Visual motor control of a 7 DOF robot manipulator using a fuzzy SOM network

A fuzzy self-organizing map (SOM) network is proposed in this paper for visual motor control of a 7 degrees of freedom (DOF) robot manipulator. The inverse kinematic map from the image plane to joint angle space of a redundant manipulator is highly nonlinear and ill-posed in the sense that a typical end-effector position is associated with several joint angle vectors. In the proposed approach, the robot workspace in image plane is discretized into a number of fuzzy regions whose center locations and fuzzy membership values are determined using a Fuzzy C-Mean (FCM) clustering algorithm. SOM network then learns the inverse kinematics by on-line by associating a local linear map for each cluster. A novel learning algorithm has been proposed to make the robot manipulator to reach a target position. Any arbitrary level of accuracy can be achieved with a number of fine movements of the manipulator tip. These fine movements depend on the error between the target position and the current manipulator position. In particular, the fuzzy model is found to be better as compared to Kohonen self-organizing map (KSOM) based learning scheme proposed for visual motor control. Like existing KSOM learning schemes, the proposed scheme leads to a unique inverse kinematic solution even for a redundant manipulator. The proposed algorithms have been successfully implemented in real-time on a 7 DOF PowerCube robot manipulator, and results are found to concur with the theoretical findings.     

Kinematic control of a redundant manipulator using an inverse-forward adaptive scheme with a KSOM based hint generator

This paper proposes an online inverse-forward adaptive scheme with a KSOM based hint generator for solving the inverse kinematic problem of a redundant manipulator. In this approach, a feed-forward network such as a radial basis function (RBF) network is used to learn the forward kinematic map of the redundant manipulator. This network is inverted using an inverse-forward adaptive scheme until the network inversion solution guides the manipulator end-effector to reach a given target position with a specified accuracy. The positioning accuracy, attainable by a conventional network inversion scheme, depends on the approximation error present in the forward model. But, an accurate forward map would require a very large size of training data as well as network architecture. The proposed inverse-forward adaptive scheme effectively approximates the forward map around the joint angle vector provided by a hint generator. Thus the inverse kinematic solution obtained using the network inversion approach can take the end-effector to the target position within any arbitrary accuracy.In order to satisfy the joint angle constraints, it is necessary to provide the network inversion algorithm with an initial hint for the joint angle vector. Since a redundant manipulator can reach a given target end-effector position through several joint angle vectors, it is desirable that the hint generator is capable of providing multiple hints. This problem has been addressed by using a Kohonen self organizing map based sub-clustering (KSOM-SC) network architecture. The redundancy resolution process involves selecting a suitable joint angle configuration based on different task related criteria.The simulations and experiments are carried out on a 7 DOF PowerCube? manipulator. It is shown that one can obtain a positioning accuracy of 1 mm without violating joint angle constraints even when the forward approximation error is as large as 4 cm. An obstacle avoidance problem has also been solved to demonstrate the redundancy resolution process with the proposed scheme.     

Visual servoing of redundant manipulator with Jacobian matrix estimation using self-organizing map

Vision based redundant manipulator control with a neural network based learning strategy is discussed in this paper. The manipulator is visually controlled with stereo vision in an eye-to-hand configuration. A novel Kohonen’s self-organizing map (KSOM) based visual servoing scheme has been proposed for a redundant manipulator with 7 degrees of freedom (DOF). The inverse kinematic relationship of the manipulator is learned using a Kohonen’s self-organizing map. This learned map is shown to be an approximate estimate of the inverse Jacobian, which can then be used in conjunction with the proportional controller to achieve closed loop servoing in real-time. It is shown through Lyapunov stability analysis that the proposed learning based servoing scheme ensures global stability. A generalized weight update law is proposed for KSOM based inverse kinematic control, to resolve the redundancy during the learning phase. Unlike the existing visual servoing schemes, the proposed KSOM based scheme eliminates the computation of the pseudo-inverse of the Jacobian matrix in real-time. This makes the proposed algorithm computationally more efficient. The proposed scheme has been implemented on a 7 DOF PowerCube? robot manipulator with visual feedback from two cameras.     

Trajectory Planning with Collision Avoidance for Redundant Robots Using Jacobian and Artificial Potential Field-based Real-time Inverse Kinematics

This study proposes an algorithm for combining the Jacobian-based numerical approach with a modified potential field to solve real-time inverse kinematics and path planning problems for redundant robots in unknown environments. With an increase in the degree of freedom (DOF) of the manipulator, however, the problems in realtime inverse kinematics become more difficult to solve. Although the analytical and geometrical inverse kinematics approach can obtain the exact solution, it is considerably difficult to solve as the DOF increases, and it necessitates recalculations whenever the robot arm DOF or Denavit-Hartenberg (D-H) parameters change. In contrast, the numerical method, particularly the Jacobian-based numerical method, can easily solve inverse kinematics irrespective of the aforementioned changes including those in the robot shape. The latter method, however, is not employed in path planning for collision avoidance, and it presents real-time calculation problems. This study accordingly proposes the Jacobian-based numerical approach with a modified potential field method that can realize real-time calculations of inverse kinematics and path planning with collision avoidance irrespective of whether the case is redundant or non-redundant. To achieve this goal, the use of a judgment matrix is proposed for obstacle condition identification based on the obstacle boundary definition; an approach for avoiding the local minimum is also proposed. After the obstacle avoidance path is generated, a trajectory plan that follows the path and avoids the obstacle is designed. Finally, the proposed method is evaluated by implementing a motion planning simulation of a 7-DOF manipulator, and an experiment is performed on a 7-DOF real robot.

