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.     

Robot arm reaching through neural inversions and reinforcement learning

We present a neural method that computes the inverse kinematics of any kind of robot manipulators, both redundant and non-redundant. Inverse kinematics solutions are obtained through the inversion of a neural network that has been previously trained to approximate the manipulator forward kinematics. The inversion provides difference vectors in the joint space from difference vectors in the workspace. Our differential inverse kinematics (DIV) approach can be viewed as a neural network implementation of the Jacobian transpose method for arm kinematic control that does not require previous knowledge of the arm forward kinematics. Redundancy can be exploited to obtain a special inverse kinematic solution that meets a particular constraint (e.g. joint limit avoidance) by inverting an additional neural network The usefulness of our DIV approach is further illustrated with sensor-based multilink manipulators that learn collision-free reaching motions in unknown environments. For this task, the neural controller has two modules: a reinforcement-based action generator (AG) and a DIV module that computes goal vectors in the joint space. The actions given by the AG are interpreted with regard to those goal vectors.     

机器人逆标定方法研究

在分析传统机器人位姿标定方法的基础上，提出了一种新的机器人标定方法：基于神经网络的逆标定方法。这种标定方法把机器人实际位姿和相应的关节角误差分别作为前馈神经网络的输入和输出来训练网络，从而获得机器人任意位姿时的关节角误差值，通过修改关节值来提高机器人的位姿精度。这种标定方法把所有因素引起的误差均归结为关节角误差，无须求解机器人逆运动学方程，实现了误差的在线补偿。把标定结果与基于运动学模型的参数法的标定结果进行了比较分析。仿真和试验结果均证明了这种方法比传统方法标定效果更好，且更方便简单，避免了其他传统标定方法繁琐的建模及参数辨识过程。     

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.     

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.     

Practical inverse kinematics of a kinematically redundant robot using a neural network

In solving inverse kinematics problems, traditional methods such as RMRC (resolved motion rate control) and the IKM (inverse kinematic method) are mostly complicated and time-consuming. Using a neural network, however, a practical algorithm for obtaining accurate joint angles in a much shorter time is possible. The neural network approach assumes a transfer function between inputs and outputs and trains the network to satisfy the representative input-output pairs in the least squares sense. First, a test of the appropriateness of the neural network method is performed for the case of a planar two degrees of freedom (DOF) robot. Then the neural network method is employed to find three joint angles of a planar 3-DOF robot maximizing local manipulability. In this algorithm, the proximal redundant joint angle is determined from a neural network and then the remaining joint angles are determined from analytical functions. The results from this method compare favourably with those from the other two traditional methods.     

A New Geometric Subproblem to Extend Solvability of Inverse Kinematics Based on Screw Theory for 6R Robot Manipulators

Geometric inverse kinematics procedures that divide the whole problem into several subproblems with known solutions, and make use of screw motion operators have been developed in the past for 6R robot manipulators. These geometric procedures are widely used because the solutions of the subproblems are geometrically meaningful and numerically stable. Nonetheless, the existing subproblems limit the types of 6R robot structural configurations for which the inverse kinematics can be solved. This work presents the solution of a novel geometric subproblem that solves the joint angles of a general anthropomorphic arm. Using this new subproblem, an inverse kinematics procedure is derived which is applicable to a wider range of 6R robot manipulators. The inverse kinematics of a closed curve were carried out, in both simulations and experiments, to validate computational cost and realizability of the proposed approach. Multiple 6R robot manipulators with different structural configurations were used to validate the generality of the method. The results are compared with those of other methods in the screw theory framework. The obtained results show that our approach is the most general and the most efficient.

     

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.     

FGA优化RBF网络的机器人逆运动学求解研究

针对如何提高六自由度机器人逆运动学的求解精度问题,采用FGA对RBF神经网络的节点中心向量、基宽向量以及网络隐含层到输出层的权向量进行优化,并将其应用于六自由度机器人的逆运动学求解。以机器人工作空间的位姿矩阵作为预测网络的输入变量,以关节空间中的关节角度作为输出变量,构建机器人逆解RBF预测网络,然后选取样本对网络进行训练。最后对网络进行测试,仿真结果显示,优化后的网络预测精度高,泛化能力强。     

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.     

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.     

结合MPGA-RBFNN的一般机器人逆运动学求解

针对一般机器人逆运动学求解过程中存在的求解速度慢、精度低的问题，将多种群遗传算法（multiple population genetic algorithm，MPGA）引入径向基函数神经网络（radial basis functions neural network，RBFNN），提出一种适用于一般机器人的高精度MPGA-RBFNN算法。该算法采用3层结构的RBFNN进行一般机器人逆运动学求解，结合一般机器人的正运动学模型，采用MPGA优化RBFNN的网络结构和连接权值的方法，同时应用混合编码和演化的方式，实现了从机器人工作空间位姿到关节角度的非线性映射，从而避免了复杂的公式推导并提高了求解速度。采用6R一般机器人作为实验平台进行实验，实验结果表明:MPGA-RBFNN算法不仅提高了一般机器人在逆运动学中的求解速度，而且MPGA-RBFNN算法的训练成功率和逆解的计算准确率也得到了提高。     

A parallel approach of the inverse kinematics solutions for robots using a transputer network

This article presents a parallel method for computing inverse kinematics solutions for robots with closed-form solutions moving along a straight line trajectory specified in Cartesian space. Zhang and Paul's approach¹ is improved for accuracy and speed. Instead of using previous joint positions as proposed by Zhang and Paul, a first order prediction strategy is used to decouple the dependency between joint positions, and a zero order approximation solution is computed. A compensation scheme using Taylor series expansion is applied to obtain the trajectory gradient in joint space to replace the correction scheme proposed by Zhang and Paul. The configuration of a Mitsubishi RV-M1 robot is used for the simulation of a closed-form inverse kinematics solutions. An Alta SuperLink/XL with four transputer nodes is used for parallel implementation. The simulation results show a significant improvement in displacement tracking errors and joint configuration errors along the straight line trajectory. The computational latency is reduced as well. The modified approach proposed in this work is more accurate and faster than Zhang and Paul's approach for robots with closed-form inverse kinematics solutions. © 1996 John Wiley & Sons, Inc.     

