A New Cable-Based Parallel Robot with Three Degrees of Freedom

In this paper, a new cable-based parallel robot is introduced. In this robot, the cables are used to not only actuate the end-effector but apply the necessary kinematic constrains to provide three pure translational degrees of freedom. In order to maintain tension in the cables, a collapsible element called “spine” is used between the end-effector and the robot’s base. The kinematic analysis of this robot is similar to that of a rigid link parallel manipulator as long as the cables are in tension. The rigidity of this robot which corresponds to having all cables in tension is studied thoroughly and it is proved that a single spine with a finite force is sufficient to guarantee rigidity for any external load at any position of the workspace.     

Joint workspace of parallel kinematic machines

Robot workspace is the set of positions a robot can reach. Workspace is one of the most useful measures for the evaluation of a robot. Workspace is usually defined as the reachable space of the end-effector in Cartesian coordinate system. However, it can be defined in joint coordinate system in terms of joint motions. In this paper, workspace of the end-effector is called task workspace, and workspace of the joint motions is called joint workspace. Joint workspace of a parallel kinematic machine (PKM) is focused, and a tripod machine tool with three degrees of freedom (DOF) is taken as an example. To study the joint workspace of this tripod machine tool, the forward kinematic model is established, and an interpolating approach is proposed to solve this model. The forward kinematic model is used to determine the joint workspace, which occupies a portion of the domain of joint motions. The following contributions have been made in this paper include: (i) a new concept so-called joint workspace has been proposed for design optimization and control of a PKM; (ii) an approach is developed to determine joint workspace based on the structural constraints of a PKM; (iii) it is observed that the trajectory planning in the joint coordinate system is not reliable without taking into considerations of cavities or holes in the joint workspace.     

The proof of a better performance by one-stage than two-stage estimation in robot calibration

Calibration of a robot manipulator requires an external instrument to measure its end-effector locations. If the parameters are estimated directly from the measurements, it is called one-stage estimation. Otherwise, it is called two-stage estimation. It was previously observed that two-stage estimation has the drawback of error propagation. Theoretically, it is known that for linear system, the minimum variance is achieved using the best linear unbiased estimator in one-stage estimation. However, the two-stage estimation can also achieve the minimum variance under certain conditions. In this paper, the statistical properties of both are explored in detail under a newly established mathematical fact. The result can be extended to the nonlinear estimation problem via approximation. Simulations of robot calibration by a coordinate measuring machine and eye-in-hand camera are conducted and the results confirm the theoretical analysis.     

Kinematic calibration of a five-bar planar parallel robot using all working modes

We present a simple low-cost calibration procedure that improves the planar positioning accuracy of a double-arm SCARA robot to levels difficult or impossible to achieve using an equivalent serial robot. Measurements are based on the use of five custom designed magnetic tooling balls fixed to the periphery of a detachable working plate. Three of these tooling balls define the world reference frame of the robot, and the positions of the centers of all balls are measured on a CMM. A special magnetic cup end-effector is used. Measurements are taken by manually positioning the end-effector over each of the tooling balls, with each of the maximum of four possible robot configurations. Each of these measurements is repeatable to within±0.015 mm. The robot calibration model includes all 12 kinematic parameters, and the calibration method used is based on the linearization of the direct kinematics model in each calibration configuration. The optimal number and location of the tooling balls is obtained by studying the observability index. Finally, an experimental validation at 14 additional tooling balls shows that the maximum position error with respect to the world frame is reduced to 0.080 mm within the entire robot's workspace of 600 mm×600 mm.     

A “3-2-1” kinematic configuration of a Stewart platform and its application to six degree of freedom pose measurements

This paper outlines a simple yet accurate approach to measuring the six degree of freedom position and orientation of a robot end-effector. The mechanism, which will be far less costly than currently available devices, can be used to make both static and dynamic measurements for robot calibration as well as real-time endpoint control. The kinematics of the approach stem from a configuration of the Stewart platform. A “3-2-1” kinematic configuration is proposed which results in a closed-form forward kinematic solution for the Stewart platform. The closed-form algorithm can be computed about 100 times faster than conventional iterative algorithms. A prototype system using six string encoders was built and tested. Issues on error compensation were also studied. The presented approach should be useful for a broad range of applications other than robot metrology where convenient, low-cost, six degree of freedom static and/or dynamic pose measurements are required or preffered.     

