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

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 robot calibration method with plane constraint based on dial indicator

In pace with the electronic technology development and the production technology improvement, industrial robot Give Scope to the Advantage in social services and industrial production. However, due to long-term mechanical wear and structural deformation, the absolute positioning accuracy is low, which greatly hinders the development of manufacturing industry. Calibrating the kinematic parameters of the robot is an effective way to address it. However, the main measuring equipment such as laser trackers and coordinate measuring machines are expensive and need special personnel to operate. Additionally, in the measurement process, due to the influence of many environmental factors, measurement noises are generated, which will affect the calibration accuracy of the robot. Basing on these, we have done the following work: a) developing a robot calibration method based on plane constraint to simplify measurement steps; b) employing Square-root Culture Kalman Filter (SCKF) algorithm for reducing the influence of measurement noises; c) proposing a novel algorithm for identifying kinematic parameters based on SCKF algorithm and Levenberg Marquardt (LM) algorithm to achieve the high calibration accuracy; d) adopting the dial indicator as the measuring equipment for slashing costs. The enough experiments verify the effectiveness of the proposed calibration algorithm and experimental platform

Symmetric Subspace Motion Generators

When moving an object endowed with continuous symmetry, an ambiguity arises in its underlying rigid body transformation, induced by the arbitrariness of the portion of motion that does not change the overall body shape. The functional redundancy caused by continuous symmetry is ubiquitously present in a broad range of robotic applications, including robot machining and haptic interface (revolute symmetry), remote center of motion devices for minimal invasive surgery (line symmetry), and motion modules for hyperredundant robots (plane symmetry). In this paper, we argue that such functional redundancy can be systematically resolved by resorting to symmetric subspaces (SSs) of the special Euclidean group SE(3), which motivates us to systematically investigate the structural synthesis of SS motion generators. In particular, we develop a general synthesis procedure that allows us to generate a wide spectrum of novel mechanisms for use in the applications mentioned

A SERIAL-PARALLEL HYBRID ROBOT FOR MACHINING OF COMPLEX SURFACES

Ph.DDOCTOR OF PHILOSOPH

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

Trajectory Generation for a Multibody Robotic System: Modern Methods Based on Product of Exponentials

This work presents several trajectory generation algorithms for multibody robotic systems based on the Product of Exponentials (PoE) formulation, also known as screw theory. A PoE formulation is first developed to model the kinematics and dynamics of a multibody robotic manipulator (Sawyer Robot) with 7 revolute joints and an end-effector. In the first method, an Inverse Kinematics (IK) algorithm based on the Newton-Raphson iterative method is applied to generate constrained joint-space trajectories corresponding to straight-line and curvilinear motions of the end effector in Cartesian space with finite jerk. The second approach describes Constant Screw Axis (CSA) trajectories which are generated using Machine Learning (ML) and Artificial Neural Networks (ANNs) techniques. The CSA method smooths the trajectory in the Special Euclidean (SE(3)) space. In the third approach, a multi-objective Swarm Intelligence (SI) trajectory generation algorithm is developed, where the IK problem is tackled using a combined SI-PoE ML technique resulting in a joint trajectory that avoids obstacles in the workspace, and satisfies the finite jerk constraint on end-effector while minimizing the torque profiles. The final method is a different approach to solving the IK problem using the Deep Q-Learning (DQN) Reinforcement Learning (RL) algorithm which can generate different joint space trajectories given the Cartesian end-effector path. For all methods above, the Newton-Euler recursive algorithm is implemented to compute the inverse dynamics, which generates the joint torques profiles. The simulated torque profiles are experimentally validated by feeding the generated joint trajectories to the Sawyer robotic arm through the developed Robot Operating System (ROS) - Python environment in the Software Development Kit (SDK) mode. The developed algorithms can be used to generate various trajectories for robotic arms (e.g. spacecraft servicing missions)

Accuracy Enhancement with Processing Error Prediction and Compensation of a CNC Flame Cutting Machine Used in Spatial Surface Operating Conditions

This study deals with the precision performance of the CNC flame-cutting machine used in spatial surface operating conditions and presents an accuracy enhancement method based on processing error modeling prediction and real-time compensation. Machining coordinate systems and transformation matrix models were established for the CNC flame processing system considering both geometric errors and thermal deformation effects. Meanwhile, prediction and compensation models were constructed related to the actual cutting situation. Focusing on the thermal deformation elements, finite element analysis was used to measure the testing data of thermal errors, the grey system theory was applied to optimize the key thermal points, and related thermal dynamics models were carried out to achieve high-precision prediction values. Comparison experiments between the proposed method and the teaching method were conducted on the processing system after performing calibration. The results showed that the proposed method is valid and the cutting quality could be improved by more than 30% relative to the teaching method. Furthermore, the proposed method can be used under any working condition by making a few adjustments to the prediction and compensation models

