Robotics I. April 1, the motion starts and ends with zero Cartesian velocity and acceleration;
|
|
- Kathryn Flynn
- 5 years ago
- Views:
Transcription
1 Robotics I April, 6 Consider a planar R robot with links of length l = and l =.5. he end-effector should move smoothly from an initial point p in to a final point p fin in the robot workspace so that the motion starts and ends with zero Cartesian velocity and acceleration; at the start, the robot is in the right arm inverse kinematics solution i.e., with positive q, and remains in this type of solution throughout the motion; coordinated motion is enforced to the joints; symmetric limits on joint velocity, acceleration, and jerk are satisfied: q i V i, q i A i, q i J i, i =,. In order to address this motion task, choose a class of trajectories and determine, within the considered class, a minimum time trajectory, given the following position data p in = p. fin =. and joint limits V = [rad/s], A = 3 [rad/s ], J = 3 [rad/s 3 ], V = [rad/s], A = 7.5 [rad/s ], J = 7 [rad/s 3 ]. Provide the minimum feasible time obtained and the maximum absolute values attained by the velocity and the acceleration at the two joints. At the trajectory midpoint, t = /, determine the values of the end-effector Cartesian velocity v and acceleration a, and draw the robot in its current configuration together with the vectors v and a. [8 minutes; open books]
2 Solution April, 6 In view of the nature of the given robot motion limits, it is highly recommended to define the trajectory in the joint space. he direct and inverse kinematics of the R planar robot are given by px l c + l c p = = = fq l s + l s q = with q +/ q +/ = p y AAN{py l + l c p x l s, p x l + l c + p y l s } AAN{s, c } c = p x + p y l l, s = ± c l l, = f p, and where the +/ associated as index to the joint angles q and q mean that for their evaluation the + or, respectively, the sign has been used in the definition of s. Substituting the link lengths and the problem data for p = p in and p = p fin, and picking up the solution with q + > yields q in = 69.5 = [rad], q.3 fin =. = [rad]..784 aking into account the smoothness requirement and the boundary conditions on velocity and acceleration, we choose a polynomial trajectory of degree 5 for each joint. In the double normalized form, its expression is qτ = q in + q τ 3 5τ 4 + 6τ 5.97, q = q fin q in = [rad], τ = t [, ] In order to obtain the maximum values reached along this trajectory by the velocity, acceleration, and jerk, which should satisfy the given limits, we compute the first four time derivatives: q = q 3τ 6τ 3 + 3τ 4 q = q 6τ 8τ + τ 3 q = q 6 36τ + 36τ 3. q = q τ. 4 We analyze the constraints imposed by the joint limits starting with the one with highest differential order. We will work now with scalar quantities, i.e., joint by joint, dropping for simplicity the joint index. he maximum jerk in the closed interval τ [, ] occurs either at the boundaries or where the fourth derivative is zero: q = q = 6 q 3,. q τ τ =.5 q.5 = 3 q 3.
3 hus, the minimum motion time that satisfies the jerk limit is given by 6 q q τ J 3 =: J. J he maximum acceleration occurs where the third derivative is zero no need to check the value at the boundaries, since we have q = q = by construction: 3 q τ = 6τ + 6τ τ =.5 ± qτ = ± q 6. he minimum motion time that satisfies the acceleration limit is given by q qτ A =: A. A Similarly, the maximum velocity occurs where the second derivative is zero again, no need to check the value at the boundaries, since q = q = : qτ = τ 3τ + τ τ = {,.5, } q.5 = 3 q 6, and thus qτ V 3 q 6 V =: V. As a result, the minimum feasible motion time is obtained as { } q q = max { J, A, V } = max J,.48 q,.875. A V Using the data all in radians of the problem at hand, we compute the minimum motion time for the first joint as = max { J,, A,, V, } = max {.579,.9468, 3.696} = [s], where the velocity limit is the most constraining one. Similarly, for the second joint it is = max { J,, A,, V, } = max {.787,.669,.5336} =.787 [s] and the jerk will be the variable reaching first its limit. Since coordinated motion of the joints should be enforced, the common minimum motion time will be = max {, } = = [s], with the second joint traveling much slower than it could in principle. he trajectory profiles of position, velocity, acceleration, and jerk of the two joints are shown in Figs. 3. he peak velocity of the two joints is reached at t = / =.8463 s max q t = q.8463 = [rad/s], max q t = q.8463 =.89 [rad/s], while the peak acceleration in module is attained at t =.5 ± 3/6, namely at t =.783 s max positive acceleration and t =.93 s max negative acceleration = max deceleration max q t = q.783 =.8339 [rad/s ], max q t = q.783 = [rad/s ]. 3
4 3 Joint motion for = Joint velocity for = position rad.5 velocity rad/s time s time s Figure : Position [left] and velocity [right] of joint blue, solid and joint red, dashed Joint acceleration for = Joint jerk for = acceleration rad/s.. jerk rad/s time s time s Figure : Acceleration [left] and jerk [right] of joint blue, solid and joint red, dashed We note also that coordinated motion is symmetric w.r.t. to the total time for all, and thus also for. herefore, the configuration reached at t = / will simply be q := q = q in + q = q in + q fin = 85.8 = [rad] Moreover, it is q := q = 3 q = 6.56 [ /s] =.89 [rad/s], q := q =. he robot analytic Jacobian Jq = fq/ q and its time derivative Hq, q = Jq, l s + l s l s Jq = l c + l c l c l c q + l c q + q l c q + q, Hq, q =, l s q + l s q + q l s q + q 4
5 .6 Cartesian motion of the R robot Figure 3: he planar R robot arm in its initial configuration blue, at the midpoint of the trajectory red, and in the final configuration green, with the Cartesian path traced by its endeffector thin blue line. he two arrows placed at the midpoint represent the end-effector velocity black and acceleration magenta, respectively. heir length has been scaled by a factor to fit. take the numerical values at q = q, q = q J := Jq = , J := Hq, q = herefore, the required Cartesian velocity and acceleration of the robot end-effector at the trajectory midpoint are ṗ = J q = [m/s] p = J q + J q = J q = [m/s ]. 5
, respectively to the inverse and the inverse differential problem. Check the correctness of the obtained results. Exercise 2 y P 2 P 1.
Robotics I July 8 Exercise Define the orientation of a rigid body in the 3D space through three rotations by the angles α β and γ around three fixed axes in the sequence Y X and Z and determine the associated
More informationRobotics I. June 6, 2017
Robotics I June 6, 217 Exercise 1 Consider the planar PRPR manipulator in Fig. 1. The joint variables defined therein are those used by the manufacturer and do not correspond necessarily to a Denavit-Hartenberg
More informationRobotics I. Figure 1: Initial placement of a rigid thin rod of length L in an absolute reference frame.
Robotics I September, 7 Exercise Consider the rigid body in Fig., a thin rod of length L. The rod will be rotated by an angle α around the z axis, then by an angle β around the resulting x axis, and finally
More informationLecture 8: Kinematics: Path and Trajectory Planning
Lecture 8: Kinematics: Path and Trajectory Planning Concept of Configuration Space c Anton Shiriaev. 5EL158: Lecture 8 p. 1/20 Lecture 8: Kinematics: Path and Trajectory Planning Concept of Configuration
More informationRobotics I June 11, 2018
Exercise 1 Robotics I June 11 018 Consider the planar R robot in Fig. 1 having a L-shaped second link. A frame RF e is attached to the gripper mounted on the robot end effector. A B y e C x e Figure 1:
More informationInverse differential kinematics Statics and force transformations
Robotics 1 Inverse differential kinematics Statics and force transformations Prof Alessandro De Luca Robotics 1 1 Inversion of differential kinematics! find the joint velocity vector that realizes a desired
More informationq 1 F m d p q 2 Figure 1: An automated crane with the relevant kinematic and dynamic definitions.
