Separation of Comprehensive Geometrical Errors of a 3-DOF Parallel Manipulator Based on Jacobian Matrix and Its Sensitivity Analysis with Monte-Carlo Method

Parallel kinematic machines (PKMs) have the advantages of a compact structure,high stiffness,a low moving inertia,and a high load/weight ratio.PKMs have been intensively studied since the 1980s,and are still attracting much attention.Compared with extensive researches focus on their type/dimensional synthesis,kinematic/dynamic analyses,the error modeling and separation issues in PKMs are not studied adequately,which is one of the most important obstacles in its commercial applications widely.Taking a 3-PRS parallel manipulator as an example,this paper presents a separation method of source errors for 3-DOF parallel manipulator into the compensable and non-compensable errors effectively.The kinematic analysis of 3-PRS parallel manipulator leads to its six-dimension Jacobian matrix,which can be mapped into the Jacobian matrix of actuations and constraints,and then the compensable and non-compensable errors can be separated accordingly.The compensable errors can be compensated by the kinematic calibration,while the non-compensable errors may be adjusted by the manufacturing and assembling process.Followed by the influence of the latter,i.e.,the non-compensable errors,on the pose error of the moving platform through the sensitivity analysis with the aid of the Monte-Carlo method,meanwhile,the configurations of the manipulator are sought as the pose errors of the moving platform approaching their maximum.The compensable and non-compensable errors in limited-DOF parallel manipulators can be separated effectively by means of the Jacobian matrix of actuations and constraints,providing designers with an informative guideline to taking proper measures for enhancing the pose accuracy via component tolerancing and/or kinematic calibration,which can lay the foundation for the error distinguishment and compensation.     

Motion error compensation of multi-legged walking robots

Existing errors in the structure and kinematic parameters of multi-legged walking robots,the motion trajectory of robot will diverge from the ideal sports requirements in movement.Since the existing error compensation is usually used for control compensation of manipulator arm,the error compensation of multi-legged robots has seldom been explored.In order to reduce the kinematic error of robots,a motion error compensation method based on the feedforward for multi-legged mobile robots is proposed to improve motion precision of a mobile robot.The locus error of a robot body is measured,when robot moves along a given track.Error of driven joint variables is obtained by error calculation model in terms of the locus error of robot body.Error value is used to compensate driven joint variables and modify control model of robot,which can drive the robots following control model modified.The model of the relation between robot’s locus errors and kinematic variables errors is set up to achieve the kinematic error compensation.On the basis of the inverse kinematics of a multi-legged walking robot,the relation between error of the motion trajectory and driven joint variables of robots is discussed.Moreover,the equation set is obtained,which expresses relation among error of driven joint variables,structure parameters and error of robot’s locus.Take MiniQuad as an example,when the robot MiniQuad moves following beeline tread,motion error compensation is studied.The actual locus errors of the robot body are measured before and after compensation in the test.According to the test,variations of the actual coordinate value of the robot centroid in x-direction and z-direction are reduced more than one time.The kinematic errors of robot body are reduced effectively by the use of the motion error compensation method based on the feedforward.     

Dynamics and Wheel’s Slip Ratio of a Wheel-legged Robot in Wheeled Motion Considering the Change of Height

The existing research on dynamics and slip ratio of wheeled mobile robot (WMR) are derived without considering the effect of height, and the existing models can not be used to analyze the dynamics performance of the robot with variable height while moving such as NOROS-Ⅱ. The existing method of dynamics modeling is improved by adding the constraint equation between perpendicular displacement of body and horizontal displacement of wheel into the constraint conditions. The dynamic model of NOROS-Ⅱ in wheel motion is built by the Lagrange method under nonholonomic constraints. The inverse dynamics is calculated in three different paths based on this model, and the results demonstrate that torques of hip pitching joints are inversely proportional to the height of robot. The relative error of calculated torques is less than 2% compared with that of ADAMS simulation, by which the validity of dynamic model is verified. Moreover, the relative horizontal motion between fore?hind wheels and body is produced when the height is changed, and thus the accurate slip ratio can not be obtained by the traditional equation. The improved slip ratio equations with the parameter of the vertical velocity of body are introduced for fore wheels and hind wheels respectively. Numerical simulations of slip ratios are conducted to reveal the effect of varied height on slip ratios of different wheels. The result shows that the slip ratios of fore?hind wheels become larger?smaller respectively as the height increases, and as the height is reduced, the reverse applies. The proposed research of dynamic model and slip ratio based on the robot height provides the effective method to analyze the dynamics of WMRs with varying height.     

