Exact solution to the inverse kinematics problem of a standard 6-axis robot manipulator

Presented are four sets of exact solutions for the vector of the joint angles {θ_i} pertaining to the inverse kinematics problem of a standard 6-axis robot manipulator with two different kinds of gripper configurations. Here a standard 6-axis robot is meant to be a general computer-controlled revolute robot with base, shoulder, elbow, wrist pitch, wrist yaw, wrist roll, and gripping action. Explicit solutions are obtained using Denavit-Hartenberg homogeneous transformations. Furthermore, the inverse solutions are examined by means of a direct kinematic computer program.     

基于遗传算法的机械臂逆运动学问题解决方案

提出应用遗传算法求解机械臂的逆运动学问题,将种群定义于机械臂的关节角轨迹层面,利用连续性函数实现算法的初始化算子,交叉算子和变异算子。算法仅使用表现型数据表示方式,克服了传统遗传算法在数据的基因型和表现型之间频繁地进行编码和解码操作。通过和传统遗传算法进行对比分析,验证了所提出的方法能够避免传统遗传算法求解逆运动学问题时存在的多重切换点现象,能够获得更平滑的关节角轨迹,缩短了算法的收敛时间,生成的笛卡尔轨迹具有更高的精度。     

基于牛顿-拉夫逊迭代法的6自由度机器人逆解算法

为解决一般6自由度旋转关节机器人逆运动学问题,提出了一种用牛顿一拉夫逊迭代法逐次逼近目标位姿的逆解算法.根据正运动学方程建立雅克比矩阵,采用基于豪斯霍尔德的SVD分解求其伪逆来避免雅克比矩阵的奇异性问题,通过建立迭代规则并逐次迭代找到最优的逆运动学单解,实际应用时无需再建立多解取优策略.本算法具有较好的局部快速收敛性,能够达到较好的精度和速度,并在基于ARM9的嵌人式系统上实现了此算法.相应的测试表明:算法实时性能够满足系统要求,可应用于机器人实时控制系统.     

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.     

Comparison of four different heuristic optimization algorithms for the inverse kinematics solution of a real 4-DOF serial robot manipulator

In this study, a 4-degree-of-freedom (DOF) serial robot manipulator was designed and developed for the pick-and-place operation of a flexible manufacturing system. The solution of the inverse kinematics equation, one of the most important parts of the control process of the manipulator, was obtained by using four different optimization algorithms: the genetic algorithm (GA), the particle swarm optimization (PSO) algorithm, the quantum particle swarm optimization (QPSO) algorithm and the gravitational search algorithm (GSA). These algorithms were tested with two different scenarios for the motion of the manipulator’s end-effector. One hundred randomly selected workspace points were defined for the first scenario, while a spline trajectory, also composed of one hundred workspace points, was used for the second. The optimization algorithms were used for solving of the inverse kinematics of the manipulator in order to successfully move the end-effector to these workspace points. The four algorithms were compared according to the execution time, the end-effector position error and the required number of generations. The results showed that the QPSO could be effectively used for the inverse kinematics solution of the developed manipulator.     

An analysis of the inverse kinematics for a 5-DOF manipulator

This paper proposes an analytical solution for a 5-DOF manipulator to follow a given trajectory while keeping the orientation of one axis in the end-effector frame. The forward kinematics and inverse kinematics for a 5-DOF manipulator are analyzed systemically. The singular problem is discussed after the forward kinematics is provided. For any given reachable position and orientation of the end-effector, the derived inverse kinematics will provide an accurate solution. In other words, there exists no singular problem for the 5-DOF manipulator, which has wide application areas such as welding, spraying, and painting. Experiment results verify the effectiveness of the methods developed in this paper.     

Optimum design of a three-dimensional serial robot manipulator

A systematic and mathematical optimization methodology is presented for the optimal design of a three link, revolute joint, three-dimensional manipulator which must perform specific prescribed tasks. The objective of interest is the minimization of average torque requirement. In particular circular and eccentric closed task paths are considered. The optimization is carried out with the link lengths and the positional coordinates of the base taken as the five design variables, and subject to assembly and geometric constraints imposed on the system. In particular restrictions are placed on the joint angle between the links and on the link lengths. The minimization is successfully performed by the application of Snymans robust dynamic trajectory method for unconstrained optimization, to a penalty function formulation of the constrained problem.     

An experiment in approximating an end effector positional error of a 6 D.O.F manipulator using neural network

In this paper, a BP network is developed to approximate an error vector in the joint displacement of a 6 D.O.F. Stanford manipulator. This error results from several causes such as physical damage to the robot structure or inherited inaccuracies in the robot design. Results show that using neural networks is a robust and efficient solution.     

