Modelling the dynamics of industrial robots for milling operations

Using industrial robots as machine tools is targeted by many industries for their lower cost and larger workspace. Nevertheless, performance of industrial robots is limited due to their mechanical structure involving rotational joints with a lower stiffness. As a consequence, vibration instabilities, known as chatter, are more likely to appear in industrial robots than in conventional machine tools. Commonly, chatter is avoided by using stability lobe diagrams to determine the stable combinations of axial depth of cut and spindle speed. Although the computation of stability lobes in conventional machine tools is a well-studied subject, developing them in robotic milling is challenging because of the lack of accurate multi-body dynamics models involving joint compliance able of predicting the posture-dependent dynamics of the robot. In this paper, two multi-body dynamics models of articulated industrial robots suitable for machining applications are presented. The link and rotor inertias along with the joint stiffness and damping parameters of the developed models are identified using a combination of multiple-input multiple-output identification approach, computer-aided design model of the robot, and experimental modal analysis. The performance of the developed models in predicting posture-dependent dynamics of a KUKA KR90 R3100 robotic arm is studied experimentally.     

Prediction of the Posture-Dependent Tool Tip Dynamics in Robotic Milling Based on Multi-Task Gaussian Process Regressions

Chatter vibration is one of the main factors that limit the productivity and quality of the robotic milling process. To predict the robotic milling stability, it is essential to obtain the tool tip frequency response function (FRF). The tool tip dynamics of a robot heavily depend on its postures and used tools. A state-of-art methodology of combining the regression model with the Receptance Coupling Substructure Analysis (RCSA) method is proved to be effective in predicting tool tip FRFs of machine tools for different positions and tools. However, for the milling robot, the cross coupling FRFs have an obvious influence on the dynamic property of the milling robot, thereby greatly affecting the milling stability boundary. It is of great challenge to directly integrate the effect of the cross coupling FRFs into the state-of-art approach to predict the tool tip dynamics. To tackle this challenge, in this paper, we propose an approach to predict the posture-dependent tool tip dynamics for different tools in robotic milling considering the cross coupling FRFs. First, a more comprehensive RCSA procedure is adopted to include the cross coupling FRFs. Then, the impact test is designed to measure the required FRF matrix. By fitting the measured FRF matrix with the multiple-degree-of-freedom (MDOF) model, the number of modal parameters is significantly reduced. Next, the Multi-Task Gaussian Process (MTGP) regression model is employed to mine the physical correlations between different modal parameters. Compared to the ordinary Gaussian Process regression model, the number of required regression models in MTGP is reduced and the prediction performance is improved in terms of accuracy and robustness. Furthermore, the effectiveness of the proposed approach is validated by the impact test and milling experiment on an industrial robot.     

Modelling and Model Fitting of Flexible Robots – a Multibody System Toolkit Approach

During the last decade robots with flexible links became a popular research object for control engineers. This is because of their sophisticated properties referring to feedback control, e.g., non-minimum phase behaviour in end-effector control. Massive problems already occur trying to obtain an accurate analytic model for multilink flexible robots. This paper presents an effective way for numerical modelling of multilink flexible robots using the multibody system toolkit MBILE. The experimental model fitting to a laboratory test bed of a two-link flexible robot is documented.     

Pose optimization in robotic machining using static and dynamic stiffness models

Industrial robots are typically not used for milling of hard materials due to their low stiffness compared to traditional machine tools. Due to milling being a five degree of freedom (dof) operation, a typical six dof serial manipulator introduces a redundant degree of freedom in the robot pose. This redundancy can be exploited to optimize the pose of the robot during milling to minimize force-induced deflections at the end-effector. Stiffness modeling and optimization techniques for industrial robots utilizing both static (no mass and damping terms) and dynamic (mass and damping terms included) models exist. This paper presents a comparative study of robot pose optimization using static and dynamic stiffness models for different cutting scenarios. Milling experiments show that while a dynamic model-based robot pose optimization yields significant improvement over a static model-based optimization for cutting conditions where the time varying cutting forces approach the robot's natural frequencies, a static model-based optimization is sufficient when the frequency content of the cutting forces are not close to the robot's natural frequencies.     