NOVEL METHOD FOR ERROR ANALYSIS AND SELF-CALIBRATION OF LASER TRACKING MIRROR MECHANISM

Laser tracking system （LTS） is an advanced device for large size 3D coordinates measuring with the advantages of broad range, high speed and high accuracy. However, its measuring accuracy is highly dominated by the geometric errors of the tracking mirror mechanism. Proper calibration of LTS is essential prior to the use of it for metrology. A kinematics model that describes not only the motion but also the geometric variations of LTS is developed. Through error analysis of the proposed model, it is claimed that gimbals axis misalignments and tracking mirror center off-set are the key contributors to measuring errors of LTS. A self-calibration method is presented of calibrating LTS with planar constraints. Various calibration strategies utilizing single-plane and multiple-plane constraints are proposed for different situations. For each calibration strategy, issues about the error parameter estimation of LTS are exploded to find out in which conditions these parameters can be uniquely estimated. Moreover, these conditions reveal the applicability of the planar constraints to LTS self-calibration. Intensive studies have been made to check validity of the theoretical results. The results show that the measuring accuracy of LTS has increased by 5 times since this technique for calibration is used.     

CALIBRATION OF A 6-DOF SPACE ROBOT USING GENETIC ALGORITHM

The kinematic error model of a 6-DOF space robot is deduced, and the cost function of kinematic parameter identification is built. With the aid of the genetic algorithm （GA） that has the powerful global adaptive probabilistic search ability, 24 parameters of the robot are identified through simulation, which makes the pose （position and orientation） accuracy of the robot a great improvement. In the process of the calibration, stochastic measurement noises are considered. Lastly, generalization of the identified kinematic parameters in the whole workspace of the robot is discussed. The simulation results show that calibrating the robot with GA is very stable and not sensitive to measurement noise. Moreover, even if the robot＇s kinematic parameters are relative, GA still has strong search ability to find the optimum solution.     

Simultaneous Position Estimation and Omnidirectional Camera Parameter Calibration for Multiple Mobile Robots

This paper proposed an algorithm on simultaneous position estimation and calibration of omnidirectional camera parameters for a group of multiple mobile robots. It is aimed at developing of exploration and information gathering robotic system in unknown environment. Here, each mobile robot is not possible to know its own position. It can only estimate its own position by using the measurement value including white noise acquired by two omnidirectional cameras mounted on it. Each mobile robot is able to obtain the distance to those robots observed from the images of two omnidirectional cameras while making calibration during moving but not in advance. Simulation of three robots moving straightly shows the effectiveness of the proposed algorithm.     

ACCURACY ANALYSIS FOR PLANAR LINKAGE WITH MULTIPLE CLEARANCES AT TURNING PAIRS

Clearance at turning pair has a strong impact on the kinetic accuracy of linkage, but there is short of a generic model to analyze it so far. Clearance error, input error, and manufacturing tolerance of links are taken into consideration as the random variables synthetically. The kinematics and dynamics accuracy analysis models for planar linkages with multiple clearances at joints are built up as well. At last a typical planar linkage is selected for nurnerical illustration. These models stated in matrix resolve the relativity of output parameter errors of mechanism and therefore are of vital significance for the reliability analysis and synthesis of mechanism with clearances.     

