Kinematic Control of Constrained Robotic Systems
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On the Configurations of Closed Kinematic Chains in Three
On the Configurations of Closed Kinematic Chains in three-dimensional Space Gerhard Zangerl Department of Mathematics, University of Innsbruck Technikestraße 13, 6020 Innsbruck, Austria E-mail: [email protected] Alexander Steinicke Department of Applied Mathematics and Information Technology, Montanuniversitaet Leoben Peter Tunner-Straße 25/I, 8700 Leoben, Austria E-mail: [email protected] Abstract A kinematic chain in three-dimensional Euclidean space consists of n links that are connected by spherical joints. Such a chain is said to be within a closed configuration when its link lengths form a closed polygonal chain in three dimensions. We investigate the space of configurations, described in terms of joint angles of its spherical joints, that satisfy the the loop closure constraint, meaning that the kinematic chain is closed. In special cases, we can find a new set of parameters that describe the diagonal lengths (the distance of the joints from the origin) of the configuration space by a simple domain, namely a cube of dimension n − 3. We expect that the new findings can be applied to various problems such as motion planning for closed kinematic chains or singularity analysis of their configuration spaces. To demonstrate the practical feasibility of the new method, we present numerical examples. 1 Introduction This study is the natural further development of [32] in which closed configurations of a two-dimensional kine- matic chain (KC) in terms of its joint angles were considered. As a generalization, we study the configuration spaces of a three-dimensional closed kinematic chain (CKC) with n links in terms of the joint angles of its spherical joints. -
Mobile Robot Kinematics
Mobile Robot Kinematics We're going to start talking about our mobile robots now. There robots differ from our arms in 2 ways: They have sensors, and they can move themselves around. Because their movement is so different from the arms, we will need to talk about a new style of kinematics: Differential Drive. 1. Differential Drive is how many mobile wheeled robots locomote. 2. Differential Drive robot typically have two powered wheels, one on each side of the robot. Sometimes there are other passive wheels that keep the robot from tipping over. 3. When both wheels turn at the same speed in the same direction, the robot moves straight in that direction. 4. When one wheel turns faster than the other, the robot turns in an arc toward the slower wheel. 5. When the wheels turn in opposite directions, the robot turns in place. 6. We can formally describe the robot behavior as follows: (a) If the robot is moving in a curve, there is a center of that curve at that moment, known as the Instantaneous Center of Curvature (or ICC). We talk about the instantaneous center, because we'll analyze this at each instant- the curve may, and probably will, change in the next moment. (b) If r is the radius of the curve (measured to the middle of the robot) and l is the distance between the wheels, then the rate of rotation (!) around the ICC is related to the velocity of the wheels by: l !(r + ) = v 2 r l !(r − ) = v 2 l Why? The angular velocity is defined as the positional velocity divided by the radius: dθ V = dt r 1 This should make some intuitive sense: the farther you are from the center of rotation, the faster you need to move to get the same angular velocity. -
Abbreviations and Glossary
Appendix A Abbreviations and Glossary Abbreviations are defined and the mathematical symbols and notations used in this book are specified. Furthermore, the random number generator used in this book is referenced. A.1 Abbreviations arccos arccosine BiRRT Bidirectional rapidly growing random tree C-space Configuration space DH Denavit-Hartenberg DLR German aerospace center DOF Degree of freedom FFT Fast fourier transformation IK Inverse kinematics HRI Human-Robot interface LWR Light weight robot MMI Institute of Man-Machine interaction PCA Principal component analysis PRM Probabilistic road map RRT Rapidly growing random tree rulaCapMap Rula-restricted capability