Metodologia para calibração de robôs industriais com medições em sub-regiões volumétricas

Tese (doutorado) — Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Mecânica, 2022.Este trabalho propõe uma metodologia para calibração de robôs industriais que utiliza o conceito de medição em sub-regiões, possibilitando soluções de baixo custo e de fácil implementação para atender os requisitos de precisão do robô em aplicações industriais. A implementação das soluções para aumentar a precisão dos robôs têm alto custo atualmente, tornando a calibração em todo o local de trabalho uma tarefa difícil e improvável na indústria. Assim, a redução do tempo gasto e do volume medido do espaço de trabalho com efetuador do robô são os principais benefícios da implementação do conceito de sub-região, garantindo flexibilidade suficiente na etapa de medição como parte dos procedimentos de calibração do manipulador. A principal contribuição deste trabalho é a proposta e discussão de uma metodologia para calibrar robôs utilizando vários pequenos volumes de medição e agrupar os dados medidos de forma equivalente às medições feitas em regiões de grande volume, viabilizando o uso de equipamentos de alta precisão, mas limitado a pequenos volumes, como sistemas de medição baseados em visão computacional. Os procedimentos de calibração do robô foram simulados de acordo com a literatura, de forma que os resultados da simulação estejam livres de erros devido a configurações experimentais para isolar os benefícios da metodologia de medição proposta. Procedimentos experimentais baseados na medição por sub-regiões foram realizados utilizando um Laser-Tracker, permitindo destacar os benefícios da medição em pequenos volumes. Além disso, é proposto um método para validar o modelo cinemático analítico off-line de robôs industriais utilizando o modelo nominal do fabricante do robô embarcado no seu controlador.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) e Fundação de Apoio à Pesquisa do Distrito Federal (FAP/DF).This work proposes a methodology for calibration of industrial robots that uses a concept of measurement sub-regions, allowing low-cost solutions and easy implementation to meet the robot accuracy requirements in industrial applications. The solutions to increasing the accuracy of robots today have highcost implementation, making calibration throughout the workplace in industry a difficult and unlikely task. Thus, reducing the time spent and the measured workspace volume of the robot end-effector are the main benefits of the implementation of the sub-region concept, ensuring sufficient flexibility in the measurement step of robot calibration procedures. The main contribution of this work is the proposal and discussion of a methodology to calibrate robots using several small measurement sub-regions and gathering the measurement data in a way equivalent to the measurements made in large volume regions, making feasible the use of high-precision measurement systems but limited to small volumes, such as vision-based measurement systems. The robot calibration procedures were simulated according to the literature, such that results from simulation are free from errors due to experimental setups as to isolate the benefits of the measurement proposal methodology. Experimental procedures based on the proposed methodology were performed using a Laser-Tracker, allowing to highlight the benefits of measurement in small regions. In addition, a method to validate the analytical off-line kinematic model of industrial robots is proposed using the nominal model of the robot supplier incorporated into its controller.Este trabajo propone una metodología para la calibración de robots industriales que utiliza el concepto de sub-regiones de medición, permitiendo que soluciones de bajo costo y fácil implementación cumplan con los requisitos de precisión del robot en aplicaciones industriales. Las soluciones para aumentar la precisión de los robots hoy en día se caracterizan por tener alto costo en la implementación, lo que hace que la calibración en todo el espacio de trabajo sea una tarea difícil e improbable en la industria. Por lo tanto, reducir el tiempo empleado y el volumen del espacio de trabajo medido del efector final del robot son los principales beneficios al implementar el concepto de sub-región, asegurando suficiente flexibilidad en la etapa de medición como parte de los procedimientos de calibración de robots. La principal contribución de este trabajo es la propuesta y discusión de una metodología para calibrar robots utilizando varias volúmenes pequeños de medición, recopilando los datos de medición de manera equivalente a las mediciones realizadas en regiones de gran volumen, haciendo factible el uso de sistemas de alta precisión, pero limitados a pequeños volúmenes, como los sistemas de medición basados en visión computacional. Los procedimientos de calibración del robot se simularon de acuerdo con la literatura, de manera que los resultados de la simulación estén libres de errores debido a las configuraciones experimentales para aislar los beneficios de la metodología de medición propuesta. Los procedimientos experimentales basados en la metodología mencionada se realizaron utilizando un Laser-Tracker, lo que permitió resaltar los beneficios de la medición en pequeñas regiones. Además, se propone un método para validar el modelo cinemático analítico off-line de robots industriales utilizando el modelo nominal del fabricante del robot incorporado en su controlador