     

A general solution for the position,velocity, and acceleration of hyperredundant planar manipulators

A new approach for the solution of the position, velocity, and acceleration of hyperredundant planar manipulators following any twice‐differentiable desired path is presented. The method is singularity free, and provides a robust solution even in the event of mechanical failure of some of the robot actuators. The approach is based on defining virtual layers, and dividing them into virtual/real three‐link or four‐link subrobots. It starts by solving the inverse kinematic problem for the subrobot located in the lowest virtual layer, which is then used to solve the inverse kinematic equations for the subrobots located in the upper virtual layers. An algorithm is developed that provides a singularity‐free solution up to the full extension through a configuration index. The configuration index can be interpreted as the average of the determinants of the Jacobians of the subrobots. The equations for the velocities and accelerations of the manipulator are solved by extending the same approach, and it is shown that the value of the configuration index is critical in maintaining joint velocity continuity. The inverse dynamic problem of the robot is also solved to obtain the torques required for the robot actuators to accomplish their tasks. Computer simulations of several hyperredundant manipulators using the proposed method are presented as numerical examples. © 2002 John Wiley & Sons, Inc.     

Analytical Inverse Kinematic Computation for 7-DOF Redundant Manipulators With Joint Limits and Its Application to Redundancy Resolution

This paper proposes an analytical methodology of inverse kinematic computation for 7 DOF redundant manipulators with joint limits. Specifically, the paper focuses on how to obtain all feasible inverse kinematic solutions in the global configuration space where joint movable ranges are limited. First, a closed-form inverse kinematic solution is derived based on a parameterization method. Second, how the joint limits affect the feasibility of the inverse solution is investigated to develop an analytical method for computing feasible solutions under the joint limits. Third, how to apply the method to the redundancy resolution problem is discussed and analytical methods to avoid joint limits are developed in the position domain. Lastly, the validity of the methods is verified by kinematic simulations.      

基于深度强化学习的机械臂控制快速训练方法

人工智能在机器人控制中得到广泛应用,机器人控制算法也逐渐从模型驱动转变为数据驱动。深度强化学习算法可在复杂环境中感知并决策,能够解决高维度和连续状态空间下的机械臂控制问题。然而,目前深度强化学习中数据驱动的训练过程非常依赖计算机GPU算力,且训练时间成本较大。提出基于深度强化学习的先简化模型（2D模型）再复杂模型（3D模型）的机械臂控制快速训练方法。采用深度确定性策略梯度算法代替机械臂传统控制算法中的逆运动学解算方法,直接通过数据驱动的训练过程控制机械臂末端到达目标位置,从而减小训练时间成本。同时,对于状态向量和奖励函数形式,使用不同的设置方式。将最终训练得到的算法模型在真实机械臂上进行实现和验证,结果表明,其控制效果达到了分拣物品的应用要求,相比于直接在3D模型中的训练,能够缩短近52%的平均训练时长。     

Robust adaptive control of redundant manipulators

This paper presents an adaptive scheme for the motion control of kinematically redundant manipulators. The proposed controller is very general and computationally efficient since it does not require knowledge of either the mathematical model or the parameter values of the robot dynamics, and is implemented without calculation of the robot inverse dynamics or inverse kinematic transformation. It is shown that the control strategy is globally stable in the presence of bounded disturbances, and that in the absence of disturbances the size of the residual tracking errors can be made arbitrarily small. The performance of the controller is illustrated through computer simulations with a nine degree-of-freedom (DOF) compound manipulator consisting of a relatively small, fast six-DOF manipulator mounted on a large three-DOF positioning device. These simulations demonstrate that the proposed scheme provides accurate and robust trajectory tracking and, moreover, permits the available redundancy to be utilized so that a high bandwidth response can be achieved over a large workspace.     

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.     

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.     

