A closed-loop jacobian transpose scheme for solving the inverse kinematics of nonredundant and redundant wrists

The solution of the inverse kinematic problem is of the utmost importance in robotic manipulator control. This article proposes a closed-loop scheme for solving the inverse kinematic problem for nonredundant and redundant wrists based on the computation of the Jacobian transpose. The manipulability measure is suitably introduced as a constraint for redundant wrists, by taking advantage of the null space of the Jacobian matrix. The resulting algorithm provides a computational tool to solve a specified orientation trajectory into a joint trajectory. Numerical results with two spherical wrists show the excellent performance of the scheme.     

Kinematic aspects of a robot-positioner system in an arc welding application

This paper focuses on the kinematic control of a redundant robotic system taking into account particularities of the arc welding technology. The considered system consists of a 6-axis industrial robot (welding tool manipulator) and a 2-axis welding positioner (workpiece manipulator) that is intended to optimise a weld joint orientation during the technological process. The particular contribution of the paper lies in the area of the positioner inverse kinematics, which is a key issue of such system off-line programming and control. It has been proposed a novel formulation and a closed-form solution of the inverse kinematic problem that deals with the explicit definition of the weld joint orientation relative to the gravity. Similar results have also been obtained for the known problem statement that is based on a unit vector transformation. For both the cases, a detailed investigation of the singularities and uniqueness-existence topics have been carried out. The presented results are implemented in a commercial software package and verified for real-life applications in the automotive industry.     

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.     

An algorithmic approach to coordinate transformation for robotic manipulators

Coordinate transformation is one of the most important issues in robotic manipulator control. Robot tasks are naturally specified in work space coordinates, usually a Cartesian frame, while control actions are developed on joint coordinates. Effective inverse kinematic solutions are analytical in nature; they exist only for special manipulator geometries and geometric intuition is usually required. Computational inverse kinematic algorithms have recently been proposed; they are based on general closed-loop schemes which perform the mapping of the desired Cartesian trajectory into the corresponding joint trajectory. The aim of this paper is to propose an effective computational scheme to the inverse kinematic problem for manipulators with spherical wrists. First an insight into the formulation of kinematics is given in order to detail the general scheme for this specific class of manipulators. Algorithm convergence is then ensured by means of the Lyapunov direct method. The resulting algorithm is based on the hand position and orientation vectors usually adopted to describe motion in the task space. The analysis of the computational burden is performed by taking the Stanford arm as a reference. Finally a case study is developed via numerical simulations.     

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.     

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.     

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.     

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。     

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。     

Inverse kinematics of variable-geometry truss manipulators

A new class of robotic arm consists of a periodic sequence of truss substructures, each of which has several variable-length members. Such variable-geometry truss manipulators (VGTMs) are inherently highly redundant and promise a significant increase in dexterity over conventional anthropomorphic manipulators. This dexterity may be exploited for both obstacle avoidance and controlled deployment in complex workspaces. The inverse kinematics problem for such unorthodox manipulators, however, becomes complex because of the large number of degrees of freedom, and conventional solutions to the inverse kinematics problem become inefficient because of the high degree of redundancy. This paper presents a solution to this problem based on a spline-like reference curve for the manipulator's shape. Such an approach has a number of advantages: (1) direct, intuitive manipulation of shape; (2) reduced calculation time; and (3) direct control over the effective degree of redundancy of the manipulator. Furthermore, although the algorithm has been developed primarily for variable-geometry-truss manipulators, it is general enough for application to other manipulator designs.     

Visual Motor Control of a 7 DOF Robot Manipulator Using Function Decomposition and Sub-Clustering in Configuration Space

This paper deals with real-time implementation of visual-motor control of a 7 degree of freedom (DOF) robot manipulator using self-organized map (SOM) based learning approach. The robot manipulator considered here is a 7 DOF PowerCube manipulator from Amtec Robotics. The primary objective is to reach a target point in the task space using only a single step movement from any arbitrary initial configuration of the robot manipulator. A new clustering algorithm using Kohonen SOM lattice has been proposed that maintains the fidelity of training data. Two different approaches have been proposed to find an inverse kinematic solution without using any orientation feedback. In the first approach, the inverse Jacobian matrices are learnt from the training data using function decomposition. It is shown that function decomposition leads to significant improvement in accuracy of inverse kinematic solution. In the second approach, a concept called sub-clustering in configuration space is suggested to provide multiple solutions for the inverse kinematic problem. Redundancy is resolved at position level using several criteria. A redundant manipulator is dexterous owing to the availability of multiple configurations for a given end-effector position. However, existing visual motor coordination schemes provide only one inverse kinematic solution for every target position even when the manipulator is kinematically redundant. Thus, the second approach provides a learning architecture that can capture redundancy from the training data. The training data are generated using explicit kinematic model of the combined robot manipulator and camera configuration. The training is carried out off-line and the trained network is used on-line to compute the joint angle vector to reach a target position in a single step only. The accuracy attained is better than the current state of art.     