Accuracy analysis and design of A3 parallel spindle head

As functional components of machine tools, parallel mechanisms are widely used in high efficiency machining of aviation components, and accuracy is one of the critical technical indexes. Lots of researchers have focused on the accuracy problem of parallel mechanisms, but in terms of controlling the errors and improving the accuracy in the stage of design and manufacturing, further efforts are required. Aiming at the accuracy design of a 3-DOF parallel spindle head(A3 head), its error model, sensitivity analysis and tolerance allocation are investigated. Based on the inverse kinematic analysis, the error model of A3 head is established by using the first-order perturbation theory and vector chain method. According to the mapping property of motion and constraint Jacobian matrix, the compensatable and uncompensatable error sources which affect the accuracy in the end-effector are separated. Furthermore, sensitivity analysis is performed on the uncompensatable error sources. The sensitivity probabilistic model is established and the global sensitivity index is proposed to analyze the influence of the uncompensatable error sources on the accuracy in the end-effector of the mechanism. The results show that orientation error sources have bigger effect on the accuracy in the end-effector. Based upon the sensitivity analysis results, the tolerance design is converted into the issue of nonlinearly constrained optimization with the manufacturing cost minimum being the optimization objective. By utilizing the genetic algorithm, the allocation of the tolerances on each component is finally determined. According to the tolerance allocation results, the tolerance ranges of ten kinds of geometric error sources are obtained. These research achievements can provide fundamental guidelines for component manufacturing and assembly of this kind of parallel mechanisms.     

A Stochastic Approach for Cooperative Position Estimation of Multiple Mobile Robots

This paper proposes the cooperative position estimation of a group of mobile robots, which pertbrms disaster relief tasks in a wide area. When searching the wide area, it becomes important to know a robot＇s position correctly. However, for each mobile robot, it is impossible to know its own position correctly. Therefore, each mobile robot estimates its position from the data of sensor equipped on it. Generally, the sensor data is incorrect since there is sensor noise, etc. This research considers two types of the sensor data errors from omnidirectional camera. One is the error of white noise of the image captured by omnidirectional camera and so on. Another is the error of position and posture between two omnidirectional cameras. To solve the error of latter case, we proposed a self-position estimation algorithm for multiple mobile robots using two omnidirectional cameras and an accelerometer. On the other hand, to solve the error of the former case, this paper proposed an algorithm of cooperative position estimation for multiple mobile robots. In this algorithm, each mobile robot uses two omnidirectional cameras to observe the surrounding mobile robot and get the relative position between mobile robots. Each mobile robot estimates its position with only measurement data of each other mobile robots. The algorithm is based on a Bayesian filtering. Simulations of the proposed cooperative position estimation algorithm for multiple mobile robots are performed. The results show that position estimation is possible by only using measurement value from each other robot.     

Pose Planning for the End-effector of Robot in the Welding of Intersecting Pipes

All-position robots are widely applied in the welding of complicated parts.Welding of intersecting pipes is one of the most typical tasks.The welding seam is a complicated saddle-like space curve,which puts a great challenge to the pose planning of end-effector.The special robots designed specifically for this kind of tasks are rare in China and lack sufficient theoretical research.In this paper,a systematic research on the pose planning for the end-effectors of robot in the welding of intersecting pipes is conducted. First,the intersecting curve of pipes is mathematically analyzed.The mathematical model of the most general intersecting curve of pipes is derived,and several special forms of this model in degraded situations are also discussed.A new pose planning approach of bisecting angle in main normal plane(BAMNP) for the welding-gun is proposed by using differential geometry and the comparison with the traditional bisecting angle in axial rotation plane(BAARP) method is also analytically conducted.The optimal pose of the welding-gun is to make the orientation posed at the center of the small space formed by the two cylinders and the intersecting curve to help the welding-pool run smoothly.The BAMNP method can make sure the pose vertical to the curve and center between the two cylinders at the same time,therefore its performance in welding-technique is superior to the BAARP method.By using the traditional BAARP method,the robot structure can become simpler and easier to be controlled,because one degree of freedom(DOF) of the robot can be reduced.For the special case of perpendicular intersecting,an index is constructed to evaluate the quality of welding technique in the process of welding.The effect of different combination of pipe size on this index is also discussed.On the basis of practical consideration,selection principle for BAARP and BAMNP is described.The simulations of those two methods for a serial joint-type robot are made in MATLAB,and the simulation results are consistent to the analysis.The mathematical model and the proposed new pose-planning method will lay a solid foundation for future researches on the control and design of all-position welding robots.     