基于双目视觉导航的仿生机器人鲁棒控制算法

仿生机器人在定姿过程中受到空间扰动因素的影响容易产生控制误差,需要对机器人进行精确标定,提高仿生机器人的定位控制精度,因此提出一种基于双目视觉导航的仿生机器人鲁棒控制算法。利用光学CCD双目视觉动态跟踪系统进行仿生机器人的末端位姿参量测量,建立被控对象的运动学模型;以机器人的转动关节的6自由度参量为控制约束参量,建立机器人的分层子维空间运动规划模型;采用双目视觉跟踪方法实现仿生机器人的位姿自适应修正,实现鲁棒性控制。仿真结果表明,采用该方法进行仿生机器人控制的姿态定位时对机器人末端位姿参量的拟合误差较低,动态跟踪性能较好。     

Improving feasibility of robotic milling through robot placement optimisation

Milling performed with robots is quite demanding, even for low-strength materials, due to the high accuracy requirements, the generally high and periodically varying milling forces and the low stiffness of robots compared to CNC machine tools. In view of the generally improved recently robot stiffness, it is desirable to perform the milling operation in regions of the robot’s workspace where manipulability, both kinematic and dynamic, is highest, thereby exhausting the robot’s potential to cope with the process. In addition, by selecting the most suitable initial pose of the robot with respect to the workpiece, a reduction in the range of necessary joint torques may be reached, to the extent of alleviating the heavy requirements on the robot. Two genetic algorithms (GAs) are employed to tackle these problems. The values of several robot variables, such as joint positions and torques, which are needed by the genetic algorithms, are calculated using inverse kinematics and inverse dynamics models. In addition, initial positions and poses leading to singularities along the milling path are penalized and, thus, avoided. The first GA deals solely with robot kinematics to maximize manipulability. The second GA takes into account milling forces, which are computed numerically according to the particular milling parameters, to minimise joint torque loads.     

Elasto-geometrical error and gravity model calibration of an industrial robot using the same optimized configuration set

Position error is a significant limitation for industrial robots in high-precision machining and manufacturing. Efficient error measurement and compensation for robots equipped with end-effectors are difficult in industrial environments. This paper proposes a robot calibration method based on an elasto–geometrical error and gravity model. Firstly, a geometric error model was established based on the D-H method, and the gravity and compliance error models were constructed to predict the elastic deformation caused by the self-weight of the robot. Subsequently, the position error model was established by considering the attitude error of the robot flange coordinate system. A two-step robot configuration selection method was developed based on the sequential floating forward selection algorithm to optimize the robot configuration for calibrating the position error and gravity models. Then, the geometric error and compliance coefficient were identified simultaneously based on the hybrid evolution algorithm. The gravity model parameters were identified based on the same algorithm using the joint torque signal provided by the robot controller. Finally, calibration and compensation experiments were conducted on a KR-160 industrial robot equipped with a spindle using a laser tracker and internal robot data. The experimental results show that the robot tool center point error can be significantly improved by using the proposed method.     

Prediction of in-process frequency response function and chatter stability considering pose and feedrate in robotic milling

Chatter occurs easily during robotic milling owing to the low structural stiffness of industrial robots and can degrade the machining quality or even cause robot failure. The accurate frequency response function (FRF) of the robot is essential for predicting chatter stability and selecting the appropriate process parameters. However, the FRF of a robot is affected by multiple factors, such as pose, operating state, and external excitation. In this study, an in-process FRF prediction method considering robot pose and feedrate was developed and used to predict chatter stability. Firstly, the static FRFs were obtained from the experimental modal analysis for different robot poses and used to train a Gaussian process regression (GPR) model. Subsequently, the static FRF predicted using GPR and the modal parameters identified by operational modal analysis (OMA) were used to calculate the in-process FRFs of the robot in the operation state. After removing the harmonic components of the vibration signals using a matrix notch filter, OMA was conducted using the least-squares complex frequency. Furthermore, the FRF of the robot was transformed from the robot flange coordinate system into the engagement coordinate system using the kinematics model and the tool path. The dynamic milling model, considering tool and robot modes was used for predicting stability. Finally, the proposed method was demonstrated by time-domain simulation of the robot-tool system and milling tests, and the effects of the running state and feed direction on chatter stability considering robot mode were analyzed.     

Flexible Multibody Systems Models Using Composite Materials Components

The use of a multibody methodology to describe the large motion of complex systems that experience structural deformations enables to represent the complete system motion, the relative kinematics between the components involved, the deformation of the structural members and the inertia coupling between the large rigid body motion and the system elastodynamics. In this work, the flexible multibody dynamics formulations of complex models are extended to include elastic components made of composite materials, which may be laminated and anisotropic. The deformation of any structural member must be elastic and linear, when described in a coordinate frame fixed to one or more material points of its domain, regardless of the complexity of its geometry. To achieve the proposed flexible multibody formulation, a finite element model for each flexible body is used. For the beam composite material elements, the sections properties are found using an asymptotic procedure that involves a two-dimensional finite element analysis of their cross-section. The equations of motion of the flexible multibody system are solved using an augmented Lagrangian formulation and the accelerations and velocities are integrated in time using a multi-step multi-order integration algorithm based on the Gear method.     

