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

Delta robot motion control

Abstract. The aim of this thesis is to generate a functional motion control to a delta robot. The motion control is based on solving the inverse kinematics problem of the delta robot. This solution is then used to form the control logic of the robot. In addition, this thesis also introduces forward kinematics solution models and, the most common industrial robots and their features. Applications of industrial robots, as well as the industries that utilize them the most are also examined. This thesis introduces a self-made delta robot and its motion control design. The functionality of motion control is studied by measuring the positioning accuracy as well as the repeatability of the self-made delta robot in the xy-plane. Accuracy measurements are performed using a separate measuring device. A small-scale comparison between the positioning accuracy of a self-made and a commercial delta robot is implemented to find out how closely can the performance of a commercial delta robot be reproduced with a self-made delta robot. The results of this thesis indicate that the inverse kinematics model of the delta robot as well as the motion control actually work. The results demonstrate that the performance of the self-made delta robot is at a good level and that further development is worthwhile. There was not enough measurement data to perform a proper comparison between the self-made and the commercial delta robot. However, despite the narrow sampling, it is assumed that the positioning accuracy of the self-made delta robot is not yet at the same level as that of the commercial product. The accuracy of the self-made delta robot presented in this thesis can be improved by developing the feeding of the robot’s drive commands. The materials used in the construction of the robot as well as the quality of the joints also affect the accuracy. The inverse kinematics model of the delta robot presented in this thesis can be easily scaled to different sized delta robots depending on the application. Motion control can be utilized in the control of delta robots implemented with a similar mechanical structure.Delta-robotin liikkeenohjaus. Tiivistelmä. Tämän työn tarkoituksena on suunnitella delta-robotille toimiva liikkeenohjaus. Liikkeenohjauksen rakentaminen perustuu delta-robotin käänteiskinematiikan ratkaisemiseen. Käänteiskinematiikan ratkaisua hyödynnetään ohjauslogiikan toteutuksessa. Työssä tutustutaan myös suorankinematiikan ratkaisumalleihin, sekä esitellään yleisimpiä teollisuusrobotteja ja niiden ominaisuuksia. Työssä tarkastellaan myös teollisuusrobottien käyttökohteita, sekä niitä eniten hyödyntävät teollisuudenalat. Työssä tutustutaan omavalmisteiseen delta-robottiin ja sen liikkeenohjauksen suunnitteluun. Liikkeenohjauksen toimivuutta tutkitaan mittaamalla omavalmisteisen delta-robotin paikoitustarkkuus, sekä toistotarkkuus xy-tasossa. Tarkkuusmittaukset toteutetaan käyttämällä erillistä mittalaitetta. Työssä pyritään myös selvittämään kuinka lähelle kaupallisen delta-robotin suorituskykyä voidaan päästä omavalmisteisella delta-robotilla. Työssä toteutetaan pienimuotoinen vertailu omavalmisteisen ja kaupallisen delta-robotin paikoitustarkkuuden välillä. Työn tulokset osoittavat, että delta-robotin käänteiskinematiikan malli, sekä liikkeenohjaus toimivat. Tuloksista selviää, että omavalmisteisen delta-robotin suorituskyky on hyvällä tasolla ja sen kehittämistä kannattaa jatkaa. Omavalmisteisen ja kaupallisen delta-robotin kunnolliseen vertailuun ei saatu riittävästi dataa. Suppeasta otannasta huolimatta on kuitenkin oletettavaa, että omavalmisteisen delta-robotin paikoitustarkkuus ei vielä yllä samalle tasolle kaupallisen tuotteen kanssa. Työssä esitellyn omavalmisteisen delta-robotin tarkkuutta saadaan parannettua kehittämällä robotin ajokomentojen syöttämistä. Myös robotin rakenteessa käytetyt materiaalit, sekä nivelten laadukkuus vaikuttavat tarkkuuteen. Työssä esitetty delta-robotin käänteiskinematiikan malli on helposti skaalattavissa myös erikokoisiin delta-robotteihin käyttökohteesta riippuen. Liikkeenohjausta voidaan hyödyntää vastaavalla mekaanisella rakenteella toteutettujen delta-robottien ohjauksessa

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

Incorporation of the influences of kinematics parameters and joints tilting for the calibration of serial robotic manipulators

