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.     

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.     

The filtering problem for continuous-time linear systems with Markovian switching coefficients

The stochastic model under consideration is a Markovian jump process θ, with finite state space, feeding the parameters of a linear diffusion process x. The processes y and z observe linearly and separately x and θ in independent white noises. Some properties of the finite optimal filter for the x and θ processes given the history of measurements z are investigated. Apart from their theoretical interest, these results have an interesting practical bearing on the general filtering problem, by providing a natural finite suboptimal solution. Preliminary experimental results show the effectiveness of our approach to estimate the state trajectory, even with a relatively low signal-to-noise ratio on the measurement processes.     

基于ANFIS的机械手运动学逆解的求取

提出一种基于自适应神经模糊推理系统（ANFIS）求取机械手运动学逆解的方法。本文以SCARA（Selective Compliance Assembly Robot Arm）型四自由度机械手为研究对象,研究SCARA机械手末端执行器笛卡儿空间坐标与机械手关节空间关节变量之间的对应关系。首先根据笛卡儿运动轨迹选取起点、终点和中间点,并求得与之对应的关节变量值序列。然后利用插值方法求得关节空间的角度变化曲线,最后在关节曲线上随机选取样本点,进而利用得到的数据训练并验证自适应神经模糊推理系统求解逆解的正确性和精确性。与传统基于BP神经网络求取运动学逆解的方法进行仿真对比分析,结果表明ANFIS在运动学逆解的求取精度和运算时间上均优于BP神经网络。     

Neural networks and the inverse kinematics problem

Inverse kinematics is a fundamental problem in robotics. Past solutions for this problem have been realized through the use of various algebraic or algorithmic procedures. In this paper the use of feedforward neural networks to solve the inverse kinematics problem is examined for three different cases. A closed kinematic linkage is used for mapping input joint angles to output joint angles. A three-degree-of-freedom manipulator in 3D space is used to test mappings from both cartesian and spherical coordinates to manipulator joint coordinates. A majority of the results have average errors which fall below 1% of the robot workspace. The accuracy indicates that neural networks are an alternate method for performing the inverse kinematics estimation, thus introducing the fault-tolerant and high-speed advantages of neural networks to the inverse kinematics problem.This paper also shows the use of a new technique which reduces neural network mapping errors with the use of error compensation networks. The results of the work are put in perspective with a survey of current applications of neural networks in robotics.     

A neuro-simulated annealing approach to the inverse kinematics solution of redundant robotic manipulators

The neural-network-based inverse kinematics solution is one of the recent topics in the robotics because of the fact that many traditional inverse kinematics problem solutions such as geometric, iterative and algebraic are inadequate for redundant robots. However, since the neural networks work with an acceptable error, the error at the end of inverse kinematics learning should be minimized. In this study, simulated annealing (SA) algorithm was used together with the neural-network-based inverse kinematics problem solution robots to minimize the error at the end effector. The solution method is applied to Stanford and Puma 560 six-joint robot models to show the efficiency. The proposed algorithm combines the characteristics of neural network and an optimization technique to obtain the best solution for the critical robotic applications. Three Elman neural networks were trained using separate training sets and different parameters, since one of them can give better results than the others can. The best result is selected within three neural network results by computing the end effector error via direct kinematics equation of the robotic manipulator. The decimal part of the neural network result was improved up to 10 digits using simulated annealing algorithm. The obtained best solution is given to the simulated annealing algorithm to find the best-fitting 10 digits for the decimal part of the solution. The end effector error was reduced significantly.     

一种基于思维进化算法的神经网络求解机器人逆运动学问题

研究了SCARA机器人的逆运动学问题,提出了一种采用思维进化算法来学习神经网络连接权值的方法。并将该算法成功地应用于求解机器人的逆运动学问题。计算机仿真表明,这种神经网络方法不仅具有较快的收敛速度,而且大大提高了求解的精度。     

“Probability transforms” of digital pictures

Let g be any local property (e.g., gray level or gradient magnitude) defined on a digital picture. Let p_g(z) be the relative frequency with which g has value z. At each point (x,y) of the picture we can display p_g[g(x,y)], appropriately scaled; the result is called the p_g transform of the picture. Alternatively, we can use joint or conditional frequencies of pairs of local properties to define transforms. This note gives examples of such transforms for various gs and discusses their possible uses and limitations.     

Algorithms of discretization of algebraic spatial curves on homogeneous cubical grids

In this paper new methods of discretization (integer approximation) of algebraic spatial curves in the form of intersecting surfaces P(x, y, z) = 0 and Q(x, y, z) = 0 are analyzed.

