Global adaptive tracking control of robot manipulators using neural networks with finite-time learning convergence

In this paper, the global adaptive neural control with finite-time (FT) convergence learning performance for a general class of nonlinear robot manipulators has been investigated. The scheme proposed in this paper offers a subtle blend of neural controller with robust controller, which palliates the limitation of neural approximation region to ensure globally uniformly ultimately bounded (GUUB) stability by integrating a switching mechanism. Morever, the proposed scheme guarantees the estimated neural weights converging to optimal values in finite time by embedding an adaptive learning algorithm driven by the estimated weights error. The optimal weights obtained through the learning process of the neural networks (NNs) will be reused next time for repeated tasks, and can thus reduce computational load, improve transient performance and enhance robustness. The simulation studies have been carried out to demonstrate the superior performance of the controller in comparison to the conventional methods.

     

Optimal convergence of on-line backpropagation.

Many researchers are quite skeptical about the actual behavior of neural network learning algorithms like backpropagation. One of the major problems is with the lack of clear theoretical results on optimal convergence, particularly for pattern mode algorithms. In this paper, we prove the companion of Rosenblatt's PC (perceptron convergence) theorem for feedforward networks (1960), stating that pattern mode backpropagation converges to an optimal solution for linearly separable patterns.     

The convergence of Hamming memory networks

The convergence properties of Hamming memory networks are studied. It is shown how to construct the network so that it probably converges to an appropriate result, and a tight bound is given on the convergence time. The bound on the convergence time is largest when several stored vectors are at the minimum distance from the input vector. For random binary vectors, the probability for such situations to occur is not small. With a specific choice of parameter values, the worst-case convergence time is on the order of p ln (pn), where p is the memory capacity and n is the vector length. By allowing the connection weights to change during the computation, the convergence time can be decreased considerably.     

Optimal polling in communication networks

Polling is the process in which an issuing node of a communication network (polling station) broadcasts a query to every other node in the network and waits to receive a unique response from each of them. Polling can be thought of as a combination of broadcasting and gathering and finds wide applications in the control of distributed systems. In this paper, we consider the problem of polling in minimum time. We give a general lower bound on the minimum number of time units to accomplish polling in any network and we present optimal polling algorithms for several classes of graphs, including hypercubes and recursively decomposable Cayley graphs     

Guaranteed convergence in a class of Hopfield networks

A class of symmetric Hopfield networks with nonpositive synapses and zero threshold is analyzed in detail. It is shown that all stationary points have a one-to-one correspondence with the minimal vertex covers of certain undirected graphs, that the sequential Hopfield algorithm as applied to this class of networks converges in at most 2n steps (n being the number of neurons), and that the parallel Hopfield algorithm either converges in one step or enters a two-cycle in one step. The necessary and sufficient condition on the initial iterate for the parallel algorithm to converge in one step are given. A modified parallel algorithm which is guaranteed to converge in [3n/2] steps ([x] being the integer part of x) for an n-neuron network of this particular class is also given. By way of application, it is shown that this class naturally solves the vertex cover problem. Simulations confirm that the solution provided by this method is better than those provided by other known methods.     

On convergence rate of projection neural networks

This note presents an analysis of the convergence rate for a projection neural network with application to constrained optimization and related problems. It is shown that the state trajectory of the projection neural network is exponentially convergent to its equilibrium point if the Jacobian matrix of the nonlinear mapping is positive definite, while the convergence rate is proportional to a design parameter if the Jacobian matrix is only positive semidefinite. Moreover, the convergence time is guaranteed to be finite if the design parameter is chosen to be sufficiently large. Furthermore, if a diagonal block of the Jacobian matrix is positive definite, then the corresponding partial state trajectory of the projection neural network is also exponentially convergent. Three optimization examples are used to show the convergence performance of the projection neural network.     

Optimal geometric modeler for robot motion planning

Planning collision‐free trajectories under real‐time restrictions is a challenging topic in robotics. In order to reduce computational cost in the collision avoidance process, some authors have proposed different model representations. This article presents an optimal method able to generate automatically geometric models of the objects in a robotic system. For each object, two models are obtained, i.e., the minimum outer and the maximum inner models. Availability of both models allows one to face more successfully robot motion applications. The geometric modeler is focused on the generation of spherically extended polytopes. Each object to model is represented by a set of points taken from its surface. Models are generated through the application of an iterative process based on the Hough transform. When both outer and inner models have been generated, a parameter for evaluating the quality of the models is introduced. This parameter can be used by a rule‐based system for increasing the complexity of the model generated and improving, therefore, the accuracy of the representation. © 2000 John Wiley & Sons, Inc.     

