레이져 포인터를 이용한 Product-of-Exponentials 기반 직렬로봇 기구학적 보정 알고리즘

학위논문(석사)--서울대학교 대학원 :공과대학 기계항공공학부,2019. 8. 박종우.This thesis proposes a kinematic calibration algorithm for serial robots based on a minimal product of exponentials (POE) forward kinematic model. Generally, robot calibration requires the measurement of the end-effector frame (position and orientation), which typically requires special measurement equipment. To avoid using complex measurement devices and to make the calibration easy to implement for even the most general serial robots, in our approach we attach a laser pointer to the end-effector, which is then aimed at a set of fixed known reference points in the plane. Treating the laser as a prismatic joint and the reference point as the tip, kinematic calibration is then performed by minimizing the Cartesian position difference between the measured and estimated Cartesian tip position of the robot. Our method is validated via simulations and experiments involving a seven-dof industrial robot arm.위 논문은 Minimal POE (product of exponentials) 정기구학 모델에 기반한 직렬로봇 캘리브레이션 알고리즘을 제안한다. 일반적으로 로봇 캘리브레이션은 엔드이펙터 프레임의 위치와 방향을 측정하는 작업을 수행해야 하는데, 이는 특별한 측정장비를 필요로 한다. 복잡한 측정장비의 사용 회피와 다양한 형태의 직렬로봇에 쉽게 응용하기 위해, 이번 논문에서는 엔드이펙터에 레이저포인터를 부착하여 평면 위의 위치가 알려진 참조점들을 추적하여 캘리브레이션을 수행하는 방법을 제시한다. 캘리브레이션은 레이저포인터와 참조점을 각각 선형조인트와 팁으로 생각하여 로봇 팁 위치의 측정값과 추정값의 차이를 최소화하는 과정으로 진행된다. 7자유도 산업용 로봇 팔에 대해 시뮬레이션과 실제 공간에서의 실험을 통해 캘리브레이션 방식을 검증했다.1 Introduction 1 1.1 Existing Methods 2 1.2 Contributions of This Thesis 4 2 Kinematics Preliminaries 6 2.1 Geometric Background 6 2.1.1 The Lie Group Formulations 6 2.1.2 Screw Motions 8 2.1.3 Adjoint Representation 9 2.2 Forward Kinematics 9 2.2.1 The Product of Exponentials Formula 9 2.2.2 The Minimal Product of Exponentials Formula 11 2.3 Kinematic Error Model 14 2.3.1 Linearizing the Forward Kinematics 15 3 Calibration Methodology 19 3.1 The Concept of the Method 19 3.1.1 Forward Kinematics of a Robot With a Laser Pointer 19 3.1.2 The Error Model for Calibration 20 3.2 Calibration Algorithm 23 3.2.1 The Estimation Method of the Length of the Laser 24 3.2.2 Identification Process 25 4 Experiments 29 4.1 Simulation 1: 6-Dof Robot With Precise Data 29 4.2 Simulation 2: 6-Dof Robot With Noisy Data 31 4.3 Experiments on a 7-Dof Robot 34 5 Conclusion 39 A Appendix 41 A.1 Conversion From dq to dS and dSM [1] 41 Bibliography 43 Abstract 46Maste

Separable Nonlinear Least Squares Algorithm for Robust Kinematic Calibration of Serial Robots

Kinematic calibration of robots is an effective way to guarantee and promote their performance characteristics. There are many mature researches on kinematic calibration, and methods based on MDH model are the most common ones. However, when employing these calibration methods, it occasionally happens that the objective function cannot converge during iterations. Through analyzing robotic forward kinematics, we found out that the Cartesian coordinates of the end-point are affine to length-related MDH parameters, where linear and nonlinear parameters can be separated. Thanks to the distinctive characteristic of the MDH model, the kinematic calibration problem can be converted into a separable nonlinear least squares problem, which can further be partitioned into two subproblems: a linear least squares problem and a reduced problem involving only nonlinear parameters. Eventually, the optimal structural parameters can be identified by solving this problem iteratively. The results of numerical and experimental validations show that: 1) the robustness during identification procedure is enhanced by eliminating the partial linear structural parameters, the convergence rate is promoted from 68.98% to 100% with different deviation vector pairs; 2) the initial values to be pre-set for kinematic calibration problem are fewer and 3) fewer parameters are to be identified by nonlinear least squares regression, resulting in fewer iterations and faster convergence, where average runtime is reduced from 33.931s to 1.874s

Automatic Denavit-Hartenberg parameter identification for serial manipulators

An automatic algorithm to identify Standard Denavit-Hartenberg parameters of serial manipulators is proposed. The method is based on geometric operations and dual vector algebra to process and determine the relative transformation matrices, from which it is computed the Standard Denavit-Hartenberg (DH) parameters (ai, ai, di, θi). The algorithm was tested in several serial robotic manipulators with varying kinematic structures and joint types: the KUKA LBR iiwa R800, the Rethink Robotics Sawyer, the ABB IRB 140, the Universal Robots UR3, the KINOVA MICO, and the Omron Cobra 650. For all these robotic manipulators, the proposed algorithm was capable of correctly identifying a set of DH parameters. The algorithm source code as well as the test scenarios are publicly available.FCT - Fundação para a Ciência e a Tecnologia(SFRH/BD/86499/2012