map RULA Rapid upper limb assessment SFE Shape fit error TCP Tool center point OV workspace overlap 130 A Abbreviations and Glossary A.2 Mathematical Symbols C configuration space K(q) direct kinematics H set of all homogeneous matrices WR reachable workspace WD dexterous workspace WV versatile workspace F(R,x) function that maps to a homogeneous matrix VRobot voxel space for the robot arm VHuman voxel space for the human arm P set of points on the sphere Np set of point indices for the points on the sphere No set of orientation indices OS set of all homogeneous frames distributed on a sphere MS capability map A.3 Mathematical Notations a scalar value a vector aT vector transposed A matrix AT matrix transposed < a,b > inner product 3 SO(3) group of rotation matrices ∈ IR SO(3) := R ∈ IR 3×3| RRT = I,detR =+1 SE(3) IR 3 × SO(3) A TB reference frame B given in coordinates of reference frame A a ceiling function a floor function A.4 Random Sampling In this book, the drawing of random samples is often used. -
Nyku: a Social Robot for Children with Autism Spectrum Disorders
University of Denver Digital Commons @ DU Electronic Theses and Dissertations Graduate Studies 2020 Nyku: A Social Robot for Children With Autism Spectrum Disorders Dan Stephan Stoianovici University of Denver Follow this and additional works at: https://digitalcommons.du.edu/etd Part of the Disability Studies Commons, Electrical and Computer Engineering Commons, and the Robotics Commons Recommended Citation Stoianovici, Dan Stephan, "Nyku: A Social Robot for Children With Autism Spectrum Disorders" (2020). Electronic Theses and Dissertations. 1843. https://digitalcommons.du.edu/etd/1843 This Thesis is brought to you for free and open access by the Graduate Studies at Digital Commons @ DU. It has been accepted for inclusion in Electronic Theses and Dissertations by an authorized administrator of Digital Commons @ DU. For more information, please contact [email protected],[email protected]. Nyku : A Social Robot for Children with Autism Spectrum Disorders A Thesis Presented to the Faculty of the Daniel Felix Ritchie School of Engineering and Computer Science University of Denver In Partial Fulfillment of the Requirements for the Degree Master of Science by Dan Stoianovici August 2020 Advisor: Dr. Mohammad H. Mahoor c Copyright by Dan Stoianovici 2020 All Rights Reserved Author: Dan Stoianovici Title: Nyku: A Social Robot for Children with Autism Spectrum Disorders Advisor: Dr. Mohammad H. Mahoor Degree Date: August 2020 Abstract The continued growth of Autism Spectrum Disorders (ASD) around the world has spurred a growth in new therapeutic methods to increase the positive outcomes of an ASD diagnosis. It has been agreed that the early detection and intervention of ASD disorders leads to greatly increased positive outcomes for individuals living with the disorders. -
A Review of Parallel Processing Approaches to Robot Kinematics and Jacobian
Technical Report 10/97, University of Karlsruhe, Computer Science Department, ISSN 1432-7864 A Review of Parallel Processing Approaches to Robot Kinematics and Jacobian Dominik HENRICH, Joachim KARL und Heinz WÖRN Institute for Real-Time Computer Systems and Robotics University of Karlsruhe, D-76128 Karlsruhe, Germany e-mail: [email protected] Abstract Due to continuously increasing demands in the area of advanced robot control, it became necessary to speed up the computation. One way to reduce the computation time is to distribute the computation onto several processing units. In this survey we present different approaches to parallel computation of robot kinematics and Jacobian. Thereby, we discuss both the forward and the reverse problem. We introduce a classification scheme and classify the references by this scheme. Keywords: parallel processing, Jacobian, robot kinematics, robot control. 1 Introduction Due to continuously increasing demands in the area of advanced robot control, it became necessary to speed up the computation. Since it should be possible to control the motion of a robot manipulator in real-time, it is necessary to reduce the computation time to less than the cycle rate of the control loop. One way to reduce the computation time is to distribute the computation over several processing units. There are other overviews and reviews on parallel processing approaches to robotic problems. Earlier overviews include [Lee89] and [Graham89]. Lee takes a closer look at parallel approaches in [Lee91]. He tries to find common features in the different problems of kinematics, dynamics and Jacobian computation. The latest summary is from Zomaya et al. [Zomaya96]. -
