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

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

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

The Probabilistic Robot Kinematics Model and Its Application to Sensor Fusion

Robots with elasticity in structural components can suffer from undesired end-effector positioning imprecision, which exceeds the accuracy requirements for successful manipulation. We present the Probabilistic-Product-Of-Exponentials robot model, a novel approach for kinematic modeling of robots. It does not only consider the robot's deterministic geometry but additionally models time-varying and configuration-dependent errors in a probabilistic way. Our robot model allows to propagate the errors along the kinematic chain and to compute their influence on the end-effector pose. We apply this model in the context of sensor fusion for manipulator pose correction for two different robotic systems. The results of a simulation study, as well as of an experiment, demonstrate that probabilistic configuration-dependent error modeling of the robot kinematics is crucial in improving pose estimation results

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)

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)

로봇 시스템의 설계 및 동작 동시 최적화

학위논문 (석사) -- 서울대학교 대학원 : 공과대학 기계공학부, 2020. 8. 박종우.A robot design has the potential for numerous combinations of the components such as the actuators, links, joints, etc. Therefore, a process of finding a good design is a challenging problem even for the robot experts. To overcome this difficulty, we present an optimization framework for the morphological shape of a robot, considering its motion. Both the design and motion parameters can be simultaneously optimized for specific tasks by our methodology. In the space where the design and motion parameters are combined, our framework seeks the steepest direction that reduces the objective function on the constraint manifold. To overcome the flaws of the previous studies, we utilize the recently discovered recursive differential dynamics, which informs of the analytic relationship between the variation of joint torques and design parameters, thus our framework brings faster and more accurate optimization results. We validate our optimization framework through two numerical experiments: the 2-R planar manipulator with a given end-effector trajectory and the quadruped robot with a locomotion task.로봇 디자인에는 액츄에이터, 링크, 관절 등과 같은 구성요소의 수많은 조합 가능성이 존재한다. 따라서, 좋은 로봇 디자인을 찾는 과정은 전문가에게도 어려운 문제이다. 위 문제점을 극복하기 위해 로봇의 동작을 고려하여 형태를 최적화하는 방법론을 제시한다. 제시된 방법론을 통해 특정 작업을 위한 로봇 형태 및 동작의 동시 최적화가 가능하다. 위 방법론은 형태 및 동작 변수가 결합된 공간 상에서 목적함수를 가장 많이 감소시키는 구속조건 매니폴드 상에서의 방향을 찾아 최적화를 진행한다. 이전 연구들의 결점을 극복하기 위해 우리는 최근 개발된 반복 미분 동역학(recursive differential dynamics) 알고리즘을 사용한다. 이 알고리즘을 통해 관절 토크 변화와 형태 변화 사이의 해석적 관계를 계산할 수 있다. 따라서, 제시된 방법론을 사용하면 더욱 빠르고 정확한 최적화 결과를 도출할 수 있다. 총 두 가지 수치적 실험을 통해 위 최적화 방법론을 검증하였다: 엔드이펙터가 주어진 궤적을 추종하는 2축 평면 매니퓰레이터, 4족로봇의 보행작업.1 Introduction 1 1.1 Design Optimization of Robotic Devices 1 1.2 Limitations of Previous Works 4 1.3 Main Contributions of This Thesis 5 2 Preliminaries 7 2.1 Lie Group Theory 7 2.1.1 SO(3) and SE(3) 8 2.1.2 Twists and Wrenches 10 2.1.3 Adjoint Mappings 10 2.2 Rigid Body Dynamics 11 2.2.1 Dynamics of a Single Rigid Body 11 2.2.2 Dynamics of Open Chains 12 2.2.3 Dynamics of Floating Bodies 14 2.3 Recursive Differential Dynamics 15 3 Simultaneous Design and Motion Optimization 18 3.1 Problem Definition 18 3.2 Optimization Parameters 20 3.2.1 Design Parameters 20 3.2.2 Motion Parameters 23 3.2.3 Constraints 24 3.2.4 Inertial Changes 26 3.3 Optimization Algorithm Description 27 4 Numerical Experiments31 4.1 2-R Planar Manipulator 31 4.1.1Experimental Settings 31 4.1.2Optimization Results 33 4.2 Quadruped Robot 36 4.2.1Experimental Settings 37 4.2.2Optimization Results 39 5 Conclusion 44 A Appendix 46 A.1 Local parametrization of the design 46 A.2 Design rule for the link 48 A.3 Derivative of the constraints 51 A.3.1 End-effector trajectory 51 A.3.2 Equations of motion of the base for quadruped robots 52 A.4 Laikago Specification 53 Bibliography 55 국문초록 60Maste

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

Hand-eye calibration, constraints and source synchronisation for robotic-assisted minimally invasive surgery

In robotic-assisted minimally invasive surgery (RMIS), the robotic system allows surgeons to remotely control articulated instruments to perform surgical interventions and introduces a potential to implement computer-assisted interventions (CAI). However, the information in the camera must be correctly transformed into the robot coordinate as its movement is controlled by the robot kinematic. Therefore, determining the rigid transformation connecting the coordinates is necessary. Such process is called hand-eye calibration. One of the challenges in solving the hand-eye problem in the RMIS setup is data asynchronicity, which occurs when tracking equipments are integrated into a robotic system and create temporal misalignment. For the calibration itself, noise in the robot and camera motions can be propagated to the calibrated result and as a result of a limited motion range, the error cannot be fully suppressed. Finally, the calibration procedure must be adaptive and simple so a disruption in a surgical workflow is minimal since any change in the setup may require another calibration procedure. We propose solutions to deal with the asynchronicity, noise sensitivity, and a limited motion range. We also propose a potential to use a surgical instrument as the calibration target to reduce the complexity in the calibration procedure. The proposed algorithms are validated through extensive experiments with synthetic and real data from the da Vinci Research Kit and the KUKA robot arms. The calibration performance is compared with existing hand-eye algorithms and it shows promising results. Although the calibration using a surgical instrument as the calibration target still requires a further development, results indicate that the proposed methods increase the calibration performance, and contribute to finding an optimal solution to the hand-eye problem in robotic surgery

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