An inverse kinematic solution for kinematically redundant robot manipulators

An inverse kinematic analysis addresses the problem of computing the sequence of joint motion from the Cartesian motion of an interested member, most often the end effector. Although the rates and accelerations are related linearly through the Jacobian, the positions go through a highly nonlinear transformation from one space to another. Hence, the closed-form solution has been obtained only for rather simple manipulator configurations where joints intersect or where consecutive axes are parallel or perpendicular. For the case of redundant manipulators, the number of joint variables generally exceeds that of the constraints, so that in this case the problem is further complicated due to an infinite number of solutions. Previous approaches have been directed to minimize a criterion function, taking into account additional constraints, which often implies a time-consuming optimization process. In this article, a different approach is taken to these problems. A Newton-Raphson numerical procedure has been developed based on a composite Jacobian which now includes rows for all members under constraint. This procedure may be applied to solve the inverse kinematic problem for a manipulator of any mechanical configuration without having to derive beforehand a closed-form solution. The technique is applicable to redundant manipulators since additional constraints on other members as well as on the end effector may be imposed. Finally, this approach has been applied to a seven degree-of-freedom manipulator, and its ability to avoid obstacles is demonstrated.     

基于QR分解的冗余度机械臂雅可比矩阵求逆方法

针对冗余度机械臂在轨操作实时性的需求,提出一种基于QR分解的冗余度机械臂雅克比矩阵求逆方法。根据具体的冗余度机械臂的构型特点,将运动学逆解过程划分为多个模块,采用修正施密特QR分解方法计算机械臂雅可比矩阵的伪逆,利用硬件描述语言在FPGA上对各个模块进行了实现。以机械臂直线运动为例,通过仿真实验与利用Matlab解算的方法进行了对比,并研究了定点数长度对硬件资源和误差的影响。实验结果验证了所提出雅克比矩阵求逆方法的可行性及有效性。     

Kinematics analysis of a novel all-attitude flight simulator

To overcome the kinematic singularity limitation of simulator, which is unavoidable in a three-axis architecture, an all-attitude flight simulator in a four-axis architecture is proposed. The simulator can always provide 3DOF motion by applying redundant manipulator mechanism. For direct kinematics of the manipulator, a dual-Euler method is adopted to solve the expressions of attitude angles; thus computation singularity of all- attitude angles is overcome. For inverse kinematics of the manipulator, pseudo-...     

Uncalibrated Eye-to-Hand Visual Servoing Using Inverse Fuzzy Models

A new uncalibrated eye-to-hand visual servoing based on inverse fuzzy modeling is proposed in this paper. In classical visual servoing, the Jacobian plays a decisive role in the convergence of the controller, as its analytical model depends on the selected image features. This Jacobian must also be inverted online. Fuzzy modeling is applied to obtain an inverse model of the mapping between image feature variations and joint velocities. This approach is independent from the robot's kinematic model or camera calibration and also avoids the necessity of inverting the Jacobian online. An inverse model is identified for the robot workspace, using measurement data of a robotic manipulator. This inverse model is directly used as a controller. The inverse fuzzy control scheme is applied to a robotic manipulator performing visual servoing for random positioning in the robot workspace. The obtained experimental results show the effectiveness of the proposed control scheme. The fuzzy controller can position the robotic manipulator at any point in the workspace with better accuracy than the classic visual servoing approach.     

6－6型Stewart机器人的可操作性分析及其定义

本文根据并联机器人的特点，运用可操作度的概念，进一步提出了位置可操作度和姿态可操作度的定义。通过对位置反解直接求导，建立了６－６型ｓｔｅｗａｒｔ机器人的位置、姿态和综合可操作度的公式，为并联机器人的运动学分析提供了依据。     

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.     

New inverse kinematic algorithms for redundant robots

New inverse kinematic algorithms for generating redundant robot joint trajectories are proposed. The algorithms utilize the kinematic redundancy to improve robot motion performance (in joint space or Cartesian space) as specified by certain objective functions. The algorithms are based on the extension of the existing “joint-space command generator” technique in which a null space vector is introduced which optimizes a specific objective function along the joint trajectories. In this article, the algorithms for generating the joint position and velocity (PV) trajectories are extensively developed. The case for joint position, velocity, and acceleration (PVA) generation is also addressed. Application of the algorithms to a four-link revolute planar robot manipulator is demonstrated through simulation. Several motion performance criteria are considered and their results analyzed.     

Fault-tolerant motion planning and control of redundant manipulator

One important issue in the motion planning of a kinematic redundant manipulator is fault tolerance. In general, if the motion planner is fault tolerant, the manipulator can achieve the required path of the end-effector even when its joint fails. In this situation, the contribution of the faulty joint to the end-effector is required to be compensated by the healthy joints to maintain the prescribed end-effector trajectory. To achieve this, this paper proposes a fault-tolerant motion planning scheme by adding a simple fault-tolerant equality constraint for the faulty joint. Such a scheme is then unified into a quadratic program (QP), which incorporates joint-physical constraints such as joint limits and joint-velocity limits. In addition, a numerical computing solver based on linear variational inequalities (LVI) is presented for the real-time QP solving. Simulative studies and experimental results based on a six degrees-of-freedom (DOF) redundant robot manipulator with variable joint-velocity limits substantiate the effectiveness of the proposed fault-tolerant scheme and its solution.     

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).