Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed...
-
Upload
ashley-bryan -
Category
Documents
-
view
218 -
download
3
Transcript of Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed...
![Page 1: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/1.jpg)
Definition of an Industrial Robot
A robot is a A robot is a re-programmable multifunctionalre-programmable multifunctional manipulator designed to move material, manipulator designed to move material, parts, tools, or specialized devices through parts, tools, or specialized devices through variable programmed motions for the variable programmed motions for the performance of a variety of tasks.performance of a variety of tasks.
Robot Institute of America
(Group within Society of Manufacturing Engineers)
![Page 2: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/2.jpg)
Components of Industrial Robot
Mechanical structure or manipulatorMechanical structure or manipulator
ActuatorActuator
SensorsSensors
Control systemControl system
![Page 3: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/3.jpg)
Modeling and Control of Manipulators
ModelingModeling
• KinematicsKinematics
• Differential kinematicsDifferential kinematics
• DynamicsDynamics
![Page 4: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/4.jpg)
Modeling and Control of Manipulators
ControlControl
• Trajectory planning
• Motion control
• Hardware/software architecture
![Page 5: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/5.jpg)
Mechanical Components
Robots are serial “chain” mechanisms Robots are serial “chain” mechanisms made up of made up of • ““links” (generally considered to be rigid), and links” (generally considered to be rigid), and • ““joints” (where relative motion takes place) joints” (where relative motion takes place)
Joints connect two links Joints connect two links • PrismaticPrismatic• revoluterevolute
![Page 6: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/6.jpg)
“Degrees of Freedom”
Degrees of freedom (DoF) is the number Degrees of freedom (DoF) is the number of independent movements the robot is cof independent movements the robot is capable of apable of
Ideally, each joint has exactly one degree Ideally, each joint has exactly one degree of freedom of freedom • degrees of freedom = number of joints degrees of freedom = number of joints
Industrial robots typically have 6 DoF, but Industrial robots typically have 6 DoF, but 3, 4, 5, and 7 are also common 3, 4, 5, and 7 are also common
![Page 7: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/7.jpg)
Mechanical Configurations
Industrial robots are categorized by the first three joint types
Five different robot configurations: • Cartesian (or Rectangular), • Cylindrical, • Spherical (or Polar), • Jointed (or Revolute), and • SCARA
![Page 8: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/8.jpg)
3-D Kinematics
![Page 9: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/9.jpg)
Position and Orientation of a Rigid BodyPosition and Orientation of a Rigid Body
![Page 10: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/10.jpg)
Coordinate transformation (translation+rotation)
3-D Homogeneous Transformations
![Page 11: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/11.jpg)
Homogeneous vector
Homogeneous transformation matrix
3-D Homogeneous Transformations
![Page 12: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/12.jpg)
Composition of coordinate transformations
3-D Homogeneous Transformations
![Page 13: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/13.jpg)
Euler AnglesEuler Angles
Minimal representation of orientation
Three parameters are sufficient
Euler Angles
Two successive rotations are not made about parallel axes
How many kinds of Euler angles are there?
][
![Page 14: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/14.jpg)
Direct Kinematics
![Page 15: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/15.jpg)
Compute the position and orientation of the end effector as a function of the joint variables
Aim of Direct Kinematics
![Page 16: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/16.jpg)
The direct kinematics function is expressed by the homogeneous transformation matrix
Direct Kinematics
![Page 17: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/17.jpg)
Open Chain
![Page 18: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/18.jpg)
Denavit-Hartenberg ConventionDenavit-Hartenberg Convention
![Page 19: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/19.jpg)
Joint Space and Operational SpaceJoint Space and Operational Space
Description of end-effector task
position: coordinates (easy)
orientation: (n s a) (difficult)
w.r.t base frame
Function of time
Operational space
Independent variables
Joint space
Prismatic: d
Revolute: theta
![Page 20: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/20.jpg)
Kinematic RedundancyKinematic Redundancy
Definition
A manipulator is termed kinematically redundant
when it has a number of degrees of mobility whic
h is greater than the number of variables that are
necessary to describe a given task.
![Page 21: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/21.jpg)
Inverse Kinematics
![Page 22: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/22.jpg)
Inverse KinematicsInverse Kinematics
we know the desired “world” or “base” coordinates for the end-effector or tool
we need to compute the set of joint coordinates that will give us this desired position (and orientation in the 6-link case).
the inverse kinematics problem is much more difficult than the forward problem!
![Page 23: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/23.jpg)
Inverse KinematicsInverse KinematicsInverse KinematicsInverse Kinematics
there is no general purpose technique that will guarantee a closed-form solution to the inverse problem!
Multiple solutions may exist Infinite solutions may exist, e.g., in the case
of redundancy There might be no admissible solutions
(condition: x in (dexterous) workspace)
![Page 24: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/24.jpg)
Differential Kinematics and Statics
![Page 25: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/25.jpg)
Differential KinematicsDifferential Kinematics
Find the relationship between the joint velocities and the end-effector linear and angular velocities.