IMU-Based Online Kinematic Calibration of Robot Manipulator

Robot calibration is a useful diagnostic method for improving the positioning accuracy in robot production and maintenance. An online robot self-calibration method based on inertial measurement unit (IMU) is presented in this paper. The method requires that the IMU is rigidly attached to the robot manipulator, which makes it possible to obtain the orientation of the manipulator with the orientation of the IMU in real time. This paper proposed an efficient approach which incorporates Factored Quaternion Algorithm (FQA) and Kalman Filter (KF) to estimate the orientation of the IMU. Then, an Extended Kalman Filter (EKF) is used to estimate kinematic parameter errors. Using this proposed orientation estimation method will result in improved reliability and accuracy in determining the orientation of the manipulator. Compared with the existing vision-based self-calibration methods, the great advantage of this method is that it does not need the complex steps, such as camera calibration, images capture, and corner detection, which make the robot calibration procedure more autonomous in a dynamic manufacturing environment. Experimental studies on a GOOGOL GRB3016 robot show that this method has better accuracy, convenience, and effectiveness than vision-based methods

Geometric and elastostatic calibration of robotic manipulator using partial pose measurements

International audienceThe paper deals with geometric and elastostatic calibration of robotic manipulator using partial pose measurements, which do not provide the end-effector orientation. The main attention is paid to the efficiency improvement of identification procedure. In contrast to previous works, the developed calibration technique is based on the direct measurements only. To improve the identification accuracy, it is proposed to use several reference points for each manipulator configuration. This allows avoiding the problem of non-homogeneity of the least-square objective, which arises in the classical identification technique with the full-pose information (position and orientation). Its efficiency is confirmed by the comparison analysis, which deals with the accuracy evaluation of different identification strategies. The obtained theoretical results have been successfully applied to the geometric and elastostatic calibration of serial industrial robot employed in a machining work-cell for aerospace industry

A screw theory based approach to determining the identifiable parameters for calibration of parallel manipulators

Establishing complete, continuous and minimal error models is fundamentally significant for the calibration of robotic manipulators. Motivated by practical needs for models suited to coarse plus fine calibration strategies, this paper presents a screw theory based approach to determining the identifiable geometric errors of parallel manipulators at the model level. The paper first addresses two specific issues: (1) developing a simple approach that enables all encoder offsets to be retained in the minimal error model of serial kinematic chains; and (2) exploiting a fully justifiable criterion that allows the detection of the unidentifiable structural errors of parallel manipulators. Merging these two threads leads to a new, more rigorous formula for calculating precisely the number of identifiable geometric errors, including both encoder offsets and identifiable structural errors, of parallel manipulators. It shows that the identifiability of structural errors in parallel manipulators depends highly upon joint geometry and actuator arrangement of the limb involved. The process is used to determine the unidentifiable structural errors of two lower mobility parallel mechanisms to illustrate the effectiveness of the proposed approach

A Novel Algorithm for Robust Calibration of Kinematic Manipulators and its Experimental Validation

Kinematic calibration of manipulators is an efficient and fundamental way to ensure reliability and high performance of robots. Research on kinematic calibration has a long tradition, and a common strategy used for calibration is to guarantee the least errors in the sense of root-mean-square deviation. However, the absolute positioning accuracy is determined by the maximum error of manipulators, and it is a key indicator for evaluating performance. For example, using manipulators to print machine elements, obviously where the error is the most, may likely cause inaccurate fit. Hence, it is crucial to study a robust calibration strategy. Considering the calibration problem, both positioning and orientation accuracy are ensured by minimizing the maximum positioning errors of three spherical mounted retro-reflectors (SMRs) on the end effector of manipulators. Unfortunately, traditional optimization methods based on gradient cannot be directly employed to solve the minimax problem. Due to the recent progress on optimization, researchers found that the minimax can be transformed into sequence quadratic programming problems under inequality conditions, thus providing solutions for solving the robust calibration. This paper applied this method to convert the calibration problem into constrained quadratic subproblems, and the subproblems can be solved through the primal-dual subgradient method. Then, convexity and robustness analysis is given to prove that these subproblems can quickly converge to a local minimum. Finally, to verify the validity of the proposed algorithm, the experiments are conducted on an IRB 2600 manipulator, and the results show that, with the minimax search algorithm, both the positioning and orientation accuracy is enhanced by 67.34% and 73.14%, respectively, which is significantly higher than the performance of the single-SMR calibration algorithm widely used in the field of industry

A SERIAL-PARALLEL HYBRID ROBOT FOR MACHINING OF COMPLEX SURFACES

Ph.DDOCTOR OF PHILOSOPH

Robust kinematic calibration for improving collaboration accuracy of dual-arm manipulators with experimental validation

Kinematic calibration has been widely employed for manipulators to promote their performance characteristics. For a dual-arm manipulator, most of the research attentions are paid to improving the absolute positioning accuracy. However, collaborative accuracy plays a critical role in mutual operations between the two arms. For example, in dangerous chemical experiments, the dual-arm manipulator is often demanded to grab a target object with the two hands, or re-grasp a test tube from one hand to the other, where the inferior collaborative accuracy may lead to the failure of experiments. Hence, in this paper, collaborative accuracy of dual-arm manipulators is well defined and fully considered as the objective for calibration. Robustness of the calibration is further guaranteed by minimizing the maximum distance error. The formulated problem is not a typical convex optimization, and gradient search algorithm does not work well for this problem. With researches on optimization moving forward, recent advances in nonlinear optimization are employed to seek for the solution effectively, and it is found that the minimax problem can be approximately linearized to a sequence quadratic programming (SQP) problem. Furthermore, a primal-dual subgradient algorithm is applied for solving the SQP problem with a fast local convergence. Finally, in order to verify the superiority of the proposed method, an experiment is performed on an IRB 14000 manipulator, and corresponding outcomes indicate that the RMS collaborative positioning and the orientation accuracies are significantly improved by and . To the best of our knowledge, our method has reached the best collaborative accuracy compared with existing works (Wang et al., 2014; Roncone et al., 2014; Motta et al., 2001)