Robotics II March 7, 018 Exercise 1 An automated crane can be seen as a mechanical system with two degrees of freedom that moves along a horizontal rail subject to the actuation force F, and that transports
More informationRobotics I. February 6, 2014
Robotics I February 6, 214 Exercise 1 A pan-tilt 1 camera sensor, such as the commercial webcams in Fig. 1, is mounted on the fixed base of a robot manipulator and is used for pointing at a (point-wise)
More information13 Path Planning Cubic Path P 2 P 1. θ 2
13 Path Planning Path planning includes three tasks: 1 Defining a geometric curve for the end-effector between two points. 2 Defining a rotational motion between two orientations. 3 Defining a time function
More informationRobotics I. Test November 29, 2013
Exercise 1 [6 points] Robotics I Test November 9, 013 A DC motor is used to actuate a single robot link that rotates in the horizontal plane around a joint axis passing through its base. The motor is connected
More informationRobotics 1 Inverse kinematics
Robotics 1 Inverse kinematics Prof. Alessandro De Luca Robotics 1 1 Inverse kinematics what are we looking for? direct kinematics is always unique; how about inverse kinematics for this 6R robot? Robotics
More informationRobotics 1 Inverse kinematics
Robotics 1 Inverse kinematics Prof. Alessandro De Luca Robotics 1 1 Inverse kinematics what are we looking for? direct kinematics is always unique; how about inverse kinematics for this 6R robot? Robotics
More informationCase Study: The Pelican Prototype Robot
5 Case Study: The Pelican Prototype Robot The purpose of this chapter is twofold: first, to present in detail the model of the experimental robot arm of the Robotics lab. from the CICESE Research Center,
More informationRobotics 1 Inverse kinematics
Robotics 1 Inverse kinematics Prof. Alessandro De Luca Robotics 1 1 Inverse kinematics what are we looking for? direct kinematics is always unique; how about inverse kinematics for this 6R robot? Robotics
More informationDifferential Kinematics
Differential Kinematics Relations between motion (velocity) in joint space and motion (linear/angular velocity) in task space (e.g., Cartesian space) Instantaneous velocity mappings can be obtained through
More informationRobotics I. Classroom Test November 21, 2014
Robotics I Classroom Test November 21, 2014 Exercise 1 [6 points] In the Unimation Puma 560 robot, the DC motor that drives joint 2 is mounted in the body of link 2 upper arm and is connected to the joint
More informationTrajectory-tracking control of a planar 3-RRR parallel manipulator
Trajectory-tracking control of a planar 3-RRR parallel manipulator Chaman Nasa and Sandipan Bandyopadhyay Department of Engineering Design Indian Institute of Technology Madras Chennai, India Abstract
More informationExample: RR Robot. Illustrate the column vector of the Jacobian in the space at the end-effector point.
Forward kinematics: X e = c 1 + c 12 Y e = s 1 + s 12 = s 1 s 12 c 1 + c 12, = s 12 c 12 Illustrate the column vector of the Jacobian in the space at the end-effector point. points in the direction perpendicular
More informationMEAM 520. More Velocity Kinematics
MEAM 520 More Velocity Kinematics Katherine J. Kuchenbecker, Ph.D. General Robotics, Automation, Sensing, and Perception Lab (GRASP) MEAM Department, SEAS, University of Pennsylvania Lecture 12: October
More informationCh. 5: Jacobian. 5.1 Introduction
5.1 Introduction relationship between the end effector velocity and the joint rates differentiate the kinematic relationships to obtain the velocity relationship Jacobian matrix closely related to the
More informationRobot Manipulator Control. Hesheng Wang Dept. of Automation
Robot Manipulator Control Hesheng Wang Dept. of Automation Introduction Industrial robots work based on the teaching/playback scheme Operators teach the task procedure to a robot he robot plays back eecute
More information(W: 12:05-1:50, 50-N202)
2016 School of Information Technology and Electrical Engineering at the University of Queensland Schedule of Events Week Date Lecture (W: 12:05-1:50, 50-N202) 1 27-Jul Introduction 2 Representing Position
More informationLecture Schedule Week Date Lecture (M: 2:05p-3:50, 50-N202)
J = x θ τ = J T F 2018 School of Information Technology and Electrical Engineering at the University of Queensland Lecture Schedule Week Date Lecture (M: 2:05p-3:50, 50-N202) 1 23-Jul Introduction + Representing
More informationIn most robotic applications the goal is to find a multi-body dynamics description formulated
Chapter 3 Dynamics Mathematical models of a robot s dynamics provide a description of why things move when forces are generated in and applied on the system. They play an important role for both simulation
More informationRobotics I Kinematics, Dynamics and Control of Robotic Manipulators. Velocity Kinematics
Robotics I Kinematics, Dynamics and Control of Robotic Manipulators Velocity Kinematics Dr. Christopher Kitts Director Robotic Systems Laboratory Santa Clara University Velocity Kinematics So far, we ve
More informationan expression, in terms of t, for the distance of the particle from O at time [3]
HORIZON EDUCATION SINGAPORE Additional Mathematics Practice Questions: Kinematics Set 1 1 A particle moves in a straight line so that t seconds after passing through O, its velocity v cm s -1, is given
More informationRobotics & Automation. Lecture 25. Dynamics of Constrained Systems, Dynamic Control. John T. Wen. April 26, 2007
Robotics & Automation Lecture 25 Dynamics of Constrained Systems, Dynamic Control John T. Wen April 26, 2007 Last Time Order N Forward Dynamics (3-sweep algorithm) Factorization perspective: causal-anticausal
More informationRobotics. Dynamics. Marc Toussaint U Stuttgart
Robotics Dynamics 1D point mass, damping & oscillation, PID, dynamics of mechanical systems, Euler-Lagrange equation, Newton-Euler recursion, general robot dynamics, joint space control, reference trajectory
More informationDisplacement, Velocity and Acceleration in one dimension
Displacement, Velocity and Acceleration in one dimension In this document we consider the general relationship between displacement, velocity and acceleration. Displacement, velocity and acceleration are
More informationAdvanced Robotic Manipulation
Advanced Robotic Manipulation Handout CS37A (Spring 017) Solution Set #3 Problem 1 - Inertial properties In this problem, you will explore the inertial properties of a manipulator at its end-effector.