Delta并联机构精度标定方法研究

以Delta并联机构为对象,研究一类含平行四边形支链的3自由度并联机构误差建模技术,所建模型可有效分离出影响末端姿态误差的几何误差源。在此基础上提出一种精度标定方法,该方法利用并联机构操作空间与关节空间非线性映射的性质,仅需检测末端沿z向的位置误差、以及在初始位形下的姿态误差便可识别出几何参数,并可通过修改系统输入实现末端位置误差补偿。给出算例以验证该方法的有效性。     

A multilevel calibration technique for an industrial robot with parallelogram mechanism

This paper presents a multilevel calibration technique for improving the absolute accuracy of an industrial robot with a parallelogram mechanism (ABB IRB2400). The parallelogram structural error is firstly modeled based on the partial differential of the position function of a general four-bar linkage and the linearization of the position constraints of the parallelogram mechanism, the model coefficients are fitted from experimental data. Secondly, an absolute kinematic calibration model is established and resolved as a linear function of all the kinematic parameters, as well as the base frame parameters and tool parameters. Finally, contrary to most other similar works, the robot joint space (rather than Cartesian space) is divided into a sequence of fan-shaped cells in order to compensate the non-geometric errors, the positioning errors on the grid points are measured and stored for the error compensation on the target points. After the multilevel calibration, the maximum/mean point positioning errors on 284 tested configurations (evenly distributed in the robot common workspace) are reduced from 1.583/0.420 mm to 0.172/0.066 mm respectively, which is almost the same level as the robot bidirectional repeatability.     

一种基于工具坐标系的机器人运动学参数标定方法

机器人末端执行器位姿误差在基础坐标系中表示时,误差模型中包含姿态误差与位置矢量的乘积项,影响了参数标定识别精度。以工具坐标系为参考系,给出一种基于指数积公式包含关节约束条件的机器人位姿误差标定模型,避免了姿态误差与位置矢量的乘积项对参数标定识别精度的影响。以UR5机器人为标定对象,采用LeciaAT960-MR激光跟踪仪为测量设备,进行参数标定试验。试验结果表明,经参数标定后UR5机器人位置误差模和姿态误差模的平均值分别减小了91.07%和89.16%。     

基于D-H矩阵的3-RSR并联机器人的误差建模

本文通过选取3-RSR并联机器人的任意一条支链作为研究对象,利用D—H矩阵建立动平台相对于静平台的位姿关系矩阵,采用矩阵微分法推导出机构原始误差到末端执行部分的误差映射模型。该模型包含了机构全部的几何原始误差,同时将末端执行部分位姿误差与原始几何误差间的非线性隐式函数关系简化为线性显式函数关系,是进一步研究误差补偿的基础。     

考虑基坐标系误差的机器人运动学标定方法

提出了一种基于机器人几何参数误差与基坐标系位姿误差的六轴串联型机器人误差标定方法.首先基于MD-H方法建立了IRB6700机器人几何参数误差模型,得到机器人连杆几何参数误差到机器人末端位姿误差的映射关系;然后进一步考虑了基坐标系的位姿误差,并建立了考虑基坐标系误差的机器人误差模型;此外,针对传统标定方法操作繁琐、偶然误...     

