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

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)

Industrial Robotics

This book covers a wide range of topics relating to advanced industrial robotics, sensors and automation technologies. Although being highly technical and complex in nature, the papers presented in this book represent some of the latest cutting edge technologies and advancements in industrial robotics technology. This book covers topics such as networking, properties of manipulators, forward and inverse robot arm kinematics, motion path-planning, machine vision and many other practical topics too numerous to list here. The authors and editor of this book wish to inspire people, especially young ones, to get involved with robotic and mechatronic engineering technology and to develop new and exciting practical applications, perhaps using the ideas and concepts presented herein

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

Improved Industrial Robot Positional Accuracy for Machining with Bias Correction

Robotic machining has the potential to provide advantages as a substitute for conventional CNC machine tool operations. However, conventional industrial robots are restricted to low accuracy tasks due to their poor positional accuracy. This creates challenges in achieving the tolerances required for machining tasks. Data-based modelling of the positional error data is a potential solution which learns the positional errors in order to compensate and minimise them. There has been some success in improving industrial robot accuracy in research literature, by first calibrating the kinematic model and then using machine learning (ML)-based bias correction to learn the positional errors. However, the limitations of ML-based bias correction applied to the industrial robot positional accuracy problem have not been fully explored with the accuracies required to achieve tight machining tolerances. Mapping the positional errors with a greater resolution of training data, and reducing the burden on bias correction by calibrating the kinematic model with a higher level of calibration, are two examples which have the potential to improve accuracy. This thesis focusses on both training data resolution and bias reduction to maximise outcomes whilst informing trade-offs when using ML-based bias correction in this application. The key finding of this thesis is that substantial gains in accuracy can be achieved using ML-based bias correction and that the accuracy limit can be achieved with practicable amounts of data gathering and processing. Also that calibration prior to bias correction did not significantly improve overall accuracy for the cases investigated. This suggests that data may be better utilised in training the bias corrector rather than for calibration of the physical model. In conclusion, ML-based bias correction methods can provide a solution that provides substantial gains in positional accuracy for conventional industrial robots, bringing them to a level that may facilitate broader adoption in machining applications