More informationControl Synthesis for Dynamic Contact Manipulation
Proceedings of the 2005 IEEE International Conference on Robotics and Automation Barcelona, Spain, April 2005 Control Synthesis for Dynamic Contact Manipulation Siddhartha S. Srinivasa, Michael A. Erdmann
More informationAutomatic Control Motion planning
Automatic Control Motion planning (luca.bascetta@polimi.it) Politecnico di Milano Dipartimento di Elettronica, Informazione e Bioingegneria Motivations 2 Electric motors are used in many different applications,
More informationME5286 Robotics Spring 2017 Quiz 2
Page 1 of 5 ME5286 Robotics Spring 2017 Quiz 2 Total Points: 30 You are responsible for following these instructions. Please take a minute and read them completely. 1. Put your name on this page, any other
More informationRobot Dynamics II: Trajectories & Motion
Robot Dynamics II: Trajectories & Motion Are We There Yet? METR 4202: Advanced Control & Robotics Dr Surya Singh Lecture # 5 August 23, 2013 metr4202@itee.uq.edu.au http://itee.uq.edu.au/~metr4202/ 2013
More informationPosition and orientation of rigid bodies
Robotics 1 Position and orientation of rigid bodies Prof. Alessandro De Luca Robotics 1 1 Position and orientation right-handed orthogonal Reference Frames RF A A p AB B RF B rigid body position: A p AB
More informationRobotics: Tutorial 3
Robotics: Tutorial 3 Mechatronics Engineering Dr. Islam Khalil, MSc. Omar Mahmoud, Eng. Lobna Tarek and Eng. Abdelrahman Ezz German University in Cairo Faculty of Engineering and Material Science October
More informationGiven U, V, x and θ perform the following steps: a) Find the rotation angle, φ, by which u 1 is rotated in relation to x 1
1 The Jacobian can be expressed in an arbitrary frame, such as the base frame located at the first joint, the hand frame located at the end-effector, or the global frame located somewhere else. The SVD
More informationLecture «Robot Dynamics» : Kinematics 3
Lecture «Robot Dynamics» : Kinematics 3 151-0851-00 V lecture: CAB G11 Tuesday 10:15-12:00, every week exercise: HG G1 Wednesday 8:15-10:00, according to schedule (about every 2nd week) office hour: LEE
More informationA scaling algorithm for the generation of jerk-limited trajectories in the operational space
A scaling algorithm for the generation of jerk-limited trajectories in the operational space Corrado Guarino Lo Bianco 1, Fabio Ghilardelli Dipartimento di Ingegneria dell Informazione, University of Parma,
More informationRobotics 2 Robot Interaction with the Environment
Robotics 2 Robot Interaction with the Environment Prof. Alessandro De Luca Robot-environment interaction a robot (end-effector) may interact with the environment! modifying the state of the environment
More informationAP Physics C Mechanics Vectors
1 AP Physics C Mechanics Vectors 2015 12 03 www.njctl.org 2 Scalar Versus Vector A scalar has only a physical quantity such as mass, speed, and time. A vector has both a magnitude and a direction associated
More informationDYNAMICS OF PARALLEL MANIPULATOR
DYNAMICS OF PARALLEL MANIPULATOR PARALLEL MANIPULATORS 6-degree of Freedom Flight Simulator BACKGROUND Platform-type parallel mechanisms 6-DOF MANIPULATORS INTRODUCTION Under alternative robotic mechanical