Approximation of Jacobian Inverse Kinematics Algorithms: Differential Geometric vs. Variational Approach

This paper addresses the approximation problem of Jacobian inverse kinematics algorithms for redundant robotic manipulators. Specifically, we focus on the approximation of the Jacobian pseudo inverse by the extended Jacobian algorithm. The algorithms are defined as certain dynamic systems driven by the task space error, and identified with vector field distributions. The distribution corresponding to the Jacobian pseudo inverse is non-integrable, while that associated with the extended Jacobian is integrable. Two methods of devising the approximating extended Jacobian algorithm are examined. The first method is referred to as differential geometric, and relies on the approximation of a non-integrable distribution (in fact: a codistribution) by an integrable one. As an alternative, the approximation problem has been formulated as the minimization of an approximation error functional, and solved using the methods of the calculus of variations. Performance of the obtained extended Jacobian inverse kinematics algorithms has been compared by means of computer simulations involving the kinematics model of the 7 dof industrial manipulator POLYCRANK. It is concluded that the differential geometric method offers a rapid, while the variational method a systematic tool for solving inverse kinematic problems.     

Optimal Extended Jacobian Inverse Kinematics Algorithms for Robotic Manipulators

Extended Jacobian inverse kinematics algorithms for redundant robotic manipulators are defined by combining the manipulator's kinematics with an augmenting kinematics map in such a way that the combination becomes a local diffeomorphism of the augmented taskspace. A specific choice of the augmentation relies on the optimal approximation by the extended Jacobian of the Jacobian pseudoinverse (the Moore--Penrose inverse of the Jacobian). In this paper, we propose a novel formulation of the approximation problem, rooted conceptually in the Riemannian geometry. The resulting optimality conditions assume the form of a Poisson equation involving the Laplace--Beltrami operator. Two computational examples illustrate the theory.      

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.     

Forward kinematics,performance analysis,and multi-objective optimization of a bio-inspired parallel manipulator

In this paper, a bio-inspired parallel manipulator with one translation along z-axis and two rotations along x- and y- axes is developed as the hybrid head mechanism of a groundhog robotic system. Several important issues including forward kinematic modeling, performance mapping, and multi-objective improvement are investigated with specific methods or technologies. Accordingly, the forward kinematics is addressed based on the integration of radial basis function network and inverse kinematics. A novel performance index called dexterous stiffness is defined, derived and mapped. The multi-objective optimization with particle swarm algorithm is conducted to search for the optimal dexterous stiffness and reachable workspace.     

Adaptive end-effector pose control for tomato harvesting robots

This paper investigates the development of a tomato-harvesting robot operating on a plant factory and primarily studies the reachable pose of tomatoes in the nondexterous workspace of manipulator. The end-effector can only reach the tomatoes with reachable poses when the tomatoes are within the nondexterous workspace. If the grasping pose is not reachable, it will lead to grasping failure. An adaptive end-effector pose control method based on a genetic algorithm (GA) is proposed to find a reachable pose. The inverse kinematic solution based on analysis method of the manipulator is analyzed and the objective function of whether the manipulator has a solution or not is obtained. The grasping pose is set as an individual owing to the position of the tomatoes is fixed and the grasping pose is variable. The GA is used to solve until a pose that can make the inverse kinematics have a solution is generated. This pose is the reachable grasping pose of the tomato at this position. The quintic interpolation polynomial is used to plan the trajectory to avoid damage to tomatoes owing to fast approaching speed and a distance based background filtering method is proposed. Experiments were performed to verify the effectiveness of the proposed method. The radius of the workspace of the UR3e manipulator with the end-effector increased from 550 to 800 mm and the grasping range expanded by 208%. The harvesting success rate using the adaptive end-effector pose control method and trajectory planning method was 88%. The cycle of harvesting a tomato was 20 s. The experimental results indicated that the proposed tomato-recognition and end-effector pose control method are feasible and effective.     