Towards Fault Diagnosis in Reconfigurable Robot

東京電機大学201

Inverse Kinematic Analysis of Robot Manipulators

An important part of industrial robot manipulators is to achieve desired position and orientation of end effector or tool so as to complete the pre-specified task. To achieve the above stated goal one should have the sound knowledge of inverse kinematic problem. The problem of getting inverse kinematic solution has been on the outline of various researchers and is deliberated as thorough researched and mature problem. There are many fields of applications of robot manipulators to execute the given tasks such as material handling, pick-n-place, planetary and undersea explorations, space manipulation, and hazardous field etc. Moreover, medical field robotics catches applications in rehabilitation and surgery that involve kinematic, dynamic and control operations. Therefore, industrial robot manipulators are required to have proper knowledge of its joint variables as well as understanding of kinematic parameters. The motion of the end effector or manipulator is controlled by their joint actuator and this produces the required motion in each joints. Therefore, the controller should always supply an accurate value of joint variables analogous to the end effector position. Even though industrial robots are in the advanced stage, some of the basic problems in kinematics are still unsolved and constitute an active focus for research. Among these unsolved problems, the direct kinematics problem for parallel mechanism and inverse kinematics for serial chains constitute a decent share of research domain. The forward kinematics of robot manipulator is simpler problem and it has unique or closed form solution. The forward kinematics can be given by the conversion of joint space to Cartesian space of the manipulator. On the other hand inverse kinematics can be determined by the conversion of Cartesian space to joint space. The inverse kinematic of the robot manipulator does not provide the closed form solution. Hence, industrial manipulator can achieve a desired task or end effector position in more than one configuration. Therefore, to achieve exact solution of the joint variables has been the main concern to the researchers. A brief introduction of industrial robot manipulators, evolution and classification is presented. The basic configurations of robot manipulator are demonstrated and their benefits and drawbacks are deliberated along with the applications. The difficulties to solve forward and inverse kinematics of robot manipulator are discussed and solution of inverse kinematic is introduced through conventional methods. In order to accomplish the desired objective of the work and attain the solution of inverse kinematic problem an efficient study of the existing tools and techniques has been done. A review of literature survey and various tools used to solve inverse kinematic problem on different aspects is discussed. The various approaches of inverse kinematic solution is categorized in four sections namely structural analysis of mechanism, conventional approaches, intelligence or soft computing approaches and optimization based approaches. A portion of important and more significant literatures are thoroughly discussed and brief investigation is made on conclusions and gaps with respect to the inverse kinematic solution of industrial robot manipulators. Based on the survey of tools and techniques used for the kinematic analysis the broad objective of the present research work is presented as; to carry out the kinematic analyses of different configurations of industrial robot manipulators. The mathematical modelling of selected robot manipulator using existing tools and techniques has to be made for the comparative study of proposed method. On the other hand, development of new algorithm and their mathematical modelling for the solution of inverse kinematic problem has to be made for the analysis of quality and efficiency of the obtained solutions. Therefore, the study of appropriate tools and techniques used for the solution of inverse kinematic problems and comparison with proposed method is considered. Moreover, recommendation of the appropriate method for the solution of inverse kinematic problem is presented in the work. Apart from the forward kinematic analysis, the inverse kinematic analysis is quite complex, due to its non-linear formulations and having multiple solutions. There is no unique solution for the inverse kinematics thus necessitating application of appropriate predictive models from the soft computing domain. Artificial neural network (ANN) can be gainfully used to yield the desired results. Therefore, in the present work several models of artificial neural network (ANN) are used for the solution of the inverse kinematic problem. This model of ANN does not rely on higher mathematical formulations and are adept to solve NP-hard, non-linear and higher degree of polynomial equations. Although intelligent approaches are not new in this field but some selected models of ANN and their hybridization has been presented for the comparative evaluation of inverse kinematic. The hybridization scheme of ANN and an investigation has been made on accuracies of adopted algorithms. On the other hand, any Optimization algorithms which are capable of solving various multimodal functions can be implemented to solve the inverse kinematic problem. To overcome the problem of conventional tool and intelligent based method the optimization based approach can be implemented. In general, the optimization based approaches are more stable and often converge to the global solution. The major problem of ANN based approaches are its slow convergence and often stuck in local optimum point. Therefore, in present work different optimization based approaches are considered. The formulation of the objective function and associated constrained are discussed thoroughly. The comparison of all adopted algorithms on the basis of number of solutions, mathematical operations and computational time has been presented. The thesis concludes the summary with contributions and scope of the future research work

Pattern Recognition

A wealth of advanced pattern recognition algorithms are emerging from the interdiscipline between technologies of effective visual features and the human-brain cognition process. Effective visual features are made possible through the rapid developments in appropriate sensor equipments, novel filter designs, and viable information processing architectures. While the understanding of human-brain cognition process broadens the way in which the computer can perform pattern recognition tasks. The present book is intended to collect representative researches around the globe focusing on low-level vision, filter design, features and image descriptors, data mining and analysis, and biologically inspired algorithms. The 27 chapters coved in this book disclose recent advances and new ideas in promoting the techniques, technology and applications of pattern recognition

Gaussian processes for state space models and change point detection

This thesis details several applications of Gaussian processes (GPs) for enhanced time series modeling. We first cover different approaches for using Gaussian processes in time series problems. These are extended to the state space approach to time series in two different problems. We also combine Gaussian processes and Bayesian online change point detection (BOCPD) to increase the generality of the Gaussian process time series methods. These methodologies are evaluated on predictive performance on six real world data sets, which include three environmental data sets, one financial, one biological, and one from industrial well drilling. Gaussian processes are capable of generalizing standard linear time series models. We cover two approaches: the Gaussian process time series model (GPTS) and the autoregressive Gaussian process (ARGP). We cover a variety of methods that greatly reduce the computational and memory complexity of Gaussian process approaches, which are generally cubic in computational complexity. Two different improvements to state space based approaches are covered. First, Gaussian process inference and learning (GPIL) generalizes linear dynamical systems (LDS), for which the Kalman filter is based, to general nonlinear systems for nonparametric system identification. Second, we address pathologies in the unscented Kalman filter (UKF). We use Gaussian process optimization (GPO) to learn UKF settings that minimize the potential for sigma point collapse. We show how to embed mentioned Gaussian process approaches to time series into a change point framework. Old data, from an old regime, that hinders predictive performance is automatically and elegantly phased out. The computational improvements for Gaussian process time series approaches are of even greater use in the change point framework. We also present a supervised framework learning a change point model when change point labels are available in training.I would like to thank Rockwell Collins, formerly DataPath, Inc., which funded my studentship