The use of homogeneous cubical grids G(h³) to discretize a curve is the essence of the method. Two new algorithms of discretization (on 6-connected grid G_6c(h³) and 26-connected grid G₂₆(h³)) are presented based on the method above. Implementation of the algorithms for algebraic spatial curves is suggested. The elaborated algorithms are adjusted for application in computer graphics and numerical control of machine tools.     

Parallel algorithms for planar dominance counting

Given n points in the plane the planar dominance counting problem is to determine for each point the number of points dominated by it. Point p is said to dominate point q if x(q)x(p) and y(q)y(p), when x(p) and y(p) are the x− and y-coordinate of p, respectively. We present two CREW PRAM parallel algorithms for the problem, one running in O(log n loglog n) time and and the other in O(lognloglogn/logloglogn) time both using O(n) processors. Some applicationsare also given.     

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．     

A neuro-genetic-simulated annealing approach to the inverse kinematics solution of robots: a simulation based study

In this study, a hybrid intelligent solution system including neural networks, genetic algorithms and simulated annealing has been proposed for the inverse kinematics solution of robotic manipulators. The main purpose of the proposed system is to decrease the end effector error of a neural network based inverse kinematics solution. In the designed hybrid intelligent system, simulated annealing algorithm has been used as a genetic operator to decrease the process time of the genetic algorithm to find the optimum solution. Obtained best solution from the neural network has been included in the initial solution of genetic algorithm with randomly produced solutions. The end effector error has been reduced micrometer levels after the implementation of the hybrid intelligent solution system.     

An algorithm for computing the distance to uncontrollability

In this paper, we present an algorithm to compute the distance to uncontrollability. The problem of computing the distance is an optimization problem of minimizing σ(x,y) over the complete plane. This new approach is based on finding zero points of grad σ(x,y ). We obtain the explicit expression of the derivative matrix of grad σ(x,y). The Newton's method and the bisection method are applied to approach these zero points. Numerical results show that these methods work well.     

Design of robotic visual servo control based on neural network and genetic algorithm

A new visual servo control scheme for a robotic manipulator is presented in this paper, where a back propagation (BP) neural network is used to make a direct transition from image feature to joint angles without requiring robot kinematics and camera calibration. To speed up the convergence and avoid local minimum of the neural network, this paper uses a genetic algorithm to find the optimal initial weights and thresholds and then uses the BP algorithm to train the neural network according to the data given. The proposed method can effectively combine the good global searching ability of genetic algorithms with the accurate local searching feature of BP neural network. The Simulink model for PUMA560 robot visual servo system based on the improved BP neural network is built with the Robotics Toolbox of Matlab. The simulation results indicate that the proposed method can accelerate convergence of the image errors and provide a simple and effective way of robot control.     

Kinematics analysis of an offset 3-UPU translational parallel robotic manipulator

The parallel robotic manipulator has attracted many researchers’ attention and it also has growing applications to different areas. This paper proposes a 3-UPU (universal–prismatic–universal) translational parallel robotic manipulator with an equal offset in its six universal joints, based on the zero offset 3-UPU parallel manipulator. The kinematics of the new manipulator is analyzed and its inverse and forward kinematics solutions are provided. The conclusion is that its forward kinematics has 16 solutions instead of two in the zero offset manipulator.     

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 systemically. 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.     

An adaptive-learning algorithm to solve the inverse kinematics problem of a 6 D.O.F serial robot manipulator

An adoptive learning strategy using an artificial neural network ANN has been proposed here to control the motion of a 6 D.O.F manipulator robot and to overcome the inverse kinematics problem, which are mainly singularities and uncertainties in arm configurations. In this approach a network have been trained to learn a desired set of joint angles positions from a given set of end effector positions, experimental results has shown an excellent mapping over the working area of the robot, to validate the ability of the designed network to make prediction and well generalization for any set of data, a new training using different data set has been performed using the same network, experimental results has shown a good generalization for the new data sets.The proposed control technique does not require any prior knowledge of the kinematics model of the system being controlled, the basic idea of this concept is the use of the ANN to learn the characteristics of the robot system rather than to specify explicit robot system model. Any modification in the physical set-up of the robot such as the addition of a new tool would only require training for a new path without the need for any major system software modification, which is a significant advantage of using neural network technology.     

Cartesian control of robots without dynamic model and observer design

Most control algorithms for rigid robots are given in joint coordinates. However, since the task to be accomplished is expressed in Cartesian coordinates, inverse kinematics has to be computed in order to implement the control law. Alternatively, one can develop the necessary theory directly in workspace coordinates. This has the disadvantage of a more complex robot model. In this paper, a control-observer scheme is given to achieve exact Cartesian tracking without the knowledge of the manipulator dynamics nor computing inverse kinematics. Also, only joint measurements are used.