用于丝驱动连续体机器人的实用运动学研究

针对单段及多段连续体机器人运动学问题,提出分段常曲率与粒子群算法相结合的完整正逆运动学分析方法.以双段丝驱动连续体机器人为研究对象,首先设计含平移段的机器人样机;然后利用分段常曲率方法建立驱动空间与关节空间的相互映射,根据齐次变换得到关节空间至工作空间的正映射关系;最后利用线性递减权重粒子群算法实现工作空间至关节空间的逆映射.对双段连续体机器人的运动学进行仿真及逆运动学求解耗时测试,并在研制样机上进行了实验验证.仿真结果说明了所提运动学研究方法的合理性及逆运动学求解的快速性,实验结果显示位置平均误差小于双段连续体机器人本体长度的6.22％,验证了所提运动学的有效性.     

A biomimetic approach to inverse kinematics for a redundant robot arm

Redundant robots have received increased attention during the last decades, since they provide solutions to problems investigated for years in the robotic community, e.g. task-space tracking, obstacle avoidance etc. However, robot redundancy may arise problems of kinematic control, since robot joint motion is not uniquely determined. In this paper, a biomimetic approach is proposed for solving the problem of redundancy resolution. First, the kinematics of the human upper limb while performing random arm motion are investigated and modeled. The dependencies among the human joint angles are described using a Bayesian network. Then, an objective function, built using this model, is used in a closed-loop inverse kinematic algorithm for a redundant robot arm. Using this algorithm, the robot arm end-effector can be positioned in the three dimensional (3D) space using human-like joint configurations. Through real experiments using an anthropomorphic robot arm, it is proved that the proposed algorithm is computationally fast, while it results to human-like configurations compared to previously proposed inverse kinematics algorithms. The latter makes the proposed algorithm a strong candidate for applications where anthropomorphism is required, e.g. in humanoids or generally in cases where robotic arms interact with humans.     

Forward and inverse kinematics of a 5-DOF hybrid robot for composite material machining

Hybrid robots consist of both serial and parallel mechanisms, which have advantages in stiffness and workspace compared with serial/parallel robots when machining composite material. However, the forward and inverse kinematics of hybrid robots generally do not have analytic solutions. This paper deals with the analytic forward and inverse kinematics solutions of a 5-degree-of-freedom (DOF) hybrid robot which consists with a 3-DOF 2UPU/SP parallel mechanism (PM) and a 2-DOF rotating head. In the forward kinematic problem, a method is proposed to transfer the high order kinematic equation to a 4th-order polynomial based on the Sylvester's dialytic elimination, and the analytic solutions can be further obtained by Ferrari's method. In the inverse problem, the redundant Euler angles expressed by four rotations are firstly proposed for decoupling different motions, then, the closed-form solution of inverse kinematics can be found. Finally, a simulation trajectory is given, and the result shows that the accuracy of the solutions’ calculation reaches femtometer grade and the efficiency reaches microsecond grade; furthermore, an experiment is performed on the prototype to validate the effectiveness of the proposed forward and inverse kinematics.     

机器人运动学标定综述

从基于运动学模型的几何参数标定、机器人自标定、神经网络的正标定和逆标定三个方面,对机器人运动学标定方法及其研究现状进行了分析总结。详细介绍了每种标定方法的特点、存在的问题以及研究现状。最后对多机器人协作系统的标定以及运动学标定的发展方向进行了简要论述。     

Recurrent neural networks for minimum infinity-norm kinematiccontrol of redundant manipulators

This paper presents two neural network approaches to minimum infinity-norm solution of the velocity inverse kinematics problem for redundant robots. Three recurrent neural networks are applied for determining a joint velocity vector with its maximum absolute value component being minimal among all possible joint velocity vectors corresponding to the desired end-effector velocity. In each proposed neural network approach, two cooperating recurrent neural networks are used. The first approach employs two Tank-Hopfield networks for linear programming. The second approach employs two two-layer recurrent neural networks for quadratic programming and linear programming, respectively. Both the minimal 2-norm and infinity-norm of joint velocity vector can be obtained from the output of the recurrent neural networks. Simulation results demonstrate that the proposed approaches are effective with the second approach being better in terms of accuracy and optimality     

An improved approach to the solution of inverse kinematics problems for robot manipulators

A structured artificial neural-network (ANN) approach has been proposed here to control the motion of a robot manipulator. Many neural-network models use threshold units with sigmoid transfer functions and gradient descent-type learning rules. The learning equations used are those of the backpropagation algorithm. In this work, the solution of the kinematics of a six-degrees-of-freedom robot manipulator is implemented by using ANN. Work has been undertaken to find the best ANN configurations for this problem. Both the placement and orientation angles of a robot manipulator are used to fin the inverse kinematics solutions.     

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.