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.     

An entropy-based algorithm to solve the facility layout design problem

This paper presents a new design approach used in order to solve the facility layout problem. The layout problem is viewed from the general perspective as a problem of the arrangement of elements within a system. The main attributes and relationships among the elements of the system are analyzed.     

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.     

机械臂逆运动学模型控制新方法

根据机械臂关节轴线方向建立了连杆坐标系,采用Denavit-Hartenberg（D-H）法得到连杆坐标系变换矩阵,通过坐标系变换矩阵得到机械臂正运动学模型,由正运动模型得到机械臂逆运动学模型。该模型是一个非线性约束优化问题。为了求解模型,基于多种群和多变异策略,提出了多变异策略的多种群差分演化算法。多种群策略可以提升个体共享群体信息的能力,多变异模式策略可以提升个体间的差异性,数值试验表明新算法可以有效求解机械臂逆运动学模型。     

An analytical C3 continuous tool path corner smoothing algorithm for 6R robot manipulator

Tool path smoothness is important to guarantee good dynamic and tracking performance of robot manipulators. An analytical C³ continuous tool path corner smoothing algorithm is proposed for robot manipulators with 6 rotational (6R) joints. The tool tip position is smoothed directly in the workpiece coordinate system (WCS). The tool orientation is smoothed after transferring the tool orientation matrix as three rotary angles. Micro-splines of the tool tip position and tool orientation are constructed under the constraints of the maximum deviation error tolerances in the WCS. Then the tool orientation and tool tip position are synchronized to the tool tip displacement with C³ continuity by replacing the remaining linear segments using specially constructed B-splines. Control points of the locally inserted micro-splines are all evaluated analytically without any iterative calculations. Simulation and experimental results show that the proposed algorithm satisfies constraints of the preset tool tip position and the tool orientation tolerances. The proposed corner smoothing algorithm achieves smoother and lower jerks than C² continuous corner smoothing algorithm. Experimental results show that the tracking errors associated to the execution of the C³ continuous tool path are up to 10% smaller than C² continuous path errors.     

An efficient algorithm to solve the small sample size problem for LDA

In this paper, we present an efficient algorithm to solve the most discriminant vectors of LDA for high-dimensional data set. The experiments on ORL face database confirm the effectiveness of the proposed method.     

An evolutionary algorithm to solve the joint replenishment problem using direct grouping

There has been much work in establishing a joint replenishment policy to minimize the total cost of inventory replenishment. Most of this work uses the indirect grouping method. Little research has been done with direct grouping methods. In this paper we develop an evolutionary algorithm (EA) that uses direct grouping to solve the joint replenishment problem (JRP). We test the EA and compare these results with results with the best available algorithm. The EA is shown to find a replenishment policy that incurs a lower total cost than the best available algorithm for some problem parameters.     

6R关节型机器人运动学建模

为满足新开发的多机器人实验系统编程需要,研究了6R机器人运动学逆解问题.推导了代数逆解结果,并研究了将其用于实际控制系统时,逆解的漏解、增根和多解问题.与传统方法比较,采用了便于程序模块化的坐标系设置方式,在需要经常更换作业工具的多机器人系统中更为适用.推导过程只需2次矩阵逆乘,步骤简单.基于VC++和OpenGL技术编制了系统程序,检验了方法的有效性.以其中一个位姿为例,对比几何方法得出的结果,验证了算法的正确性.研究的结果适用于MOTOMAN-UP6和PUMA560等相似构型的所有机器人.     

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.     

全局和声搜索方法及其在仿人灵巧臂逆运动学求解中的应用

仿人灵巧臂逆运动学(IK)问题可转化为等效的最小化问题,并采用数值优化方法求解.和声搜索(HS)是模拟乐师在音乐演奏中调整音调现象的一种启发式搜索方法,目前还尚未在机器人机械臂逆运动学问题中得到应用.本文提出一种基于粒子群体智能的全局和声搜索方法(GHSA),该方法在和声搜索算法中引入微粒群操作(PSO),采用粒子群策略替代常规和声搜索算法中的搜索法则创作新和声,通过粒子自身认知和群体知识更新和声变量位置信息平衡算法对解空间全局探索与局部开发间能力;同时算法还引入变异操作增强算法跳出局部最优解能力,基准函数测试表明该方法改善了全局搜索能力及求解可靠性.在此基础上以七自由度(7-DOF)冗余仿人灵巧臂为例,考虑以灵巧臂末端位姿误差和“舒适度”指标构建适应度函数并采用GHSA算法求解其逆运动学(IK)问题,数值仿真结果表明了该方法是解决仿人灵巧臂逆运动学问题的一种有效方法.     

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.