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 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 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.     

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.     

Applications of neural networks for coordinate transformations in robotics

The use of artificial neural networks is investigated for application to trajectory control problems in robotics. The relative merits of position versus velocity control is considered and a control scheme is proposed in which neural networks are used as static maps (trained off-line) to compute the inverse of the manipulator Jacobian matrix. A proof of the stability of this approach is offered, assuming bounded errors in the static map. A representative two-link robot is investigated using an artificial neural network which has been trained to compute the components of the inverse of the Jacobian matrix. The controller is implemented in the laboratory and its performance compared to a similar controller with the analytical inverse Jacobian matrix.     

Neutral learning of constrained nonlinear transformations

Two issues that are fundamental to developing autonomous intelligent robots, namely rudimentary learning capability and dexterous manipulation, are examined. A powerful neural learning formalism is introduced for addressing a large class of nonlinear mapping problems, including redundant manipulator inverse kinematics, commonly encountered during the design of real-time adaptive control mechanisms. Artificial neural networks with terminal attractor dynamics are used. The rapid network convergence resulting from the infinite local stability of these attractors allows the development of fast neural learning algorithms. Approaches to manipulator inverse kinematics are reviewed, the neurodynamics model is discussed, and the neural learning algorithm is presented     

On the computation of the direct kinematics of parallelmanipulators using polynomial networks

Polynomial learning networks are proposed in this paper to solve the forward kinematic problem for a planar three-degree-of-freedom parallel manipulator with revolute joints. These networks rapidly learn complex nonlinear functions based on a database mapping. The networks learn the forward kinematics of the manipulator based on examples of the transformation. The obtained networks are then used to follow a test trajectory. For comparison purposes, a neural network approach using backpropagation is also used for this problem. The results show that, in this application, polynomial networks learn much faster and exhibit less error than neural networks     

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。     

Canonical parameterization of excess motor degrees of freedom withself-organizing maps

The problem of sensorimotor control is underdetermined due to excess (or "redundant") degrees of freedom when there are more joint variables than the minimum needed for positioning an end-effector. A method is presented for solving the nonlinear inverse kinematics problem for a redundant manipulator by learning a natural parameterization of the inverse solution manifolds with self-organizing maps. The parameterization approximates the topological structure of the joint space, which is that of a fiber bundle. The fibers represent the "self-motion manifolds" along which the manipulator can change configuration while keeping the end-effector at a fixed location. The method is demonstrated for the case of the redundant planar manipulator. Data samples along the self-motion manifolds are selected from a large set of measured input-output data. This is done by taking points in the joint space corresponding to end-effector locations near "query points", which define small neighborhoods in the end-effector work space. Self-organizing maps are used to construct an approximate parameterization of each manifold which is consistent for all of the query points. The resulting parameterization is used to augment the overall kinematics map so that it is locally invertible. Joint-angle and end-effector position data, along with the learned parameterizations, are used to train neural networks to approximate direct inverse functions.     

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.     

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.     

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.     

基于解析法和遗传算法的机械手运动学逆解

研究优化机械手轨迹规划问题,机械手运动时要具有稳定性避障性能。针对平面3自由度冗余机械手优化控制问题,建立机械手的结构模型。提出用解析法和遗传算法相结合满足具有计算量小和适应性强的特点。在给定机械手末端执行器的运动轨迹,按着机械手冗余自由度,运动轨迹上每个点对应的关节角有无穷多个解。而通过算法可以找到一组最优的关节角,可得到优化机械手运动过程中柔顺性和避障点。仿真结果表明,该算法可以快速收敛到全局最优解,可用于计算冗余机械手运动学逆解,并可实现机器人的轨迹规划和避障优化控制。     

A Neuro-Sliding Mode Control Scheme for Constrained Robots with Uncertain Jacobian

The joint robot control requires to map desired cartesian tasks into desired joint trajectories, by using the ill-posed inverse kinematics mapping. In order to avoid inverse kinematics, the control problem is formulated directly in task space to gives rise to cartesian robot control. In addition, when the robot is constrained due to its kinematic mappings yields a stiff system and an additional complexity arises to implement cartesian control for constrained robots. In this paper, an alternative approach is proposed to guarantee global convergence of force and position cartesian tracking errors under the assumption that the jacobian is not exactly known. A neuro-sliding mode controller is presented, where a small size adaptive neural network compensates approximately for the inverse dynamics and an inner control loop induces second order sliding modes to guarantee tracking. The sliding mode variable tunes the online adaptation of the weights. A passivity analysis yields the energy Lyapunov function to prove boundedness of all closed-loop signals and variable structure control theory is used to finally conclude convergence of position and force tracking errors. Experimental results are provided to visualize the expected performance.     

Adaptive neural network tracking control for manipulators with uncertain kinematics, dynamics and actuator model

A neural-network-based adaptive controller is proposed for the tracking problem of manipulators with uncertain kinematics, dynamics and actuator model. The adaptive Jacobian scheme is used to estimate the unknown kinematics parameters. Uncertainties in the manipulator dynamics and actuator model are compensated by three-layer neural networks. External disturbances and approximation errors are counteracted by robust signals. The actuator controller is designed based on the backstepping scheme. Compared with the existing work, the proposed method considers the manipulator kinematics uncertainty, does not need the “linearity-in-parameters” assumption for the uncertain terms in the dynamics of manipulator and actuator, and guarantees the tracking error to be as small as desired. Finally, the performance of the proposed approach is illustrated by the simulation example.     

A Dual Neural Network for Kinematic Control of Redundant Manipulators Using Input Pattern Switching

This paper presents a dual neural network for kinematic control of a seven degrees of freedom robot manipulator. The first network is a static multilayer perceptron with two hidden layers which is trained to mimic the Jacobian of a seven DOF manipulator. The second network is a recurrent neural network which is used for determining the inverse kinematics solutions of the manipulator; The redundancy is used to minimize the joint velocities in the least squares sense. Simulation results show relatively good comparison between the outputs of the actual Jacobian matrix and multilayer neural network. The first network maps motions of the seven joints of the manipulator into 42 elements of the Jacobian matrix, with surprisingly smaller computations than the actual trigonometric function evaluations. A new technique, input-pattern-switching, is presented which improves the global training of the static network. The recurrent network was designed to work with the neural network approximation of the Jacobian matrix instead of the actual Jacobian. The combination of these two networks has resulted in a time-efficient procedure for kinematic control of robot manipulators which avoids most of the complexity present in the classical-trigonometric-based methods. Also, by electronic implementation of the networks, kinematic solutions can be obtained in a very timely manner (few nanoseconds).     

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.     

Geometrical approach of planar hyper-redundant manipulators: Inverse kinematics,path planning and workspace

A new method for inverse kinematics for hyper-redundant manipulators is proposed in this paper to plan the path of the end-effector. The basic idea is that for a given smooth path consisting of points close enough to each other; computing the inverse kinematics for these points is carried out geometrically using the proposed method. In this method, the angles between the adjacent links are set to be the same, which makes lining up of two or more joint axes impossible; therefore, avoiding singularities. The manipulability index has been used to show how far the manipulator from the singularity configuration is. The determination of the workspace of the manipulator using the proposed method has been presented in this paper. The simulation results have been carried out on a planar and a three dimensional manipulators. The effectiveness of the proposed method is clearly demonstrated by comparing its result with results calculated by the well-known method of measuring manipulability which is used for singularity avoidance for the last two decades.     

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。