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 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.     

Obstacle avoidance of redundant manipulators using neural networks based reinforcement learning

This paper proposes a new approach for solving the problem of obstacle avoidance during manipulation tasks performed by redundant manipulators. The developed solution is based on a double neural network that uses Q-learning reinforcement technique. Q-learning has been applied in robotics for attaining obstacle free navigation or computing path planning problems. Most studies solve inverse kinematics and obstacle avoidance problems using variations of the classical Jacobian matrix approach, or by minimizing redundancy resolution of manipulators operating in known environments. Researchers who tried to use neural networks for solving inverse kinematics often dealt with only one obstacle present in the working field. This paper focuses on calculating inverse kinematics and obstacle avoidance for complex unknown environments, with multiple obstacles in the working field. Q-learning is used together with neural networks in order to plan and execute arm movements at each time instant. The algorithm developed for general redundant kinematic link chains has been tested on the particular case of PowerCube manipulator. Before implementing the solution on the real robot, the simulation was integrated in an immersive virtual environment for better movement analysis and safer testing. The study results show that the proposed approach has a good average speed and a satisfying target reaching success rate.     

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.     

基于遗传算法的机器人运动学逆解

在分析以往逆解方法的基础上，提出了用遗传算法求解机器人运动学逆解的方法，给出了用于优化求解的适合度函数，并提出用二次编码法提高解的精度．计算机模拟证明：该方法能快速收敛于全局最优解，能给出机器人的可能解，并能计算冗余度机器人的逆解．     

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 Neural Network Adaptive Controller for End-effector Tracking of Redundant Robot Manipulators

In this paper we propose a neural network adaptive controller to achieve end-effector tracking of redundant robot manipulators. The controller is designed in Cartesian space to overcome the problem of motion planning which is closely related to the inverse kinematics problem. The unknown model of the system is approximated by a decomposed structure neural network. Each neural network approximates a separate element of the dynamical model. These approximations are used to derive an adaptive stable control law. The parameter adaptation algorithm is derived from the stability study of the closed loop system using Lyapunov approach with intrinsic properties of robot manipulators. Two control strategies are considered. First, the aim of the controller is to achieve good tracking of the end-effector regardless the robot configurations. Second, the controller is improved using augmented space strategy to ensure minimum displacements of the joint positions of the robot. Simulation examples are also presented to verify the effectiveness of the proposed approach.     

Obstacle avoidance for kinematically redundant manipulators using a dual neural network.

One important issue in the motion planning and control of kinematically redundant manipulators is the obstacle avoidance. In this paper, a recurrent neural network is developed and applied for kinematic control of redundant manipulators with obstacle avoidance capability. An improved problem formulation is proposed in the sense that the collision-avoidance requirement is represented by dynamically-updated inequality constraints. In addition, physical constraints such as joint physical limits are also incorporated directly into the formulation. Based on the improved problem formulation, a dual neural network is developed for the online solution to collision-free inverse kinematics problem. The neural network is simulated for motion control of the PA10 robot arm in the presence of point and window-shaped obstacle.     

A Lagrangian network for kinematic control of redundant robotmanipulators

A recurrent neural network, called the Lagrangian network, is presented for the kinematic control of redundant robot manipulators. The optimal redundancy resolution is determined by the Lagrangian network through real-time solution to the inverse kinematics problem formulated as a quadratic optimization problem. While the signal for a desired velocity of the end-effector is fed into the inputs of the Lagrangian network, it generates the joint velocity vector of the manipulator in its outputs along with the associated Lagrange multipliers. The proposed Lagrangian network is shown to be capable of asymptotic tracking for the motion control of kinematically redundant manipulators.     

Comparison of RBF and MLP neural networks to solve inverse kinematic problem for 6R serial robot by a fusion approach

In this paper, a fusion approach to determine inverse kinematics solutions of a six degree of freedom serial robot is proposed. The proposed approach makes use of radial basis function neural network for prediction of incremental joint angles which in turn are transformed into absolute joint angles with the assistance of forward kinematics relations. In this approach, forward kinematics relations of robot are used to obtain the data for training of neural network as well to estimate the deviation of predicted inverse kinematics solution from the desired solution. The effectiveness of the fusion process is shown by comparing the inverse kinematics solutions obtained for an end-effector of industrial robot moving along a specified path with the solutions obtained from conventional neural network approaches as well as iterative technique. The prominent features of the fusion process include the accurate prediction of inverse kinematics solutions with less computational time apart from the generation of training data for neural network with forward kinematics relations of the robot.     

