Calibration of a hexapod machine tool using a redundant leg

Parallel configurations are recently being applied to the machine tool with the hopes of greater rigidity, stability, and accuracy than conventional multi-axis structures allow. However, the many calibration methods presently available for serial machine tools are not applicable to hexapod type structures. A calibration method is presented that uses a ball–bar or other simple length measuring device to act as an ‘extra leg,’ allowing calibration of the hexapod's true kinematic parameters. This method utilizes a total least squares minimization, does not require any special hexapod configuration or difficult six degree of freedom pose measurements, and is effective with as few as one additional length sensor. Selection of calibration pose sets is briefly discussed, as well as the influence of measurement noise on calibration accuracy. Simulations show the potential for this algorithm to significantly reduce errors to the point where machining errors are within 5–10 times the measurement errors.     

Geometrical tolerances: Improved linear approximation of least squares evaluation of circularity by minimum variance

We present a new computational algorithm for the least squares evaluation of circularity of a two-dimensional (2D) circle in coordinate metrology. This algorithm takes a good geometrical approximation of the orthogonal Euclidean distance in measuring the deviational errors of sample data so that the assessment criterion of normal least squares is faithfully implemented. This algorithm provides the solution of best-fit circle in two steps; first the circle center coordinates are obtained by an eigenvalue analysis to minimize the total variance of deviational error; and then the circle radius is determined so as to minimize the mean of deviational errors. Several measurement examples are discussed to verify the robustness and goodness of the algorithm, and as a result it is concluded that the new algorithm provides improved performances as compared to existing relevant least squares algorithms.     

A total solution to kinematic calibration of hexapod machine tools with a minimum number of measurement configurations and superior accuracies

A total solution to the kinematic calibration should encompass various procedures consisting of error modeling, measurement, identification of kinematic parameters and compensation for the errors. A viable solution should further entail a feasible number of measurement configurations while yielding accuracies acceptable to machine tool industries. The existing solutions suffer deficiencies especially with respect to the totality, viability and acceptable accuracies. In an attempt to remedy these deficiencies, the authors of this paper have proposed an optimized method encompassing the whole kinematic calibration procedures. This method has been verified by simulation and experiments and could give considerably superior results compared with the existing achievements. By employing only eleven measurement configurations, the maximum position and orientation errors of the upper platform in the experiments amounted to 0.1 mm and 0.03°, respectively. Much better results have been obtained by simulation, which implies that the accuracies can still further improve if some uncertainties such as backlash and other manufacturing errors usually existing in a laboratory device diminish in its industrial counterpart. In the proposed model, the hexapod workspace was first investigated to find general guidelines for maximum observability. The results were subsequently used in the main identification module. The required number of optimized configurations to achieve acceptable accuracies could thus considerably decrease to a feasible limit. A simple and accurate image processing method has been employed for the spatial measurement of the position and orientation of the moving platform. The identification jacobian matrix was used to evaluate the observability of the measurement configurations and determine optimum number of configurations for minimum identification error. Singular value decomposition and observability indices were used for this purpose. The real values of the kinematic parameters were identified by minimization of a cost function based on Levenberg-Marquardt least-square algorithm. In order to provide clues as to optimally directing the expensive manufacturing time and resources, a comparative study has also been carried out on the degree of influence each kinematic parameter exerts on the final accuracy.     

基于RBF-BP算法的工业机械臂轨迹控制与跟踪

针对现有机械臂轨迹控制补偿算法偏差大、效率低的不足,提出一种基于RBF-BP的机械臂行进轨迹控制与跟踪算法研究.从机械臂各轴向的空间移动、角度旋转等6个自由度出发建模,描述机械臂末端的位置移动和姿态变化,并计算向量的移动距离和偏转角度;面对机械臂系统误差和摩擦扰动导致的轨迹偏差问题,利用RBF-BP算法局部逼近最优控制...     

深度Q-RBF网络下的瓶装食品装箱机械臂无碰轨迹规划

由于机械臂存在高度的灵活性，可模拟人类手臂完成易碎瓶装食品的装箱工作，并实时矫正机械臂轨迹规划所存在的误差，提升稳定性与精准度。分析装箱机械臂的基本架构，提出基于深度Q-RBF强化学习网络的机械臂无碰轨迹规划模型，通过资源分配自适应方法，根据待建模的样本，调整RBF网络隐含层单元，从而提升网络学习速率与在线学习能力，结合自适应Q强化学习算法，获得最优操作集合。并选用学习率调参法完成网络的参数学习。仿真与实验结果表明：与其他两种方法对比，此方法具有较强的避障能力，机械臂能够较好地依据预定轨迹行进；避碰进程变化缓和，且能够尽快收敛并逐步趋向稳定。     