零参考模型用于工业机器人定位精度提升研究* .txt

摘要：几何参数建模是机器人标定的基础,直接影响机器人定位精度。为解决常用几何参数模型当机器人相邻两轴线垂直及接近垂直时存在奇异性,建立了基于方向矢量和连接矢量的零参考模型(ZRM),该模型不仅满足完备性与连续性要求,而且使用该模型计算机器人末端位置和姿态简单直观;建立了几何参数标定误差模型,通过使用LeicaAT960激光跟踪仪对Staubli TX60和ER10L C10两种工业机器人末端大量位姿实测,经正交三角分解去除冗余参数,采用LM算法对几何参数误差辨识,并与基于MDH模型的标定结果比较,实验结果证实,采用零参考模型标定后机器人末端平均绝对定位精度提升75%~90%,明显高于采用MDH模型标定结果,该模型适于在有高精度定位精度要求工业机器人中推广。 .txt     

Kinematic calibration of precise 6-DOF stewart platform-type positioning systems for radio telescope applications

The pose accuracy of a parallel robot is a function of the mobile platform posture. Thus, there is no a single value of the robot’s accuracy. In this paper, two novel methods for estimating the accuracy of parallel robots are presented. In the first method, the pose accuracy estimation is calculated by considering the propagation of each error, i.e., error variations are considered as a function of the actuator’s stroke. In the second method, it is considered that each actuator has a constant error at any stroke. Both methods can predict pose accuracy of precise robots at design stages, and/or can reduce calibration time of existing robots. An example of a six degree-of-freedom parallel manipulator is included to show the application of the proposed methods.     

可变胞并联机械臂样机的研制与误差分析

提出了一种通过驱动副锁定组合实现变胞的超冗余并联机械臂,其基础构型是3-PUPS并联机构,对机械臂进行了误差建模与分析,并通过标定系统测量了机械臂实验样机的定位误差。首先,提出了通过对3-PUPS机构各驱动副的组合锁定实现机械臂变胞的设计思路,从而使机械臂可以根据任务需求改变自身构型和性能;然后,采用含误差源的闭环矢量回路法,建立了机械臂3-PUPS机构的误差传递模型,并以此为基础,分析了机械臂的各误差源对其运动平台输出误差的影响规律;接着,根据各误差源对机械臂的输出误差影响程度,确定了各主要运动副配合零件的加工精度等级及公差,在此基础上研制出机械臂的实验样机;最后,采用一套高精度的工业机器人标定系统对机械臂的实验样机进行了定位误差测量,实验表明:机械臂的运动平台的位置误差均在0.005~0.038mm之间,姿态误差均在0.010~0.044°之间,位置误差比通用式工业机器人的位置重复定位精度0.05mm略有提高,姿态误差与通用式工业机器人的姿态重复定位精度0.045°相当。     

一种协作机器人位姿重复性优化综合

在给定位姿重复性要求的前提下,寻找各关节随机运动精度的最优分配方案能够使协作机器人设计更加合理,对降低机器人制造成本有重要意义.首先,在机器人位姿重复性分析的基础上,建立了位姿重复性数学模型,该数学模型包含机器人位置重复性和姿态重复性;其次,以协作机器人KUKA iiwa 7为例,以关节运动误差最大化为优化目标,对该机...     

基于单目视觉的并联机器人末端位姿检测

高效、准确地检测机器人末端位姿误差是实现运动学标定的关键环节。提出一种基于单目摄像机拍摄立体靶标序列图像信息的末端执行器6维位姿误差辨识方法,构造具有平行四边形几何约束的四个空间特征点,并以平行四边形的两个消隐点为约束,建立空间刚体位姿与其二维图像映射关系模型,实现末端位姿的精确定位,然后以Delta高速并联机器人为对象,进行了运动学标定试验,验证该方法的有效性,为这类机器人低成本、快速、在线运动学标定提供重要的理论与技术基础。