Linear velocity
Angular velocity
i
ii dq
for a revolute joint
for a prismatic joint
![Page 26: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/26.jpg)
Jacobian ComputationJacobian Computation
nOn
Pni
Oi
Pi
O
P qJ
Jq
J
Jq
J
Jv
1
1
1
The contribution of single joint i to the end-effector angular velocity
The contribution of single joint i to the end-effector linear velocity
![Page 27: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/27.jpg)
Jacobian ComputationJacobian Computation
![Page 28: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/28.jpg)
Kinematic SingularitiesKinematic Singularities
The Jacobian is, in general, a function of the configuration q; those configurations at which J is rank-deficient are termed Kinematic singularities.
![Page 29: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/29.jpg)
Reasons to Find SingularitiesReasons to Find Singularities
Singularities represent configurations at which mobility of the structure is reduced
Infinite solutions to the inverse kinematics problem may exist
In the neighborhood of a singularity, small velocities in the operational space may cause large velocities in the joint space
![Page 30: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/30.jpg)
Dynamics
![Page 31: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/31.jpg)
DynamicsDynamics
relationship between the joint actuator torques relationship between the joint actuator torques and the motion of the structureand the motion of the structure
Derivation of dynamic model of a manipulatorDerivation of dynamic model of a manipulator
Simulation of motion
Design of control algorithms
Analysis of manipulator structures
Method based on Lagrange formulationMethod based on Lagrange formulation
![Page 32: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/32.jpg)
Lagrange FormulationLagrange Formulation
Generalized coordinatesGeneralized coordinates n variables which describe the link positions of an
n-degree-of-mobility manipulator
The Lagrange of the mechanical system
![Page 33: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/33.jpg)
Lagrange FormulationLagrange Formulation
The Lagrange’s equations
Generalized force Given by the nonconservative force Joint actuator torques, joint friction torques, joint to
rques induced by interaction with environment
![Page 34: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/34.jpg)
Computation of Kinetic EnergyComputation of Kinetic Energy
Consider a manipulator with n rigid links
Kinetic energy of link i
Kinetic energy of the motor
actuating link i
![Page 35: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/35.jpg)
Kinetic Energy of LinkKinetic Energy of Link
Express the kinetic energy as a function of the generalized coordinates of the system, that are the joint variables
![Page 36: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/36.jpg)
Computation of Potential EnergyComputation of Potential Energy
Consider a manipulator with n rigid links
![Page 37: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/37.jpg)
Joint Space Dynamic ModelJoint Space Dynamic Model
Viscous friction torques Coulomb
friction torques
Actuation torques
Force and moment exerted on the environment
Multi-input-multi-output; Strong coupling; NonlinearityMulti-input-multi-output; Strong coupling; Nonlinearity
![Page 38: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/38.jpg)
Direct Dynamics and Inverse Dynamics
Direct Dynamics and Inverse Dynamics
Direct dynamics:Direct dynamics: Given joint torques and initial joint position and Given joint torques and initial joint position and
velocity, determine joint accelerationvelocity, determine joint acceleration Useful for simulationUseful for simulation
Inverse dynamics:Inverse dynamics:
Given joint position, velocity and acceleration, determine joint torques
Useful for trajectory planning and control algorithm implementation
![Page 39: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/39.jpg)
Trajectory Planning
![Page 40: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/40.jpg)
Trajectory PlanningTrajectory Planning
Goal: to generate the reference inputs to the Goal: to generate the reference inputs to the motion control system which ensures that the motion control system which ensures that the manipulator executes the planned trajectorymanipulator executes the planned trajectory
Motion control system
Robot Trajectory planning system
torques
Position, velocity, acceleration
![Page 41: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/41.jpg)
Joint Space TrajectoryJoint Space Trajectory
Inverse kinematics algorithm
Trajectory parameters in
operation space
Joint (end-effector) trajectories in terms of position, velocity and acce
leration
Trajectory parameters in joint space Trajectory
planning algorithmInitial and final en
d-effector location, traveling time, etc.
![Page 42: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/42.jpg)
Polynomial interpolationPolynomial interpolation
Trapezoidal velocity profileTrapezoidal velocity profile
Point-to-point MotionPoint-to-point Motion
011
1)( atatatatq nnnn
![Page 43: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/43.jpg)
Motion Control
![Page 44: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/44.jpg)
Motion ControlMotion Control
Determine the time history of the generalized
forces to be developed by the joint actuators so
as to guarantee execution of the commanded
task while satisfying given transient and steady-
state requirements
![Page 45: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/45.jpg)
The Control ProblemThe Control Problem
Joint space control problem
Open loop
![Page 46: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/46.jpg)
Independent Joint ControlIndependent Joint Control
Regard the manipulator as formed by n Regard the manipulator as formed by n
independent systems (n joints)independent systems (n joints)
control each joint as a SISO systemcontrol each joint as a SISO system
treat coupling effects as disturbancetreat coupling effects as disturbance
![Page 47: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/47.jpg)
Independent Joint ControlIndependent Joint Control
Assuming that the actuator is a rotary dc motor Assuming that the actuator is a rotary dc motor
![Page 48: Definition of an Industrial Robot A robot is a re-programmable multifunctional manipulator designed to move material, parts, tools, or specialized devices.](https://reader033.fdocuments.in/reader033/viewer/2022051516/56649dff5503460f94ae7728/html5/thumbnails/48.jpg)
Position and Velocity FeedbackPosition and Velocity Feedback