UKF算法在七自由度机械臂逆运动学求解的应用北大核心

针对七自由度冗余度机械臂逆运动学求解问题,提出一种求解逆运动学的新方法。采用闭环模型建模的多维序列处理方法,将无迹卡尔曼滤波算法作为递推算法对机械臂实时状态进行估计,输入向量由前向模型的输入序列和反馈模型中的测量输出序列组成,建立具有闭环框架的七自由度冗余机械手逆运动学的状态空间模型,降低了计算的复杂度。与传统雅可比矩阵的伪逆计算方法对比分析,结果表明:所提方法具有较高的位置误差精度和计算效率,在末端执行器的轨迹中加入噪声,显示所提方法具有较好的收敛性能,通过实验表明该方法具有一定的通用性和可靠性。     

An improved genetic algorithm for planar and spatial straightness error evaluation

The measurement data obtained from the Coordinate Measuring Machines (CMMs) have to be further processed and analyzed to evaluate the form errors of manufactured components. An improved genetic algorithm (GA) is proposed to implement the minimum zone evaluation of planar and spatial straightness errors simultaneously. The algorithm employs the generation alternation model based Minimal Generation Gap (MGP) and blend crossover operators (BLX-α). Compared to traditional GAs, it is efficient and robust. Then, the objective function calculation approaches of planar and spatial straightness error are developed, which directly originate from the definition of minimum zone solution and conform to the ISO standard. Finally, the experimental results evaluated by different methods confirm the effectiveness of the proposed GA. Compared to conventional evaluation methods; it has the advantages of algorithm simplicity and good flexibility. Also it is a unified approach for other form error evaluations and is well suited for the form error evaluation on CMMs.     

基于改进粒子群算法的六自由度机械臂时间最优轨迹规划

针对六自由度机械臂时间最优轨迹规划问题,提出一种基于改进粒子群算法的4-3-4混合多项式插值轨迹规划算法。算法采用自适应惯性权重,它能根据搜索过程的各个阶段采用相应大小的权重,有利于跳出局部最优陷阱,保持粒子群多样性;以非线性学习因子代替传统粒子群算法中固定的学习因子,有效提高算法的收敛速度和求解精度。通过MATLAB进行仿真验证,结果表明改进粒子群算法收敛速度提高46%,寻优精度提高38%,同时机械臂轨迹规划时间缩短了大约36%,充分地证明了该轨迹规划算法的可靠性和优越性。     

基于改进人工蜂群算法的冗余机器臂逆解研究

针对具有移动关节的7自由度机械臂逆运动学求解困难的问题,提出了一种基于改进人工蜂群算法的逆运动学求解方法。首先根据冗余机械臂的物理结构简化出几何模型,利用D-H法建立运动学模型,由坐标系变换得到正运动学的解。由于该冗余机械臂不满足Pieper准则,难以用传统方法求得封闭解;因此采用改进人工蜂群智能算法,利用位置误差与姿态误差的标准差作为目标函数,求取逆运动学的最优解,并利用Matlab编程进行仿真验证,仿真结果表明该方法准确有效,为具有移动关节的冗余机械臂逆运动学的求解提供了一种新的途径。     

基于烟花灰狼算法的冗余机械臂运动学逆解

针对常规方法无法有效求解冗余机械臂逆运动学解问题，提出改进灰狼算法的机械臂逆运动学求解方法，采用一般反向学习初始化与烟花算法爆炸机制相结合，使得算法具有较强的抗干扰与全局求解性，有效避免早熟、局部最优问题。采用10种经典测试函数对改进灰狼算法进行性能测试，测试结果证明改进灰狼具有收敛精度高、抗干扰能力强等特点。以凿岩机器人的七自由度机械臂逆运动学求解为例，采用MDH法建立运动学模型，运用改进灰狼算法求解并与粒子群、模拟退火、传统灰狼算法进行对比，仿真结果表明：该算法性能优于其他算法，能对冗余机械臂逆运动学进行有效求解。     

An effective genetic algorithm for circularity error unified evaluation

There are four methods commonly used to evaluate the circularity error. They are: minimum zone circle (MZC) method, minimum circumscribed circle (MCC) method, maximum inscribed circle (MIC) method and least square circle (LSC) method. However, so far there is no a robust and effective approach to implement a unified evaluation of these four methods. In this paper, an effective genetic algorithm is presented for searching the above four circularity error evaluation methods simultaneously. The algorithm is implemented in real-code and only blend crossover operators are applied to two randomly selected individuals from the existing population. The algorithm does not require genetic parameters such as crossover and mutation probabilities to be set in advance as does a canonical GA; therefore it is very convenient to use in engineering metrology. The objective function calculation approaches of four circularity errors are developed and the initial population generation methods are given in order to save optimization time. Finally, the experimental results evaluated by different methods confirm that the proposed method can find the optimal solutions of these four methods. In comparison with existing evaluation methods, the algorithm is not only simple and robust, but also it unifies these four kinds of circularity evaluation. The algorithm can also be used for solving difficult form error minimization and profile evaluation problems of various geometric parts in engineering metrology.     