Dynamic analysis of a 6 DOF CKCM robot end-effector for dual-arm telerobot systems

In this paper, we present the dynamical analysis of a six-degree-of-freedom robot end-effector built to study telerobotic service and maintenance of NASA hardwares in space. The design of the end-effector is based on the concept of closed-kinematic chain mechanism capable of performing precise motion in a small workspace. After presenting a closed-form solution for the inverse kinematic problem, we employ the Lagrangian approach to derive a set of equations of motion for the end-effector where the generalized coordinates are selected to be the Cartesian coordinates. Computer simulation study shows that the centrifugal and Coriolis terms can be neglected fow slow motion. Effects of system parameters on the end-effector dynamics are also studied using computer simulation.     

Singularity-robust decoupled control of dual-elbow manipulators

The ability of a robot manipulator to move inside its workspace is inhibited by the presence of joint limits and obstacles and by the existence of singular positions in the configuration space of the manipulator. Several kinematic control strategies have been proposed to ameliorate these problems and to control the motion of the manipulator inside its workspace. The common base of these strategies is the manipulability measure which has been used to: (i) avoid singularities at the task-planning level; and (ii) to develop a singularity-robust inverse Jacobian matrix for continuous kinematic control. In this paper, a singularity-robust resolved-rate control strategy is presented for decoupled robot geometries and implemented for the dual-elbow manipulator. The proposed approach exploits the decoupled geometry of the dual-elbow manipulator to control independently the shoulder and the arm subsystems, for any desired end-effector motion, thus incurring a significantly lower computational cost compared to existing schemes.     

Accurate error compensation for a MR-compatible surgical robot based on a novel kinematic calibration method

Kinematic calibration is an effective and economical way to improve the accuracy of surgical robot, and in most cases, it is a necessary procedure before the robot is put into operation. This study investigates a novel kinematic calibration method where the effect of controller error is taken into account when formulating the model based on screw theory, which is applied to the kinematic control of magnetic resonance compatible surgical robot. Based on screw theory, the kinematic error model is established for the relationship between error of controller and the deviation of the measured pose of the end-effector. Therefore, the error of controller can be figured out and parameters of controller can be adjusted accordingly. Control strategy based on the kinematic calibration framework is proposed. According to artificial neural network, the deviation of end-effector in arbitrary configuration can be effectively obtained. Comparative experiments are carried out to show the validity and effectiveness of the proposed framework with the help of commercial visual system and joint encoders.     

Kinematic calibration of modular reconfigurable robots using product-of-exponentials formula

A modular reconfigurable robot system is a collection of individual link and joint components that can be assembled into different robot geometries for specific task requirements. However, the machining tolerance and assembly errors at the module interconnections affect the positioning accuracy of the end-effector. This article describes a novel kinematic calibration algorithm for modular robots based on recursive forward dyad kinematics. The forward kinematic model derived from the Product-of-Exponentials formula is configuration independent. The error correction parameters are assumed to be in the relative initial positions of the dyads. Two calibration models, namely the six- and seven-parameter methods, are derived on the grounds of the linear superposition principle and differential transformation. An iterative least square algorithm is employed for the calibration solution. Two simulation examples of calibrating a three-module manipulator and a 4-DOF SCARA type manipulator are demonstrated. The result has shown that the average positioning accuracy of the end-effector increases two orders of magnitude after the calibration. © 1997 John Wiley & Sons, Inc.     

In-field self-calibration of robotic manipulator using stereo camera: application to Humanitarian Demining Robot

A robotic manipulator using a stereo camera mounted on one of its links requires a precise kinematic transformation calibration between the manipulator and the camera coordinate frames, the so-called hand–eye calibration, to achieve high-accuracy end-effector positioning. This paper introduces a new method that performs simultaneous joint angle and hand–eye calibration, based on a traditional method that uses a sequence of pure rotations of the manipulator links. The new method considers an additional joint angle constraint, which improves the calibration accuracy when the circular arc that can be measured by the stereo camera is very limited. Experimental results using a manipulator developed for humanitarian demining demonstrate that relative errors between the end effector and the external points mapped by the stereo camera are greatly reduced compared to traditional methods.     