Department of Mechanical Engineering ME 8492 – Kinematics of Machinery Unit I – Introduction to Mechanism - MCQ Bank 1
ChettinadTech Dept. of MECH Department of Mechanical Engineering ME 8492 – Kinematics of Machinery Unit I – Introduction to Mechanism - MCQ Bank 1. In a reciprocating steam engine, which of the following forms a kinematic link ? (a) cylinder and piston (b) piston rod and connecting rod (c) crank shaft and flywheel (d) flywheel and engine frame Answer: (c) 2. The motion of a piston in the cylinder of a steam engine is an example of (a) completely constrained motion (b) incompletely constrained motion (c) successfully constrained motion (d) none of these Answer: (a) 3. The motion transmitted between the teeth of gears in mesh is (a) sliding (b) rolling (c) may be rolling or sliding depending upon the shape of teeth (d) partly sliding and partly rolling Answer: (d) 4. The cam and follower without a spring forms a (a) lower pair (b) higher pair (c) self closed pair (d) force closed pair Answer: (c) 5. A ball and a socket joint forms a (a) turning pair (b) rolling pair (c) sliding pair (d) spherical pair Answer: (d) 6. The lead screw of a lathe with nut forms a (a) sliding pair (b) rolling pair (c) screw pair (d) turning pair ME 8692 – Finite Element Analysis Page 1 ChettinadTech Dept. of MECH Answer: (c) 7. When the elements of the pair are kept in contact by the action of external forces, the pair is said to be a (a) lower pair (b) higher pair (c) self closed pair (d) force closed pair Answer: (d) 8. Which of the following is a turning pair ? (a) Piston and cylinder of a reciprocating steam engine (b) Shaft with collars at both ends fitted in a circular hole (c) Lead screw of a lathe with nut (d) Ball and socket joint Answer: (b) 9. -
Acknowledgements Acknowl
2161 Acknowledgements Acknowl. B.21 Actuators for Soft Robotics F.58 Robotics in Hazardous Applications by Alin Albu-Schäffer, Antonio Bicchi by James Trevelyan, William Hamel, The authors of this chapter have used liberally of Sung-Chul Kang work done by a group of collaborators involved James Trevelyan acknowledges Surya Singh for de- in the EU projects PHRIENDS, VIACTORS, and tailed suggestions on the original draft, and would also SAPHARI. We want to particularly thank Etienne Bur- like to thank the many unnamed mine clearance experts det, Federico Carpi, Manuel Catalano, Manolo Gara- who have provided guidance and comments over many bini, Giorgio Grioli, Sami Haddadin, Dominic Lacatos, years, as well as Prof. S. Hirose, Scanjack, Way In- Can zparpucu, Florian Petit, Joshua Schultz, Nikos dustry, Japan Atomic Energy Agency, and Total Marine Tsagarakis, Bram Vanderborght, and Sebastian Wolf for Systems for providing photographs. their substantial contributions to this chapter and the William R. Hamel would like to acknowledge work behind it. the US Department of Energy’s Robotics Crosscut- ting Program and all of his colleagues at the na- C.29 Inertial Sensing, GPS and Odometry tional laboratories and universities for many years by Gregory Dudek, Michael Jenkin of dealing with remote hazardous operations, and all We would like to thank Sarah Jenkin for her help with of his collaborators at the Field Robotics Center at the figures. Carnegie Mellon University, particularly James Os- born, who were pivotal in developing ideas for future D.36 Motion for Manipulation Tasks telerobots. by James Kuffner, Jing Xiao Sungchul Kang acknowledges Changhyun Cho, We acknowledge the contribution that the authors of the Woosub Lee, Dongsuk Ryu at KIST (Korean Institute first edition made to this chapter revision, particularly for Science and Technology), Korea for their provid- Sect. -
Forward and Inverse Kinematics Analysis of Denso Robot
