffusion BAM neural networks is investigated, where both discrete and distributed delays are taken into account. Combining Lyapunov stability theory and several integral inequalities, fixed-time synchronization criteria are established. Through sensitivity analysis, we find the key controller parameters that have a great influence on the maximum settling time. Using the chaotic sequences generated by the neural network, the color image can be encrypted by the Arnold Cat Map and the pixel diffusion. Experiments show that the image encryption algorithm designed in this paper has good properties of security and anti-attacking, which meets the requirements for the secure transmission of image information.     

Aggregating multiple classification results using fuzzy integration and stochastic feature selection

Classifying magnetic resonance spectra is often difficult due to the curse of dimensionality; scenarios in which a high-dimensional feature space is coupled with a small sample size. We present an aggregation strategy that combines predicted disease states from multiple classifiers using several fuzzy integration variants. Rather than using all input features for each classifier, these multiple classifiers are presented with different, randomly selected, subsets of the spectral features. Results from a set of detailed experiments using this strategy are carefully compared against classification performance benchmarks. We empirically demonstrate that the aggregated predictions are consistently superior to the corresponding prediction from the best individual classifier.     

Exact controllability for quasilinear hyperbolic systems and its application to unsteady flows in a network of open canals

In this paper we establish the exact boundary controllability for quasilinear hyperbolic systems with interface conditions. As an application, we get the exact boundary controllability of unsteady flows in a string‐like network of open canals. Copyright © 2004 John Wiley & Sons, Ltd.     

Dynamics and stability of a hybrid serial-parallel mobile robot

Kinematics, dynamics, and stability analysis of a hybrid serial-parallel wheeled mobile robot is detailed in this paper. Privileging the advantages of both serial and parallel robots, the suggested structure will provide higher stability for heavy object manipulation by a mobile robotic system. The proposed system is made of a differentially-driven wheeled platform, a planar parallel manipulator, which is called here as star-triangle (ST) mechanism, and a serial Puma-type manipulator arm. In order to develop a comprehensive kinematics model of the robot; first it is divided into three modules, i.e. a mobile platform, a parallel ST mechanism, and a serial robot. Next, a closed-form dynamics model is derived for the whole hybrid system based on a combined Newton–Euler and Lagrange formulation. Then, a careful validation procedure is presented to verify the obtained dynamics model. Finally, using the new postural stability metric named as moment-height stability (MHS), the important role of the parallel ST mechanism for stabilizing the mobile robotic system is demonstrated. The obtained results show that the proposed hybrid serial–parallel arrangement effectively enhances the tip-over stability of the overall mobile robotic system. Hence, it can be successfully exploited to prevent tip-over instability particularly during heavy object manipulation tasks.     

A new method for ranking fuzzy numbers and its application to group decision making

In this paper, a new method for comparing fuzzy numbers based on a fuzzy probabilistic preference relation is introduced. The ranking order of fuzzy numbers with the weighted confidence level is derived from the pairwise comparison matrix based on 0.5-transitivity of the fuzzy probabilistic preference relation. The main difference between the proposed method and existing ones is that the comparison result between two fuzzy numbers is expressed as a fuzzy set instead of a crisp one. As such, the ranking order of n fuzzy numbers provides more information on the uncertainty level of the comparison. Illustrated by comparative examples, the proposed method overcomes certain unreasonable (due to the violation of the inequality properties) and indiscriminative problems exhibited by some existing methods. More importantly, the proposed method is able to provide decision makers with the probability of making errors when a crisp ranking order is obtained. The proposed method is also able to provide a probability-based explanation for conflicts among the comparison results provided by some existing methods using a proper ranking order, which ensures that ties of alternatives can be broken.     

Developments in network location with mobile and congested facilities

We review four facility location problems which are motivated by urban service applications and which can be thought of as extensions of the classic Q-median problem on networks. In problems P1 and P2 it is assumed that travel times on network links change over time in a probabilistic way. In P2 it is further assumed that the facilities (servers) are movable so that they can be relocated in response to new network travel times. Problems P3 and P4 examine the Q-median problem for the case when the service capacity of the facilities is finite and, consequently, some or all of the facilities can be unavailable part of the time. In P3 the facilities have stationary home locations but in P4 they have movable locations and thus can be relocated to compensate for the unavailability of the busy facilities. We summarize our main results to date on these problems.     

Evaluation of fully fuzzy matrix equations by fuzzy neural network

In this paper, a new hybrid method based on fuzzy neural network for approximate solution of fully fuzzy matrix equations of the form AX=D$\mathit{AX}=D$, where A and D are two fuzzy number matrices and the unknown matrix X is a fuzzy number matrix, is presented. Then, we propose some definitions which are fuzzy zero number, fuzzy one number and fuzzy identity matrix. Based on these definitions, direct computation of fuzzy inverse matrix is done using fuzzy matrix equations and fuzzy neural network. It is noted that the uniqueness of the calculated fuzzy inverse matrix is not guaranteed. Here a neural network is considered as a part of a large field called neural computing or soft computing. Moreover, in order to find the approximate solution of fuzzy matrix equations that supposedly has a unique fuzzy solution, a simple algorithm from the cost function of the fuzzy neural network is proposed. To illustrate the easy application of the proposed method, numerical examples are given and the obtained results are discussed.     

集对Fuzzy格及其在格表示论中的应用

用幂集格构造了集对 Ｆｕｚｚｙ 格（这与用整数对构造有理数集有相似之处）,并用它证明了完整的软代数表示定理,即定义了到自身的映射且有最大元和最小元的格为软代数的充要条件是它与某个集对 Ｆｕｚｚｙ 格的子格同构．这样,与分配格在幂集 Ｂｏｏｌｅ 格中表示相对应,软代数在集对 Ｆｕｚｚｙ 格中有表示,在理论上是很完美的     

Fixed point optimization algorithm and its application to network bandwidth allocation

A convex optimization problem for a strictly convex objective function over the fixed point set of a nonexpansive mapping includes a network bandwidth allocation problem, which is one of the central issues in modern communication networks. We devised an iterative algorithm, called a fixed point optimization algorithm, for solving the convex optimization problem and conducted a convergence analysis on the algorithm. The analysis guarantees that the algorithm, with slowly diminishing step-size sequences, weakly converges to a unique solution to the problem. Moreover, we apply the proposed algorithm to a network bandwidth allocation problem and show its effectiveness.     

Intelligent data analysis and model interpretation with spectral analysis fuzzy symbolic modeling

This paper proposes fuzzy symbolic modeling as a framework for intelligent data analysis and model interpretation in classification and regression problems. The fuzzy symbolic modeling approach is based on the eigenstructure analysis of the data similarity matrix to define the number of fuzzy rules in the model. Each fuzzy rule is associated with a symbol and is defined by a Gaussian membership function. The prototypes for the rules are computed by a clustering algorithm, and the model output parameters are computed as the solutions of a bounded quadratic optimization problem. In classification problems, the rules’ parameters are interpreted as the rules’ confidence. In regression problems, the rules’ parameters are used to derive rules’ confidences for classes that represent ranges of output variable values. The resulting model is evaluated based on a set of benchmark datasets for classification and regression problems. Nonparametric statistical tests were performed on the benchmark results, showing that the proposed approach produces compact fuzzy models with accuracy comparable to models produced by the standard modeling approaches. The resulting model is also exploited from the interpretability point of view, showing how the rule weights provide additional information to help in data and model understanding, such that it can be used as a decision support tool for the prediction of new data.