Application of self-tuning fuzzy controller for a Cartesian manipulator on unknown contours

Owing to the relative difficulty in achieving contour tracking on 3D objects, this study presents a novel compliant motion controller by applying the self-tuning fuzzy control to have a Cartesian manipulator implement contour tracking on unknown contours. A data fitting method is also developed to reduce the noise errors of the measurement. Moreover, the radius compensating method is used to correct the measured data. The Cartesian manipulator is tested and calibrated beforehand. Results in this study demonstrate the feasibility of the control strategy proposed herein.     

A systematic optimization approach for the calibration of parallel kinematics machine tools by a laser tracker

Parallel kinematics machine has attracted attention as machine tools because of the outstanding features of high dynamics and high stiffness. Although various calibration methods for parallel kinematics machine have been studied, the influence of inaccurate motion of joints is rarely considered in these studies. This paper presents a high-accuracy and high-effective approach for calibration of parallel kinematics machine. In the approach, a differential error model, an optimized model and a statistical method are combined, and the errors of parallel kinematics machine due to inaccurate motion of joints can be reduced by this approach. Specifically, the workspace is symmetrically divided into four subspaces, and a measurement method is suggested by a laser tracker to require the actual pose of the platform in these subspaces. An optimized model is proposed to solve the kinematic parameters in symmetrical subspaces, and then arithmetical mean method is proposed to calculate the final kinematic parameter. In order to achieve the global optimum quickly and precisely, the initial value of the optimal parameter is directly solved based on the differential error model. The proposed approach has been realized on the developed 5-DOF hexapod machine tool, and the experiment result proves that the presented method is very effective and accurate for the calibration of the hexapod machine tool.     

A unified least-squares approach to the evaluation of geometric errors using discrete measurement data

This paper presents a unified least-squares approach to the best fit of geometric features and evaluation of dimensional errors. The study originated from the need for advanced algorithms for the dimensional measurement of high precision manufactured parts. The proposed algorithm differs from traditional least-squares in that no linearization or approximation is employed and that it is general to all kinds of geometric features. Instead of computing a substitute best fit feature, the algorithm inversely transforms the measurement coordinates to best fit the nominal geometry. The sum of the squared errors in the surface normal direction is thus minimized with respect to the parameters of a rigid body transformation. Form tolerances are then evaluated using the peak-to-valley deviations after the best fit. To examine the uncertainty of the transformation obtained, sensitivity analysis was investigated to relate transformation errors to dimensional errors. A sensitivity measure is used to estimate the joint effect of the measurement locations and the number of measurement data on the accuracy of the coordinate transformation. Computer simulations have been performed on different geometric features to study the robustness and efficiency of the algorithm. Application to the measurement of high precision fuel injectors is also presented.     

采用混合算法优化的3?P RRR并联冗余机械手驱动力矩研究

为了降低平面3-PRRR并联冗余机械手驱动力矩,提高机械手运动平台运动的稳定性,采用混合算法优化机械手运动参数,并对驱动力矩进行仿真验证。针对传统非冗余机械手驱动系统进行改进,给出了平面3-PRRR并联冗余机械手简图,设计了冗余机械手驱动系统,采用雅克比矩阵对冗余机械手运动平台运动轨迹进行转换,推导出冗余机械手3个分支闭环运动轨迹方程式。引用粒子群算法并进行改进,添加了遗传算法中交叉和变异操作,设计出了混合粒子群算法。采用混合算法优化冗余机械手运动参数,通过MATLAB软件对冗余机械手3个分支驱动力矩变化进行仿真,与优化前进行对比。结果显示:优化前,平面3-PRRR并联冗余机械手驱动力矩较大,整体波动幅度较大;优化后,平面3-PRRR并联冗余机械手驱动力矩较小,整体波动幅度较小。采用混合算法优化平面3-PRRR并联冗余机械手运动参数,可以降低机械手驱动力矩,减少冗余机械手运动系统能量消耗。     

On the suitability of induction coils for crack detection and sizing in metals by the surface magnetic field measurement technique