More informationAnalysis of the Effect of Number of Knots in a Trajectory on Motion Characteristics of a 3R Planar Manipulator
Analysis of the Effect of Number of Knots in a Trajectory on Motion Characteristics of a Planar Maniulator Suarno Bhattacharyya & Tarun Kanti Naskar Mechanical Engineering Deartment, Jadavur University,
More informationLecture «Robot Dynamics»: Dynamics and Control
Lecture «Robot Dynamics»: Dynamics and Control 151-0851-00 V lecture: CAB G11 Tuesday 10:15 12:00, every week exercise: HG E1.2 Wednesday 8:15 10:00, according to schedule (about every 2nd week) Marco
More informationControl of constrained spatial three-link flexible manipulators
Control of constrained spatial three-link flexible manipulators Sinan Kilicaslan, M. Kemal Ozgoren and S. Kemal Ider Gazi University/Mechanical Engineering Department, Ankara, Turkey Middle East Technical
More informationWe are IntechOpen, the world s leading publisher of Open Access books Built by scientists, for scientists. International authors and editors
We are IntechOpen, the world s leading publisher of Open Access books Built by scientists, for scientists 3,350 108,000 1.7 M Open access books available International authors and editors Downloads Our
More informationOperational Space Control of Constrained and Underactuated Systems
Robotics: Science and Systems 2 Los Angeles, CA, USA, June 27-3, 2 Operational Space Control of Constrained and Underactuated Systems Michael Mistry Disney Research Pittsburgh 472 Forbes Ave., Suite Pittsburgh,
More informationREDUCING the torque needed to execute a given robot
IEEE ROBOTICS AND AUTOMATION LETTERS. PREPRINT VERSION. ACCEPTED JANUARY, 29 Stable Torque Optimization for Redundant Robots using a Short Preview Khaled Al Khudir Gaute Halvorsen Leonardo Lanari Alessandro
More informationRIGID BODY MOTION (Section 16.1)
RIGID BODY MOTION (Section 16.1) There are cases where an object cannot be treated as a particle. In these cases the size or shape of the body must be considered. Rotation of the body about its center
More informationCONSTANT KINETIC ENERGY ROBOT TRAJECTORY PLANNING
PERIODICA POLYTECHNICA SER. MECH. ENG. VOL. 43, NO. 2, PP. 213 228 (1999) CONSTANT KINETIC ENERGY ROBOT TRAJECTORY PLANNING Zoltán ZOLLER and Peter ZENTAY Department of Manufacturing Engineering Technical
More informationRobotics I Midterm classroom test November 24, 2017
xercise [8 points] Robotics I Midterm classroom test November, 7 Consider the -dof (RPR) planar robot in ig., where the joint coordinates r = ( r r r have been defined in a free, arbitrary way, with reference
More informationExercise 1b: Differential Kinematics of the ABB IRB 120
Exercise 1b: Differential Kinematics of the ABB IRB 120 Marco Hutter, Michael Blösch, Dario Bellicoso, Samuel Bachmann October 5, 2016 Abstract The aim of this exercise is to calculate the differential
More information14 F Time Optimal Control
14 F Time Optimal Control The main job of an industrial robot is to move an object on a pre-specified path, rest to rest, repeatedly. To increase productivity, the robot should do its job in minimum time.