Adaptive hierarchical positioning error compensation for long-term service of industrial robots based on incremental learning with fixed-length memory window and incremental model reconstruction

Industrial robots have been extensively used in industry, however, geometric errors mainly caused by connecting rod parameter error and non-geometric errors caused by deflection and friction, etc., limit its application in high-accuracy machining. Aiming at addressing these two types of errors, parametric methods for error compensation based on the kinematic model and non-parametric methods of directly establishing the mapping relationship between the actual and target poses of the robot end-effector are investigated and proposed. Currently both types of methods are mainly offline and will be no longer applicable when the pose of the end-effector in the workspace changes dramatically or the working performance of the robot degrades. Thus, to compensate the positioning error of an industrial robot during long-term operation, this research proposes an adaptive hierarchical compensation method based on fixed-length memory window incremental learning and incremental model reconstruction. Firstly, the correlation between positioning errors and robot poses is studied, a calibration sample library is created, and thus the actively evaluating mechanism of the pose mapping model is established to overcome the problem of the robot’ workspace having a differential distribution of error levels. Then, an incremental learning algorithm with fixed-length memory window and an incremental model reconstruction algorithm are designed to optimize the pose mapping model in terms of its parameters and architecture and overcome the problem that the performance degradation of the robot exacerbates the positioning error and affects the applicability of the pose mapping model, ensuring that the pose mapping model runs stably above the target accuracy level. Finally, the proposed method is applied to the long-term compensation case of a Stäubli industrial robot and a UR robot, and compared to state-of-art methods. Verification results show the proposed method reduces the position error of the Stäubli robot from 0.85mm to 0.13mm and orientation error from 0.68° to 0.07°, as well as reduces the position error of the UR robot from 2.11mm to 0.17mm, demonstrating that the proposed method works in real world scenarios and outperforms similar methods.     

一种新型机器人自标定装置及其算法

针对传统基于几何约束的机器人自标定装置仅能对局部工作空间内的机器人位型进行标定测量的问题,提出了一种由安装于机器人末端的球心位置测量装置和可移动球杆组成的新型便携式机器人自标定装置,通过利用球面约束和距离约束,可在较大工作空间内对机器人进行标定测量,从而提高标定结果的可靠性．根据可移动球杆的单、双球布置方式,分别建立了基于向量差和距离差的2种机器人自标定模型及其算法．通过采用局部指数积公式并引入位置伴随变换矩阵,简化了2种自标定模型,从而降低了对运动学方程线性化的计算量．最后,对一种6自由度串联机器人进行了仿真实验,实验结果表明2种自标定算法均能够快速收敛,验证了2种算法的有效性和鲁棒性．     

Experimental identification of the static model of the HPKM Tricept industrial robot

The present paper addresses the modelling and the experimental identification of the static behaviour of the Tricept robot, a hybrid parallel kinematic machine. Mass properties of robot links are initially hypothesized from solid modelling and then incorporated in the identification procedure. Coulomb friction and gravity contributions to motor torques are taken into account: their identification is carried out by means of ordinary least-squares algorithms based on motor currents measurements during several slow motion tests. Moreover, the effect of external forces applied at the end-effector is introduced in the model and analysed by driving the robot end-effector against a calibrated compliant cell. Eventually, the static model is profitably used in an industrial operation of Friction Stir Welding to estimate the external forces applied at the tool mechanical interface providing some benefits: a deeper understanding of the technological process parameters and the possibility to realize model-based controls.     

工业机器人的工作空间综合

根据机器人工作位姿要求确定其自由度数，关节类型及排列，杆件尺寸，关节运动范围，机器人的位置等过程称为机器人的工作空间综合过程，本文侧重对已知的机器人结构提出了进行工作空间综合的优化方法。     

Posture optimization methodology of 6R industrial robots for machining using performance evaluation indexes