Stress recovery with Krylov-subspaces in reduced elastic multibody systems

A method for the recovery of stresses in reduced elastic multibody systems is presented. Elastic coordinates of a flexible body belonging to a reduced elastic multibody system are therefore premultiplied with a matrix of shape functions for stresses. Whereas the classic procedures for stress recovery in elastic multibody systems use shape functions for stresses that belong to eigenmodes and particular modes, this work also investigates shape functions for stresses that are derived from a Krylov-subspace projection. The presented method for stress recovery is implemented in a process chain containing different software tools and allows the evaluation of stresses during the runtime of the elastic multibody simulation. Accordingly, the performance of the developed process is examined with the help of a simple example. Results show that the usage of shape functions for stresses that are derived from a Krylov-subspace projection can improve the approximation of stresses in a user-defined frequency range.     

Drive based damping for robots with secondary encoders

Robot machining is a growing field due to the combination of large working envelope with relatively low investment and operating costs, compared to milling machine. Besides, the flexibility, which robot serial kinematics bring along, makes application of robot machining possible for different use cases. However, an occurring drawback of robot based machining systems is low stiffness compared to milling machines and, thus, poor accuracy and low eigenfrequencies with few damping. By that, robots for machining are prone to vibrations, resulting in poor machining results. In this paper the authors therefore present an approach for damping these vibrations, using state-of-the-art drives. Secondary encoders, which are increasingly available on industrial robots, are applied to detect these vibrations. This presented strategy has already been proven applicable on feed drives in milling machines and is now applied on industrial robots. To do so, the robot's vibrational behavior, like eigenfrequencies and eigenmodes, is examined in the whole workspace via measurements on real robots. Additionally the excitation by the milling process has been examined in relation to the occurring oscillations at the robot structure. The results of these research is adduced to estimate the applicability of this approach. Based on these results simulations are carried out to test the applicability of the damping strategy on industrial robots. As compliance of robots results mostly from gearboxes, simulation is carried out using a rigid-body-flexible-joint model. The simulations show that the dynamic behavior of the robots axes can be influenced in a positive way and vibration of the robots tool center point can be reduced significantly. Based on these findings, it is planned to implement this method on real hardware to perform tests, develop it further and optimize it.     

Robot path planning by genetic programming

This paper describes a method to determine the path of a robot that travels around between machine tools in a production line FA factory. This decision is made by the genetic algorithm with Lisp language programming. In the algorithm, the building block method to decide fitness is adopted. The method is applied to a flexible manufacturing system (FMS) that has four machine tools and a robot. This work was presented, in part, at the International Symposium on Artificial Life and Robotics, Oita, Japan, February 18–20, 1996     

Special Genetic Identification Algorithm with smoothing in the frequency domain

Due to the increase in speed and lightweight construction, modern robots vibrate significantly during motion. Thus, accurate mechanical modeling and detailed controller behavior is essential for accurate path planning and control design of robots. For the suppression of undesired vibrations detailed models are used to develop robust controllers. Least square identification methods require deep insight in the analytical equations and thus are not very suitable for identification of different highly nonlinear robot models. Recently, we presented our genetic parameter identification in Brussels, Ludwig and Gerstmayr (2011). It minimizes the error of measured and simulated quantities. Highly efficient models in the multibody system tool HOTINT lead to short computational times for various simulations with different parameters. The simulation models can easily be assembled by engineers without a detailed knowledge of the underlying multibody system. As drawback of genetic optimization, many sub-minima were detected. Many simulations were required for the determination of the global minimum. Our current approach was to extend our previous algorithm. Measured and simulated quantities are transformed into the frequency domain. In contrast to previous work, Ludwig and Gerstmayr (2013), amplitude spectra of measured and simulated quantities are smoothed prior to the L2-norm computation. The presented method is tested using small scale test problems as well as real robots. Smoothing in the frequency domain leads to a smaller number of simulations needed for obtaining higher accuracy. It turns out that the presented algorithm is more accurate and precise than a standard algorithm and reduces the computational cost.     