Proceedings of the International Symposium of Mechanism and Machine Science, 2017 AzC IFToMM – Azerbaijan Technical University 11-14 September 2017, Baku, Azerbaijan Forward and Inverse Kinematics Analysis of Denso Robot Mehmet Erkan KÜTÜK 1*, Memik Taylan DAŞ2, Lale Canan DÜLGER1 1*Mechanical Engineering Department, University of Gaziantep Gaziantep/ Turkey E-mail: [email protected] 2 Mechanical Engineering Department, University of Kırıkkale Abstract used Robotic Toolbox in forward kinematics analysis of A forward and inverse kinematic analysis of 6 axis an industrial robot [4]. DENSO robot with closed form solution is performed in This study includes kinematics of robot arm which is this paper. Robotics toolbox provides a great simplicity to available Gaziantep University, Mechanical Engineering us dealing with kinematics of robots with the ready Department, Mechatronics Lab. Forward and Inverse functions on it. However, making calculations in kinematics analysis are performed. Robotics Toolbox is traditional way is important to dominate the kinematics also applied to model Denso robot system. A GUI is built which is one of the main topics of robotics. Robotic for practical use of robotic system. toolbox in Matlab® is used to model Denso robot system. GUI studies including Robotic Toolbox are given with 2. Robot Arm Kinematics simulation examples. Keywords: Robot Kinematics, Simulation, Denso The robot kinematics can be categorized into two Robot, Robotic Toolbox, GUI main parts; forward and inverse kinematics. Forward kinematics problem is not difficult to perform and there is no complexity in deriving the equations in contrast to the 1. Introduction inverse kinematics. Especially nonlinear equations make the inverse kinematics problem complex. -
Kinematic Singularities of Mechanisms Revisited
IMA Conference on Mathematics of Robotics 9 – 11 September 2015, St Anne’s College, University of Oxford 1 Kinematic Singularities of Mechanisms Revisited By Andreas M¨uller1, Dimiter Zlatanov2 1Johannes Kepler University, Linz, Austria; 2University of Genoa, Genoa, Italy Abstract The paper revisits the definition and the identification of the singularities of kinematic chains and mechanisms. The degeneracy of the kinematics of an articulated system of rigid bodies cannot always be identified with the singularities of the configuration space. Local analysis can help identify kinematic chain singularities and better understand the way the motion characteristics change at such configurations. An example is shown that exhibits a kinematic singularity although its configuration space is a smooth manifold. 1. Introduction Kinematic singularities of a mechanism are critical configurations that can lead to a loss of structural stability or controllability. This has been a central topic in mechanism theory and still is a field of active research. A systematic approach to the study of singular configurations involves a mathematical model for the kinematic chain and its interaction with the environment via inputs and outputs. Thereupon critical configurations can be identified for the kinematic chain itself and for the input and output relations. A kinematic chain is a system of rigid bodies (links), some pairs of which are connected with joints. It is defined by specifying exactly which links are jointed (by a connectiv- ity graph [Wittenburg (1994)]), the type of each joint, and the joint's locations in the adjacent links. Mathematically, a kinematic chain is modeled by specifying its possible motions as a subset of the smooth curves on an ambient manifold, usually assumed to have a global parametrization, Vn. -
Planar Kinematics