Serial robotic manipulators are calibrated to improve and restore their accuracy and repeatability. Kinematics parameters calibration of a robot reduces difference between the model of a robot in the controller and its actual mechanism to improve accuracy. Kinematics parameter’s error identification in the standard kinematics calibration has been configuration independent which does not consider the influence of kinematics parameter on robot tool pose accuracy for a given configuration. This research analyses the configuration dependent influences of kinematics parameters error on pose accuracy of a robot. Based on the effect of kinematics parameters, errors in the kinematics parameters are identified. Another issue is that current kinematics calibration models do not incorporate the joints tilting as a result of joint clearance, backlash, and flexibility, which is critical to the accuracy of serial robotic manipulators, and therefore compromises a pose accuracy. To address this issue which has not been carefully considered in the literature, this research suggested an approach to model configuration dependent joint tilting and presents a novel approach to encapsulate them in the calibration of serial robotic manipulators. The joint tilting along with the kinematics errors are identified and compensated in the kinematics model of the robot. Both conventional and proposed calibration approach are tested experimentally, and the calibration results are investigated to demonstrate the effectiveness of this research. Finally, the improvement in the trajectory tracking accuracy of the robot has been validated with the help of proposed low-cost measurement set-up.Thesis (M.Phil.) (Research by Publication) -- University of Adelaide, School of Mechanical Engineering , 201

A new approach of kinematic geometry for error identification and compensation of industrial robots

A new approach for kinematic calibration of industrial robots, including the kinematic pair errors and the link errors, is developed in this paper based on the kinematic invariants. In most methods of kinematic calibration, the geometric errors of the robots are considered in forms of variations of the link parameters, while the kinematic pairs are assumed ideal. Due to the errors of mating surfaces in kinematic pairs, the fixed and moving axes of revolute pairs, or the fixed and moving guidelines of prismatic pairs, are separated, which can be concisely identified as the kinematic pair errors and the link errors by means of the kinematic pair errors model, including the self-adaption fitting of a ruled surface, or the spherical image curve fitting and the striction curve fitting. The approach is applied to the kinematic calibration of a SCARA robot. The discrete motion of each kinematic pair in the robot is completely measured by a coordinate measuring machine. Based on the global kinematic properties of the measured motion, the fixed and moving axes, or guidelines, of the kinematic pairs are identified, which are invariants unrelated to the positions of the measured reference points. The kinematic model of the robot is set up using the identified axes and guidelines. The results validate the approach developed has good efficiency and accuracy. </jats:p

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

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

Mathematical modeling and kinematic analysis of 5 degrees of freedom serial link manipulator for online real-time pick and place applications

Modeling and kinematic analysis are crucial jobs in robotics that entail identifying the position of the robot’s joints in order to accomplish particular tasks. This article uses an algebraic approach to model the kinematics of a serial link, 5 degrees of freedom (DOF) manipulator. The analytical method is compared to an optimization strategy known as sequential least squares programming (SLSQP). Using an Intel RealSense 3D camera, the colored object is picked up and placed using vision-based technology, and the pixel location of the object is translated into robot coordinates. The LOBOT LX15D serial bus servo controller was used to transmit these coordinates to the robotic arm. Python3 programming language was used throughout the entire analysis. The findings demonstrated that both analytical and optimized inverse kinematic solutions correctly identified colored objects and positioned them in their appropriate goal points

Automatic Modeling for Modular Reconfigurable Robotic Systems: Theory and Practice

A modular reconfigurable robot consists of a collection of individual link and joint components that can be assembled into a number of different robot ge-ometries. Compared to a conventional industrial robot with fixed geometry, such a system can provide flexibility to the user to cope with a wide spectru

Contribution to improving the accuracy of serial robots

The goal of the present study is to improve the accuracy of six-revolute industrial robots using calibration methods. These methods identify the values of the calibrated robot model to improve the correspondence between the real robot and the mathematical model used in its controller. The calibrated robot model adds error parameters to the nominal model, which correspond to the geometric errors of the robot as well as the stiffness behavior of the robot. The developed methods focus on using low cost measurement equipment. For instance, the first work makes a comparison between a robot calibration performed using a laser tracker and a stereo camera (MMT optique) separately. The accuracy performance is validated using a telescoping ballbar for each of the two methods. While the calibration result is the same for both methods, the price of a laser tracker is more than twice the price of a stereo camera. The method is tested using an ABB IRB120 robot, a Faro ION laser tracker, and a Creaform CTrack stereo camera to calibrate the robot. A Renishaw QC20-W ballbar is used to validate the accuracy. A novel measurement system to measure a set of poses is described in the second work. The device is an extension of a known approach using an hexapod (a Stewart-Gough platform). One fixture is attached to the robot base and the other to the robot end-effector, each having three magnetic cups. By taking six ballbar measurements at a time, it is possible to measure 144 poses of the triangular fixture attached to the robot end-effector with respect to the base fixture. The position accuracy of the device is 3.2 times the accuracy of the QC20-W ballbar: ± 0.003 mm. An absolute robot calibration using this novel 6D measurement system is performed in the third work of this thesis. The robot is calibrated in 61 configurations and the absolute position accuracy of the robot after calibration is validated with a Faro laser tracker in about 10,000 robot configurations. The mean distance error is improved from 1.062 mm to 0.400 mm in 50 million pairs of measurements throughout the complete robot workspace. To allow a comparison, the robot is also calibrated using the laser tracker and the robot accuracy validated in the same 10,000 robot configurations