More informationA Cascaded-Based Hybrid Position-Force Control for Robot Manipulators with Nonnegligible Dynamics
21 American Conference Marriott Waterfront, Baltimore, MD, USA June 3-July 2, 21 FrA16.4 A Cascaded-Based Hybrid Position-Force for Robot Manipulators with Nonnegligible Dynamics Antonio C. Leite, Fernando
More informationRobust Model Free Control of Robotic Manipulators with Prescribed Transient and Steady State Performance
Robust Model Free Control of Robotic Manipulators with Prescribed Transient and Steady State Performance Charalampos P. Bechlioulis, Minas V. Liarokapis and Kostas J. Kyriakopoulos Abstract In this paper,
More informationPLANAR RIGID BODY MOTION: TRANSLATION & ROTATION
PLANAR RIGID BODY MOTION: TRANSLATION & ROTATION Today s Objectives : Students will be able to: 1. Analyze the kinematics of a rigid body undergoing planar translation or rotation about a fixed axis. In-Class
More informationResearch Article Simplified Robotics Joint-Space Trajectory Generation with a via Point Using a Single Polynomial
Robotics Volume, Article ID 75958, 6 pages http://dx.doi.org/.55//75958 Research Article Simplified Robotics Joint-Space Trajectory Generation with a via Point Using a Single Polynomial Robert L. Williams
More informationInterpolated Rigid-Body Motions and Robotics
Interpolated Rigid-Body Motions and Robotics J.M. Selig London South Bank University and Yuanqing Wu Shanghai Jiaotong University. IROS Beijing 2006 p.1/22 Introduction Interpolation of rigid motions important
More informationThe Principle of Virtual Power Slide companion notes
The Principle of Virtual Power Slide companion notes Slide 2 In Modules 2 and 3 we have seen concepts of Statics and Kinematics in a separate way. In this module we shall see how the static and the kinematic
More informationVideo 3.1 Vijay Kumar and Ani Hsieh
Video 3.1 Vijay Kumar and Ani Hsieh Robo3x-1.3 1 Dynamics of Robot Arms Vijay Kumar and Ani Hsieh University of Pennsylvania Robo3x-1.3 2 Lagrange s Equation of Motion Lagrangian Kinetic Energy Potential
More informationControl of Redundant Robots under End-Effector Commands: A Case Study in Underactuated Systems
to appear in the Journal of Applied Mathematics and Computer Science special issue on Recent Developments in Robotics Control of Redundant Robots under End-Effector Commands: A Case Study in Underactuated
More informationLecture Note 4: General Rigid Body Motion
ECE5463: Introduction to Robotics Lecture Note 4: General Rigid Body Motion Prof. Wei Zhang Department of Electrical and Computer Engineering Ohio State University Columbus, Ohio, USA Spring 2018 Lecture
More informationEXAM-3 PHYS 201 (Fall 2006), 10/31/06
EXAM-3 PHYS 201 (Fall 2006), 10/31/06 Name: Signature: Duration: 75 minutes Show all your work for full/partial credit! Include the correct units in your final answers for full credit! Unless otherwise
More informationMotion Tasks for Robot Manipulators on Embedded 2-D Manifolds
Motion Tasks for Robot Manipulators on Embedded 2-D Manifolds Xanthi Papageorgiou, Savvas G. Loizou and Kostas J. Kyriakopoulos Abstract In this paper we present a methodology to drive the end effector
More informationKINEMATICS. File:The Horse in Motion.jpg - Wikimedia Foundation. Monday, June 17, 13
KINEMATICS File:The Horse in Motion.jpg - Wikimedia Foundation 1 WHERE ARE YOU? Typical Cartesian Coordinate System usually only the X and Y axis meters File:3D coordinate system.svg - Wikimedia Foundation
More informationKinematic representation! Iterative methods! Optimization methods
Human Kinematics Kinematic representation! Iterative methods! Optimization methods Kinematics Forward kinematics! given a joint configuration, what is the position of an end point on the structure?! Inverse
More information5 Projectile Motion. Projectile motion can be described by the horizontal and vertical components of motion.
Projectile motion can be described by the horizontal and vertical components of motion. In the previous chapter we studied simple straight-line motion linear motion. Now we extend these ideas to nonlinear
More informationLecture «Robot Dynamics»: Dynamics 2
Lecture «Robot Dynamics»: Dynamics 2 151-0851-00 V lecture: CAB G11 Tuesday 10:15 12:00, every week exercise: HG E1.2 Wednesday 8:15 10:00, according to schedule (about every 2nd week) office hour: LEE
More informationLecture 20: Isoparametric Formulations.