Research on the directionality of end dynamic compliance dominated by milling robot body structure and milling vibration suppression

The end dynamic characteristics dominated by the milling robot's body structure play a crucial role in vibration control and chatter avoidance in robotic milling. As the excitation source, the milling force may exist in any direction under different process parameters. Consequently, investigating the directional distribution of the end dynamic characteristics becomes essential for studying the direction-dependent dynamic response of a milling robot. In this paper, firstly, the directionality of the end modal vibration is proved based on the body structure mode shape of the milling robot. Subsequently, combined with the multi-body dynamics model of milling robots, the distribution of the end dynamic compliance with the excitation direction in the robot mode is modeled and found to be double-sphere, which is verified experimentally. A convenient method for acquiring the double-sphere dynamic compliance (DSDC) is given and its portability is shown. Then, two application cases of the DSDC in milling vibration suppression are given. In Case 1, based on the DSDC, the milling vibration amplitude is found to be distributed as an eccentric ellipse with a non-orthogonal basis with the feed angle in a robot mode, wherein a feed direction selection method for reducing milling vibration without traversal calculation is given with experimental validation. Case 2 shows that according to the guidance of the DSDC, the tuned mass damper can significantly suppress the milling vibration. It is worth noting that the directionality of the end modal vibration and DSDC constitute fundamental dynamic properties of milling robots, which may provide a new theoretical basis for the research related to the robotic end dynamic characteristics (such as frequency response function identification, mode coupling chatter mechanism and its suppression, etc.), which are well worth exploring.     

钢结构建筑探伤机器人刚柔耦合空间位姿解析与实验研究

针对传统钢结构建筑健康监测中存在检测盲区和检测不全面的问题,研究了磁吸附式刚柔耦合柔性探伤机器人并对其控制系统进行了改进．建立了柔性机器人前、后车体位移和姿态运动学数学模型与机器人刚柔耦合结构位姿解算方程,通过惯性测量单元和编码器获取柔性探伤机器人前、后车体实时动态位姿参数,分别采用显性互补滤波器和扩展卡尔曼滤波器解算前、后车体在不同工况中的静态、动态姿态,利用航迹推算算法确定机器人的位置,通过数据融合得到柔性机器人刚柔耦合结构的空间位姿．实验结果表明,扩展卡尔曼滤波算法的动态跟踪性能更好,可为柔性探伤机器人在复杂建筑结构越障运动中提供精确的空间位姿参数．     

满足不同交互任务的人机共融系统设计

人与机器人共同协作的灵活生产模式已经成为工业成产的迫切需求,因此,近年来人机共融系统方面的研究受到了越来越多关注.设计并实现了一种满足不同交互任务的人机共融系统,人体动作的估计和机器人的交互控制是其中的关键技术.首先,提出了一种基于多相机和惯性测量单元信息融合的人体姿态解算方法,通过构造优化问题,融合多相机下的2D关节检测信息和所佩戴的惯性测量单元测量信息,对人体运动学姿态进行优化估计,改善了单一传感器下,姿态信息不全面以及对噪声敏感的问题,提升了姿态估计的准确度.其次,结合机器人的运动学特性和人机交互的特点,设计了基于目标点跟踪和模型预测控制的机器人控制策略,使得机器人能够通过调整控制参数,适应动态的环境和不同的交互需求,同时保证机器人和操作人员的安全.最后,进行了动作跟随、物品传递、主动避障等人机交互实验,实验结果表明了所设计的机器人交互系统在人机共融环境下的有效性和可靠性.     

Adaptive control for mobile robot using wavelet networks

This work improves recent results concerning the adaptive control of mobile robots via neural and wavelet networks, in the sense that the stability proof, based on the second method of Lyapunov, encompasses (1) unmodeled dynamics and disturbances in the robot model; (2) adaptation of all parameters in the wavelet networks; and (3) a flexible procedure for automatically adjusting the wavelet architecture. Prior knowledge of dynamic of the mobile robot and network training is not necessary because the controller learns the dynamics online. The wavelet network's parameters and structure are also adapted online. Simulation results are presented by using parameters of the Magellan mobile robot from IS Robotics, Inc.     

A control for spatial motions of a robot in a rectangular Cartesian coordinate system

Two mathematical models of a robot with elastic or rigid links working in a rectangular Cartesian coordinate system are proposed. The problems of dynamic and kinematic controls for such a robot are posed within the framework of the specified models. The difficulties of mathematical simulation of real robots of such a type with sliding joints are discussed in connection with the presence of elastic flexibility in the actuators. The technique for estimating the accuracy of positioning of the load carried by the robot based on joint use of the specified mathematical models is presented. As an example, solution of the problems of kinematic control of flexible and rigid robots with equivalent geometric and physical parameters functioning in a rectangular Cartesian coordinate system is considered.     

Design of global tracking controllers for flexible-joint robots

An approach to design control laws for trajectory tracking of robots having flexible joints is presented. An application to the adaptive control is also given with reference to a single-link robot with one revolute elastic joint whose parameters are unknown.