A dual neural network for kinematic control of redundant robotmanipulators

The inverse kinematics problem in robotics can be formulated as a time-varying quadratic optimization problem. A new recurrent neural network, called the dual network, is presented in this paper. The proposed neural network is composed of a single layer of neurons, and the number of neurons is equal to the dimensionality of the workspace. The proposed dual network is proven to be globally exponentially stable. The proposed dual network is also shown to be capable of asymptotic tracking for the motion control of kinematically redundant manipulators.     

Computer generation of symbolic kinematics for robot manipulators

Computer generation of symbolic solutions for the direct and inverse robot kinematics is a desired capability not previously available to robotics engineers. In this article, we present a methodology for the design of a software system capable of solving the direct and inverse kinematics for n degree of freedom (dof) manipulators in symbolic form. The inputs to the system are the Denavit-Hartenberg parameters of the manipulator. The outputs of the system are the direct and inverse kinematics solutions in symbolic form. The system consists of a symbolic processor to perform matrix and algebraic manipulations and an expert system to solve the class of nonlinear equations involved in the solution of the inverse kinematics problem. The system can be used to study robot kinematics configurations whose inverse kinematics solutions are not known to exist a priori. Two examples are included to illustrate its capabilities. The first example provides explicit analytical solutions, previously believed nonexistent, for a 3 dof manipulator. A second example is included for a robot whose inverse kinematics solution requires intensive algebraic manipulations.     

Linear Hopfield networks and constrained optimization

It is shown that a Hopfield neural network (with linear transfer functions) augmented by an additional feedforward layer can be used to compute the Moore-Penrose generalized inverse of a matrix. The resultant augmented linear Hopfield network can be used to solve an arbitrary set of linear equations or, alternatively, to solve a constrained least squares optimization problem. Applications in signal processing and robotics are considered. In the former case the augmented linear Hopfield network is used to estimate the "structured noise" component of a signal and adjust the parameters of an appropriate filter on-line, whereas in the latter case it is used to implement an on-line solution to the inverse kinematics problem.     

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.     

A hybrid strategy to solve the forward kinematics problem in parallel manipulators

A parallel manipulator is a closed kinematic structure with the necessary rigidity to provide a high payload to self-weight ratio suitable for many applications in manufacturing, flight simulation systems, and medical robotics. Because of its closed structure, the kinematic control of such a mechanism is difficult. The inverse kinematics problem for such manipulators has a mathematical solution; however, the forward kinematics problem (FKP) is mathematically intractable. This work addresses the FKP and proposes a neural-network-based hybrid strategy that solves the problem to a desired level of accuracy, and can achieve the solution in real time. Two neural-network (NN) concepts using a modified form of multilayered perceptrons with backpropagation learning were implemented. The better performing concept was then combined with a standard Newton-Raphson numerical technique to yield a hybrid solution strategy. Simulation studies were carried out on a flight simulation syystem to check the validity o the approach. Accuracy of close to 0.01 mm and 0.01/spl deg/ in the position and orientation parameters was achieved in less than two iterations and 0.02 s of execution time for the proposed strategy.     

Kinematic analysis of a novel 3-DOF actuation redundant parallel manipulator using artificial intelligence approach

Kinematic analysis is one of the key issues in the research domain of parallel kinematic manipulators. It includes inverse kinematics and forward kinematics. Contrary to a serial manipulator, the inverse kinematics of a parallel manipulator is usually simple and straightforward. However, forward kinematic mapping of a parallel manipulator involves highly coupled nonlinear equations. Therefore, it is more difficult to solve the forward kinematics problem of parallel robots. In this paper, a novel three degrees-of-freedom (DOFs) actuation redundant parallel manipulator is introduced. Different intelligent approaches, which include the Multilayer Perceptron (MLP) neural network, Radial Basis Functions (RBF) neural network, and Support Vector Machine (SVM), are applied to investigate the forward kinematic problem of the robot. Simulation is conducted and the accuracy of the models set up by the different methods is compared in detail. The advantages and the disadvantages of each method are analyzed. It is concluded that ν-SVM with a linear kernel function has the best performance to estimate the forward kinematic mapping of a parallel manipulator.     

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.     

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．     

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.     

基于扩展雅可比矩阵的冗余液压驱动四足机器人运动控制

针对冗余液压驱动四足机器人运动学逆解问题,提出一种基于扩展雅可比矩阵的冗余液压驱动四足机器人运动控制方法.该方法既能解决冗余自由度带来的逆解多解问题,还能使机器人足端入地角度满足摩擦锥要求避免足端滑动.首先,规划机器人足端轨迹得到机器人足端速度,在分析机器人足端入地角度对机器人运动性能影响的基础上,结合机器人腿部结构几...