Optimal task assignment in homogeneous networks

This paper considers the problem of assigning the tasks of a distributed application to the processors of a distributed system such that the sum of execution and communication costs is minimized. Previous work has shown this problem to be tractable for a system of two processors or a linear array of N processors, and for distributed programs of serial parallel structures. Here we focus on the assignment problem on a homogeneous network, which is composed of N functionally-identical processors, each with its own memory. Some processors in the network may have unique resources, such as data files or certain peripheral devices. Certain tasks may have to use these unique resources; they are called attached tasks. The tasks of a distributed program should therefore be assigned so as to make use of specific resources located at certain processors in the network while minimizing the amount of interprocessor communication. The assignment problem in such a homogeneous network is known to be NP-hard even for N=3, thus making it intractable for a network with a medium to large number of processors. We therefore focus on task assignment in general array networks, such as linear arrays, meshes, hypercubes, and trees. We first develop a modeling technique that transforms the assignment problem in an array or tree into a minimum-cut maximum-flow problem. The assignment problem is then solved for a general array or tree network in polynomial time     

Optimal dynamic scheduling in Jackson networks

A Jackson-like network that supports J types of interactive traffic (e.g., interactive messages) as well as I types of noninteractive traffic (e.g., file transfers, facsimile) is considered. The service-time distributions and the internal routing are homogeneous for all traffic types but can be node (queue) dependent. The problem is to find a scheduling control that minimizes a weighted sum of the average end-to-end delay for the interactive types and at the same time ensures that the average end-to-end delays for the interactive types will be below given design constraints. Conservation laws are first established and shown to yield the base of a polymatroid. The optimal control problem is then transformed into a linear program with the feasible region being the polymatroid base truncated by delay constraints. An optimal control is identified that partitions the traffic types into I+r (0⩽r⩽J) ordered groups and applies a strict priority rule among the groups. An algorithm is developed that does the grouping and solves the optimization problem. A decentralized implementation of the optimal control is also discussed     

The cost of probabilistic agreement in oblivious robot networks

In this paper, we look at the time complexity of two agreement problems in networks of oblivious mobile robots, namely, at the gathering and scattering problems. Given a set of robots with arbitrary initial locations and no initial agreement on a global coordinate system, gathering requires that all robots reach the exact same but not predetermined location. In contrast, scattering requires that no two robots share the same location. These two abstractions are fundamental coordination problems in cooperative mobile robotics. Oblivious solutions are appealing for self-stabilization since they are self-stabilizing at no extra cost. As neither gathering nor scattering can be solved deterministically under arbitrary schedulers, probabilistic solutions have been proposed recently.The contribution of this paper is twofold. First, we propose a detailed time complexity analysis of a modified probabilistic gathering algorithm. Using Markov chains tools and additional assumptions on the environment, we prove that the convergence time of gathering can be reduced from O(n²) (the best known bound) to O(1) or , depending on the model of multiplicity detection. Second, using the same technique, we prove that scattering can also be achieved in fault-free systems with the same bounds.     

Optimal Steffensen-type methods with eighth order of convergence

This paper proposes two classes of three-step without memory iterations based on the well known second-order method of Steffensen. Per computing step, the methods from the developed classes reach the order of convergence eight using only four evaluations, while they are totally free from derivative evaluation. Hence, they agree with the optimality conjecture of Kung-Traub for providing multi-point iterations without memory. As things develop, numerical examples are employed to support the underlying theory developed for the contributed classes of optimal Steffensen-type eighth-order methods.     