基于改进天牛须算法的电力攀爬机器人运动学逆解算法

为了提高电力系统的自动化水平,减轻电力工人在检修高压输电系统时的劳动强度,同时保障电力工人人身安全,提出并设计一种可以攀爬电力铁塔的六自由度关节式机器人,针对该构型进行运动学分析和求解.为解决传统的解析法用于机械臂逆运动学求解过程中存在操作繁琐和奇异点无法逆运算等问题,提出一种基于改进天牛须算法的电力攀爬机器人运动学逆解算法.首先,对电力攀爬机器人进行DH建模,得到正运动学方程;然后,使用正运动学方程和目标位姿建立代价函数,采用改进天牛须算法对代价函数优化;最后,使用Matlab实现此算法进行仿真验证.实验结果表明,与传统的天牛须算法、改进遗传算法以及改进粒子群算法相比,所提出算法具有较好的收敛性,求解精度较高.     

Inverse kinematics and planning/control co-design method of redundant manipulator for precision operation: Design and experiments

In this paper, we proposed two novel algorithms to improve the operating accuracy and operating efficiency of the 7-DoF redundant manipulator. Firstly, an improved adaptive particle swarm optimization (APSO) algorithm is proposed to improve the solution precision and solution speed of the inverse kinematics of the 7-DoF redundant manipulator by introducing the probability transfer mechanism and the quality evaluation criterion. Meanwhile, the velocity directional manipulability measure (VDM) is introduced as an optimization index to search for the singular-free configuration with the optimal motion performance. Then, in order to further improve the execution efficiency and stability of the 7-DoF redundant manipulator, a novel planning/control co-design (PCC) algorithm is proposed based on the Dynamic Movement Primitives (DMPs-PCC), which ensures that the motion planner and actuator of the 7-DoF redundant manipulator can work synchronously, while optimizing the velocity and acceleration profiles of each joint of the manipulator in the operating process. Finally, an experimental platform is established based on the Robot Operating System (ROS), and the effectiveness and reliability of the two novel algorithms are demonstrated by the simulations and prototype experiments.     

Dynamic formulation of a planar 3-DOF parallel manipulator with actuation redundancy

In this paper, based on the conventional Newton–Euler approach, a simplification method is proposed to derive the dynamic formulation of a planar 3-DOF parallel manipulator with actuation redundancy. Closed-form solutions are developed for the inverse kinematics. Based on the kinematics, the Newton–Euler approach in simplification form is used to derive the inverse dynamic model of the redundant parallel manipulator. Then, the driving force optimization is performed by minimizing an objective function which is the square of the sum of four driving forces. The dynamic simulations are done for the parallel manipulator with both the redundant and non-redundant actuations. The result shows that the dynamic characteristics of the manipulator in the redundant case are better than that in the non-redundancy. The redundantly actuated parallel manipulator was incorporated into a 4-DOF hybrid machine tool which includes a feed worktable.     

Kinematics analysis of a hybrid manipulator for computer controlled ultra-precision freeform polishing

As one of the final processing steps of precision machining, polishing process is a very key decision for surface quality. This paper presents a novel hybrid manipulator for computer controlled ultra-precision (CCUP) freeform polishing. The hybrid manipulator is composed of a three degree-of-freedom (DOF) parallel module, a two DOF serial module and a turntable providing a redundant DOF. The parallel module gives the workpiece three translations without rotations. The serial module holds the polishing tool and gives it no translations on the polishing contact area due to its particular mechanical design. A detailed kinematics model is established for analyzing the kinematics of the parallel module and the serial module, respectively. For the parallel module, the inverse kinematics, the forward kinematics, the Jacobian matrix, the workspace and the dexterity distribution are analyzed systematically. Workspaces are also investigated for varying structural parameters. For the serial module, the inverse kinematics, the forward kinematics, the workspace and the precession motion analysis are carried out. An example of saddle surface finishing with this manipulator is given and the movement of actuators with respect to this shape is analyzed theoretically. These analysis results illustrate that the proposed hybrid manipulator is a very suitable machine structure for CCUP freeform polishing.