Chapter #0 Isoparametric Formulation. Isoparametric formulations help us solve two problems. Help simplify the definition of the approimate displacement field for more comple planar elements (4-sided elements,
More informationDIFFERENTIAL KINEMATICS. Geometric Jacobian. Analytical Jacobian. Kinematic singularities. Kinematic redundancy. Inverse differential kinematics
DIFFERENTIAL KINEMATICS relationship between joint velocities and end-effector velocities Geometric Jacobian Analytical Jacobian Kinematic singularities Kinematic redundancy Inverse differential kinematics
More informationLecture Note 8: Inverse Kinematics
ECE5463: Introduction to Robotics Lecture Note 8: Inverse Kinematics Prof. Wei Zhang Department of Electrical and Computer Engineering Ohio State University Columbus, Ohio, USA Spring 2018 Lecture 8 (ECE5463
More informationMotion Tasks and Force Control for Robot Manipulators on Embedded 2-D Manifolds
Motion Tasks and Force Control for Robot Manipulators on Embedded 2-D Manifolds Xanthi Papageorgiou, Savvas G. Loizou and Kostas J. Kyriakopoulos Abstract In this paper we present a methodology to drive
More informationRobotics. Dynamics. University of Stuttgart Winter 2018/19
Robotics Dynamics 1D point mass, damping & oscillation, PID, dynamics of mechanical systems, Euler-Lagrange equation, Newton-Euler, joint space control, reference trajectory following, optimal operational
More informationLearning Dynamical System Modulation for Constrained Reaching Tasks
In Proceedings of the IEEE-RAS International Conference on Humanoid Robots (HUMANOIDS'6) Learning Dynamical System Modulation for Constrained Reaching Tasks Micha Hersch, Florent Guenter, Sylvain Calinon
More informationLecture Notes: (Stochastic) Optimal Control
Lecture Notes: (Stochastic) Optimal ontrol Marc Toussaint Machine Learning & Robotics group, TU erlin Franklinstr. 28/29, FR 6-9, 587 erlin, Germany July, 2 Disclaimer: These notes are not meant to be
More informationRobot Arm Transformations, Path Planning, and Trajectories!
Robot Arm Transformations, Path Planning, and Trajectories Robert Stengel Robotics and Intelligent Systems MAE 345, Princeton University, 217 Forward and inverse kinematics Path planning Voronoi diagrams
More informationJerk derivative feedforward control for motion systems
Jerk derivative feedforward control for motion systems Matthijs Boerlage Rob Tousain Maarten Steinbuch Abstract This work discusses reference trajectory relevant model based feedforward design. For motion
More informationEXAM 1. OPEN BOOK AND CLOSED NOTES Thursday, February 18th, 2010
ME 35 - Machine Design I Spring Semester 010 Name of Student Lab. Div. Number EXAM 1. OPEN BOOK AND CLOSED NOTES Thursday, February 18th, 010 Please use the blank paper provided for your solutions. Write
More informationVisual Servoing with Quick Eye-Vergence to Enhance Trackability and Stability
x x The 21 IEEE/RSJ International Conference on Intelligent Robots and Systems October 18-22, 21, Taipei, Taiwan Visual Servoing with Quick Eye-Vergence to Enhance Trackability and Stability Abstract Visual
More informationEngineering Mechanics Prof. U. S. Dixit Department of Mechanical Engineering Indian Institute of Technology, Guwahati Kinematics
Engineering Mechanics Prof. U. S. Dixit Department of Mechanical Engineering Indian Institute of Technology, Guwahati Kinematics Module 10 - Lecture 24 Kinematics of a particle moving on a curve Today,
More informationThe Dynamics of Fixed Base and Free-Floating Robotic Manipulator
The Dynamics of Fixed Base and Free-Floating Robotic Manipulator Ravindra Biradar 1, M.B.Kiran 1 M.Tech (CIM) Student, Department of Mechanical Engineering, Dayananda Sagar College of Engineering, Bangalore-560078
More informationINSTRUCTIONS TO CANDIDATES:
NATIONAL NIVERSITY OF SINGAPORE FINAL EXAMINATION FOR THE DEGREE OF B.ENG ME 444 - DYNAMICS AND CONTROL OF ROBOTIC SYSTEMS October/November 994 - Time Allowed: 3 Hours INSTRCTIONS TO CANDIDATES:. This
More informationA new large projection operator for the redundancy framework
21 IEEE International Conference on Robotics and Automation Anchorage Convention District May 3-8, 21, Anchorage, Alaska, USA A new large projection operator for the redundancy framework Mohammed Marey
More informationEnergy Optimum Reactionless Path Planning for Capture of Tumbling Orbiting Objects using a Dual-Arm Robot
Energy Optimum Reactionless Path Planning for Capture of Tumbling Orbiting Objects using a Dual-Arm Robot S. V. Shah and A. Gattupalli Robotics Research Center International Institute of Information Technology
More informationRobotics. Kinematics. Marc Toussaint University of Stuttgart Winter 2017/18