Introduction to Robotics, H. Harry Asada 1 Chapter 4 Planar Kinematics Kinematics is Geometry of Motion. It is one of the most fundamental disciplines in robotics, providing tools for describing the structure and behavior of robot mechanisms. In this chapter, we will discuss how the motion of a robot mechanism is described, how it responds to actuator movements, and how the individual actuators should be coordinated to obtain desired motion at the robot end-effecter. These are questions central to the design and control of robot mechanisms. To begin with, we will restrict ourselves to a class of robot mechanisms that work within a plane, i.e. Planar Kinematics. Planar kinematics is much more tractable mathematically, compared to general three-dimensional kinematics. Nonetheless, most of the robot mechanisms of practical importance can be treated as planar mechanisms, or can be reduced to planar problems. General three-dimensional kinematics, on the other hand, needs special mathematical tools, which will be discussed in later chapters. 4.1 Planar Kinematics of Serial Link Mechanisms Example 4.1 Consider the three degree-of-freedom planar robot arm shown in Figure 4.1.1. The arm consists of one fixed link and three movable links that move within the plane. All the links are connected by revolute joints whose joint axes are all perpendicular to the plane of the links. There is no closed-loop kinematic chain; hence, it is a serial link mechanism. y A 3 E End Effecter ⎛ xe ⎞ Link 3 ⎜ ⎟ ⎝ ye ⎠ A 2 θ3 φ B e A1 Link 2 Joint 3 θ 2 Link 1 A Joint 2 Joint 1 θ O 1 x Link 0 Figure 4.1.1 Three dof planar robot with three revolute joints To describe this robot arm, a few geometric parameters are needed. -
Robot Systems Integration
Transformative Research and Robotics Kazuhiro Kosuge Distinguished Professor Department of Robotics Tohoku University 2020 IEEE Vice President-elect for Technical Activities IEEE Fellow, JSME Fellow, SICE Fellow, RSJ Fellow, JSAE Fellow My brief history • March 1978 Bachelor of Engineering, Department of Control Engineering, Tokyo Institute of Technology • Marcy 1980 Master of Engineering, Department of Control Engineering, Tokyo Institute of Technology • April 1980 Research staff, Department of Production Engineering Nippondenso (Denso) Corporation • October 1982 Research Associate, Tokyo Institute of Technology • July 1988 Dr. of Engineering, Tokyo Institute of Technology • September 1989 - August 1990 Visiting Research Scientist, Department of Mechanical Engineering, Massachusetts Institute of Technology • September 1990 Associate Professor, Faculty of Engineering, Nagoya University • March 1995 Professor, School of Engineering, Tohoku University • April 1997 Professor, Graduate School of Engineering, Tohoku University • December 2018 Tohoku University Distinguished Professor 略 歴 • 1978年3月 東京工業大学工学部制御工学科卒業 • 1980年3月 東京工業大学大学院理工学研究科修士課程修了(制御工学専攻,工学修士) • 1980年4月 日本電装株式会社(現 株式会社デンソー) • 1982年10月 東京工業大学工学部制御工学科助手(工学部) • 1988年7月 東京工業大学大学院理工学研究科 工学博士(制御工学専攻) • 1989年9月-1990年8月 米国マサチューセッツ工科大学機械工学科客員研究員 (Visiting Research Scientist, Department of Mechanical Engineering, Massachusetts Institute of Technology) • 1990年 9月 名古屋大学 助教授(工学部) • 1995年 3月 東北大学 教授(工学部) • 1997年 4月 東北大学 教授(工学研究科)大学院重点化による配置換 • 2018年12月 東北大学 Distinguished Professor My another -
1.0 Simple Mechanism 1.1 Link ,Kinematic Chain
SYLLABUS 1.0 Simple mechanism 1.1 Link ,kinematic chain, mechanism, machine 1.2 Inversion, four bar link mechanism and its inversion 1.3 Lower pair and higher pair 1.4 Cam and followers 2.0 Friction 2.1 Friction between nut and screw for square thread, screw jack 2.2 Bearing and its classification, Description of roller, needle roller& ball bearings. 2.3 Torque transmission in flat pivot& conical pivot bearings. 2.4 Flat collar bearing of single and multiple types. 2.5 Torque transmission for single and multiple clutches 2.6 Working of simple frictional brakes.2.7 Working of Absorption type of dynamometer 3.0 Power Transmission 3.1 Concept of power transmission 3.2 Type of drives, belt, gear and chain drive. 3.3 Computation of velocity ratio, length of belts (open and cross)with and without slip. 3.4 Ratio of belt tensions, centrifugal tension and initial tension. 3.5 Power transmitted by the belt. 3.6 Determine belt thickness and width for given permissible stress for open and crossed belt considering centrifugal tension. 3.7 V-belts and V-belts pulleys. 3.8 Concept of crowning of pulleys. 3.9 Gear drives and its terminology. 3.10 Gear trains, working principle of simple, compound, reverted and epicyclic gear trains. 4.0 Governors and Flywheel 4.1 Function of governor 4.2 Classification of governor 4.3 Working of Watt, Porter, Proel and Hartnell governors. 4.4 Conceptual explanation of sensitivity, stability and isochronisms. 4.5 Function of flywheel. 4.6 Comparison between flywheel &governor.