The surface magnetic field measurement (SMFM) technique has proved to be an accurate means for crack detection and sizing cracks in ferrous metals. The technique involves the use of two U-shaped current-carrying wires of sufficiently high frequency while measuring the discontinuity in the resultant magnetic field at the crack edge with an appropriate magnetic field sensor. In this work, we describe a mathematical algorithm to obtain the crack signal from the output of an induction coil used in a SMFM probe. We also discuss the measurement errors due to the coil size and shape. To reduce the measurement errors, we present an algorithm in which the crack signal is recovered by appropriate deconvolution of the coil output signal and its spatial transfer function. The algorithm is then used to recover crack signals for various coil shapes and sizes. The study of the results demonstrates the effectiveness of the algorithm in the case of large coils.     

一种基于混合神经网络的机械手移动轨迹自动控制技术研究

针对现有机械手移动偏差控制技术存在的轨迹控制不连续、复杂度高、综合效率低等问题,以机器学习和深度学习为基础提出一种混合神经网络控制算法。分析机械手各关节、连杆的空间坐标转换关系,以RBF为基础构建混合神经网络模型,选用逆多二次函数作为模型的激活函数,分别确定中间隐层和输出层的权值;引入LSTM长短记忆算法,利用LSTM算法的输入门、遗忘门和输出门结构设计,抑制坐标数据训练时出现的梯度膨胀问题,并给出精确的轨迹修正指令。仿真结果表明：提出的混合神经网络算法采样点轨迹偏差均值为0.02 mm,VARP值趋近于0,具有更好的自动控制稳定性和更高的控制效率。     

基于优化位姿控制的并联液压机械手跟踪控制研究

针对二自由度并联液压机械手控制系统容易受到外界干扰问题,对机械手控制系统输出误差进行研究。结合机械手平面简图分析了并联液压机械手工作原理,推导出机械手运动学和动力学方程式。引用模糊PID控制系统,采用差分进化算法和前馈补偿方法对模糊PID控制系统进行优化,将优化后的控制系统通过MATLAB软件进行误差仿真,同时与模糊PID控制系统输出误差进行比较和分析。仿真误差显示：在无干扰环境中,优化前和优化后的二自由度并联液压机械手模糊PID控制系统,其运动位移和角位移输出误差差别不大,跟踪效果较好。在有干扰环境中,优化前二自由度并联液压机械手模糊PID控制系统,运动位移和角位移输出误差较大,而优化后二自由度并联液压机械手模糊PID控制系统,其运动位移和角位移输出误差较小。采用差分进化算法和前馈补偿控制方法,能够抑制外界信号波的干扰,提高二自由度并联液压机械手的跟踪精度,其控制效果较好     

Actively Searching for an Effective Neural Network Ensemble

A neural network NN ensemble is a very successful technique where the outputs of a set of separately trained NNs are combined to form one unified prediction. An effective ensemble should consist of a set of networks that are not only highly correct, but ones that make their errors on different parts of the input space as well; however, most existing techniques only indirectly address the problem of creating such a set. We present an algorithm called ADDEMUP that uses genetic algorithms to search explicitly for a highly diverse set of accurate trained networks. ADDEMUP works by first creating an initial population, then uses genetic operators to create new networks continually, keeping the set of networks that are highly accurate while disagreeing with each other as much as possible. Experiments on four real-world domains show that ADDEMUP is able to generate a set of trained networks that is more accurate than several existing ensemble approaches. Experiments also show ADDEMUP is able to incorporate prior knowledge effectively, if available, to improve the quality of its ensemble.     

Selection of an optimum sample size for flatness error estimation while using coordinate measuring machine

In the present day manufacturing environments it is becoming increasingly important to be able to deliver quality products at the right time to the market at competitive costs. The quality, cost and time to market depend not only on the design and manufacturing but also on the inspection process adopted. Design specifications rely on extensive usage of form tolerances to ensure that the functionality of surfaces and features of the product are maximized. The use of the coordinate measuring machines (CMM) has greatly improved the efficacy of form tolerance measurement and is also used as the key device in this work. The focus of this work is to deal with the method and strategies for measurement of flatness error so as to be able to predict the flatness error accurately at reduced sample sizes in batch and mass production setups. Accurate evaluation of flatness will require large sample sizes which increase the cost and time of inspection and hence a need to reduce the sample sizes without compromising on the accuracy. In the absence of robust models that can predict the errors due to manufacturing processes, an alternative technique has been devised to arrive at a reduced sample size. The procedure involves using large sample data inspected on the first component as the basis for evolving smaller sample sizes for subsequent components.Experimental verification of the developed algorithm shows that flatness error can be predicted with sufficient accuracy at small sample sizes.