Robotics Kinematics 3D geometry, homogeneous transformations, kinematic map, Jacobian, inverse kinematics as optimization problem, motion profiles, trajectory interpolation, multiple simultaneous tasks,
More informationRobotics & Automation. Lecture 17. Manipulability Ellipsoid, Singularities of Serial Arm. John T. Wen. October 14, 2008
Robotics & Automation Lecture 17 Manipulability Ellipsoid, Singularities of Serial Arm John T. Wen October 14, 2008 Jacobian Singularity rank(j) = dimension of manipulability ellipsoid = # of independent
More informationDocument downloaded from: This paper must be cited as:
Document downloaded from: http://hdl.handle.net/10251/49990 This paper must be cited as: Gracia Calandin, LI.; Sala Piqueras, A.; Garelli, F. (2014). Robot coordination using taskpriority and sliding-mode
More informationAdaptive Robust Tracking Control of Robot Manipulators in the Task-space under Uncertainties
Australian Journal of Basic and Applied Sciences, 3(1): 308-322, 2009 ISSN 1991-8178 Adaptive Robust Tracking Control of Robot Manipulators in the Task-space under Uncertainties M.R.Soltanpour, M.M.Fateh
More informationFinal Exam April 30, 2013
Final Exam Instructions: You have 120 minutes to complete this exam. This is a closed-book, closed-notes exam. You are allowed to use a calculator during the exam. Usage of mobile phones and other electronic
More informationVectors. Slide 2 / 36. Slide 1 / 36. Slide 3 / 36. Slide 4 / 36. Slide 5 / 36. Slide 6 / 36. Scalar versus Vector. Determining magnitude and direction
Slide 1 / 3 Slide 2 / 3 Scalar versus Vector Vectors scalar has only a physical quantity such as mass, speed, and time. vector has both a magnitude and a direction associated with it, such as velocity
More informationDistance vs. Displacement, Speed vs. Velocity, Acceleration, Free-fall, Average vs. Instantaneous quantities, Motion diagrams, Motion graphs,
Distance vs. Displacement, Speed vs. Velocity, Acceleration, Free-fall, Average vs. Instantaneous quantities, Motion diagrams, Motion graphs, Kinematic formulas. A Distance Tells how far an object is from
More informationReinforcement Learning of Variable Admittance Control for Human-Robot Co-manipulation
2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) Congress Center Hamburg Sept 28 - Oct 2, 2015. Hamburg, Germany Reinforcement Learning of Variable Admittance Control for
More informationAnalysis of the Acceleration Characteristics of Non-Redundant Manipulators
Analysis of the Acceleration Characteristics of Non-Redundant Manipulators Alan Bowling and Oussama Khatib Robotics Laboratory Computer Science Depart men t Stanford University Stanford, CA, USA 94305
More information400 5 Kinematics of Rigid Bodies
4 5 Kinematics of Rigid odies The absolute angular acceleration of link 4 and the acceleration of are: alpha4=[,,88.9] (rad/sˆ) a5=[,-66.866,] (m/sˆ) 5. Problems 5. The dimensions for the mechanism shown
More informationAn experimental robot load identification method for industrial application
An experimental robot load identification method for industrial application Jan Swevers 1, Birgit Naumer 2, Stefan Pieters 2, Erika Biber 2, Walter Verdonck 1, and Joris De Schutter 1 1 Katholieke Universiteit
More informationRobust Control of Cooperative Underactuated Manipulators
Robust Control of Cooperative Underactuated Manipulators Marcel Bergerman * Yangsheng Xu +,** Yun-Hui Liu ** * Automation Institute Informatics Technology Center Campinas SP Brazil + The Robotics Institute
More informationPosition: Angular position =! = s r. Displacement: Angular displacement =!" = " 2
Chapter 11 Rotation Perfectly Rigid Objects fixed shape throughout motion Rotation of rigid bodies about a fixed axis of rotation. In pure rotational motion: every point on the body moves in a circle who
More informationLecture Note 8: Inverse Kinematics
ECE5463: Introduction to Robotics Lecture Note 8: Inverse Kinematics Prof. Wei Zhang Department of Electrical and Computer Engineering Ohio State University Columbus, Ohio, USA Spring 2018 Lecture 8 (ECE5463
More informationAdvanced Robotic Manipulation
Advanced Robotic Manipulation Handout CS37A (Spring 017 Solution Set # Problem 1 - Redundant robot control The goal of this problem is to familiarize you with the control of a robot that is redundant with
More informationNonlinear PD Controllers with Gravity Compensation for Robot Manipulators
BULGARIAN ACADEMY OF SCIENCES CYBERNETICS AND INFORMATION TECHNOLOGIES Volume 4, No Sofia 04 Print ISSN: 3-970; Online ISSN: 34-408 DOI: 0.478/cait-04-00 Nonlinear PD Controllers with Gravity Compensation
More information