Bipartite Byzantine-resilient event-triggered consensus control of heterogeneous multi-agent systems

This article studies the bipartite resilient event-triggered consensus control for a class of the heterogeneous multi-agent systems. Due to the external cyberattacks, some agents may become the Byzantine agents and will affect the behavior of the other agents. To improve the security of the multi-agent systems against the Byzantine agents, a novel bipartite event-triggered heterogeneous mean-subsequence-reduced algorithm is designed. First, to handle the heterogeneous multi-agent systems, a state transformation is carefully designed, to facilitate the design and analysis of the bipartite resilient consensus algorithm. Based upon the designed state transformation, the bipartite resilient control inputs are constructed, where the structural balance analysis shows that the resulting effective signed graph and the equivalent signed graph are both structurally balanced, if the signed graph of the multi-agent systems is structurally balanced. In addition, a dynamic event-triggered mechanism is proposed, where a set of dynamic factors are introduced into the event-triggered functions to prevent the usage of the global topology information. By virtue of the designed algorithm, it is guaranteed that the heterogeneous multi-agent systems can achieve the bipartite consensus in the presence of the Byzantine agents, and the communication burden among the agents can be reduced. The numerical simulations are conducted to verify the effectiveness of the proposed algorithm.     

月球机器人运动学建模与运动收敛性分析

首先建立了月面坐标系中月球机器人的直角坐标运动学方程，并在此基础上推导出运动学方程的极坐标表达形式，然后，针对月球机器人的运动控制问题，推导了为保证月球机器人的运动全局渐近收敛其线速度和角速度所应满足的充分条件，并进行证明。     

Parameter convergence and learning curves for neural networks

We revisit the oft-studied asymptotic (in sample size) behavior of the parameter or weight estimate returned by any member of a large family of neural network training algorithms. By properly accounting for the characteristic property of neural networks that their empirical and generalization errors possess multiple minima, we rigorously establish conditions under which the parameter estimate converges strongly into the set of minima of the generalization error. Convergence of the parameter estimate to a particular value cannot be guaranteed under our assumptions. We then evaluate the asymptotic distribution of the distance between the parameter estimate and its nearest neighbor among the set of minima of the generalization error. Results on this question have appeared numerous times and generally assert asymptotic normality, the conclusion expected from familiar statistical arguments concerned with maximum likelihood estimators. These conclusions are usually reached on the basis of somewhat informal calculations, although we shall see that the situation is somewhat delicate. The preceding results then provide a derivation of learning curves for generalization and empirical errors that leads to bounds on rates of convergence.     

受限移动机器人构建地图的最优探测法

对复杂未知环境构建地图是移动机器人面临的一大问题.通常忽略未知环境的几何特征,将其抽象成未知无向连通图,机器人只沿着图的边进行搜索,并将走过每条边的成本看成是1.机器人构建地图的成本用走过的总边数来表示.对于一个完全未知的环境,从一点S出发,限制移动机器人最远能走r(如燃料问题及安全线或通信线等)步(边数)的范围内,基于深度受限剪枝生成子树的方法,结合广度优先搜索和受限的深度优先搜索染色策略,给出了对未知环境构建完整地图的有效算法,该算法的成本为|E|+O|V|,这是目前最优结果.     

Optimal robot task scheduling based on genetic algorithms

Industrial robots should perform complex tasks in the minimum possible cycle time in order to obtain high productivity. The problem of determining the optimum route of a manipulator's end effector visiting a number of task points is similar but not identical to the well-known travelling salesman problem (TSP). Adapting TSP to Robotics, the measure to be optimized is the time instead of the distance. In addition, the travel time between any two points is significantly affected by the choice of the manipulator's configuration. Therefore, the multiple solutions of the inverse kinematics problem should be taken into consideration.In this paper, a method is introduced to determine the optimum sequence of task points visited by the tip of the end effector of an articulated robot and it can be applied to any non-redundant manipulator. This method is based on genetic algorithms and an innovative encoding is introduced to take into account the multiple solutions of the inverse kinematic problem. The results show that the method can determine the optimum sequence of a considerable number of task points for robots up to six-degrees of freedom.     

Optimal layouts of midimew networks

Midimew networks are mesh-connected networks derived from a subset of degree-4 circulant graphs. They have minimum diameter and average distance among all degree-4 circulant graphs, and are better than some of the most common topologies for parallel computers in terms of various cost measures. Among the many midimew networks, the rectangular ones appear to be most suitable for practical implementation. Unfortunately, with the normal way of laying out these networks on a 2D plane, long cross wires that grow with the size of the network exist. In this paper, we propose ways to lay out rectangular midimew networks in a 2D grid so that the length of the longest wire is at most a small constant. We prove that these constants are optimal under the assumption that rows and columns are moved as a whole during the layout process