For industrial robots, the relatively low posture-dependent stiffness deteriorates the absolute accuracy in the robotic machining process. Thus, it is reasonable to consider performing machining in the regions of the robot workspace where the kinematic, static and even dynamic performances are highest, thereby reducing machining errors and exhausting the advantages of the robot. Simultaneously, an optimum initial placement of the workpiece with respect to the robot can be obtained by optimizing the above performances of the robot. In this paper, a robot posture optimization methodology based on robotic performance indexes is presented. First, a deformation evaluation index is proposed to directly illustrate the deformation of the six-revolute (6R) industrial robot (IR) end-effector (EE) when a force is applied on it. Then, the kinematic performance map drawn according to the kinematic performance index is utilized to refine the regions of the robot workspace. Furthermore, main body stiffness index is proposed here to simplify the performance index of the robot stiffness, and its map is used to determine the position of the EE. Finally, the deformation map obtained according to the proposed deformation evaluation index is used to determine the orientation of the EE. Following these steps, the posture of the 6R robot with the best performance can be obtained, and the initial workpiece placement can be consequently determined. Experiments on a Comau Smart5 NJ 220-2.7 robot are conducted. The results demonstrate the feasibility and effectiveness of the present posture optimization methodology.     

Adaptive calibration and control of 2D monocular visual servo systems

For most visual servo systems, accurate camera/robot calibration is essential for precision tasks, such as tracking time-varying end-effector trajectories in the image plane of a remote (or fixed) camera. This paper presents details of control-theoretic approaches to the calibration and control of monocular visual servo systems in the case of a planar robot with a workspace perpendicular to the optical axis of the imaging system. An on-line adaptive calibration and control scheme is developed, along with an associated stability and convergence theorem. A redundancy-based refinement of this scheme is proposed and demonstrated via simulation.     

Internal singularity analysis of a class of lower mobility parallel manipulators with articulated traveling plate

This paper deals with a particular family of lower mobility parallel kinematic manipulators. The four degrees of freedom of the end-effector consist of three translations plus one rotation with a high tilting angle. Robots belonging to this family are first introduced, and a common parameterization is established. Then an extended kinematic model is proposed for this family of robots using a new Jacobian matrix. Relevant information about robot kinematic singularities, internal singularities, and possible end-effector motions can be obtained by resorting to this matrix. The efficiency of this method is proven by applying it to several traveling-plate architectures corresponding to already built robot prototypes. The results of the expected behavior are compared with the prototype's real behavior. The goal of this paper is to show that internal (or constraint) singularities can occur in lower mobility parallel kinematic manipulators, and to underline the influence they have during the design stage.     

Camera calibration issues in robot calibration with eye-on-hand configuration

One of the possible methods for accurate, fast, low-cost and automated robot calibration is to employ a single camera rigidly mounted to the robot end-effector together with a single camera calibration board. The end-effector pose is measured by calibration of the camera at every robot measurement configuration. This paper contends that, with several modifications, Tsai's radial alignment constraint (RAC) camera calibration method can be made a fast and sufficiently accurate pose measurement technique. This paper focuses on speed, accuracy and cost enhancement of RAC-based camera calibration. A fast RAC-based algorithm is proposed, which cuts the computation time of Tsai's original algorithm by about a 5: 1 ratio while keeping its accuracy within the tolerances required for a successful robot calibration. A low-cost method for estimation of the ratio of scale factors of the camera/vision system is also proposed. This method does not require a precision vertical micrometer stage to provide non-coplanar calibration points data for camera calibration. Finally, the phenomenon of perspective projection distortion of circular camera calibration points is fully analyzed and error compensation methods are proposed.     

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.     

A novel XY-Theta precision table and a geometric procedure for its kinematic calibration

Spatial precision positioning devices are often based on parallel robots, but when it comes to planar positioning, the well-known serial architecture is virtually the only solution available to industry. Problems with parallel robots are that most are coupled, more difficult to control than serial robots, and have a small workspace. In this paper, new parallel robot is proposed, which can deliver accurate movements, is partially decoupled and has a relatively large workspace. The novelty of this parallel robot lies in its ability to achieve the decoupled state by employing legs of a different kinematic structure. The robot repeatability is evaluated using a CMM and so are the actual lead errors of its actuators. A simple geometric method is proposed for directly identifying the actual base and mobile reference frames, two actuator's offsets and one distance parameter, using a measurement arm from FARO Technologies. While this method is certainly not the most efficient one, it yields a satisfactory improvement of the robot accuracy without the need for any background in robot calibration. An experimental validation shows that the position accuracy achieved after calibration is better than 0.339 mm within a workspace of approximately 150 mm×200 mm.