2. Introduction to Robotics (ES159) Advanced Introduction to Robotics (ES259) Spring 2010 Ahmed Fathi
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3. Personnel
Instructor: Me
TFs:
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4. Texts
Primary:
M. Spong, S. Hutchinson, and M. Vidyasagar, “Robot Modeling and Control”, Wiley
Secondary:
Li, Murray, Sastry, “A Mathematical Introduction to Robotic Manipulation”, CRC Press
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5. Course outline First 2/3: traditional analysis of robotic manipulators
Homogeneous transforms
Forward/inverse kinematics
Velocity kinematics, dynamics
Motion planning
Control
Final 1/3: introduction to special topics
Sensors and actuators
Mobile agents, SLAM
Computer vision
MEMS, microrobotics
Surgical robotics, teleoperation
Biomimetic systems
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6. Introduction Historical perspective Science fiction
The acclaimed Czech playwright Karel Capek ( ) made the first use of the word ‘robot’, from the Czech word for forced labor or serf.
The use of the word Robot was introduced into his play R.U.R. (Rossum's Universal Robots) which opened in Prague in January In R.U.R., Capek poses a paradise, where the machines initially bring so many benefits but in the end bring an equal amount of blight in the form of unemployment and social unrest.
Science fiction
Asimov, among others glorified the term ‘robotics’, particularly in I, Robot, and early films such as Metropolis (1927) paired robots with a dystopic society
Formal definition (Robot Institute of America):
"A reprogrammable, multifunctional manipulator designed to move material, parts, tools, or specialized devices through various programmed motions for the performance of a variety of tasks".
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7. Common applications Industrial Commercial Military Medical
Robotic assembly
Commercial
Household chores
Military
Medical
Robot-assisted surgery
Congressional act: more autonomous military vehicles/agents
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8. Common applications Planetary Exploration Undersea exploration
Fast, Cheap, and Out of Control
Mars rover
Undersea exploration
Finding the titanic using the first underwater robot
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9. 01_01 Industrial robots High precision and repetitive tasks
Pick and place, painting, etc
Hazardous environments
01_01.jpg
Industrial robot movie. Use industrial robots as a basis for analysis.
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10. 01_03
Representations
For the majority of this class, we will consider robotic manipulators as open or closed chains of links and joints
Two types of joints: revolute (q) and prismatic (d)
01_03.jpg
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11. Definitions End-effector/Tool Configuration State space Work space
Device that is in direct contact with the environment. Usually very task-specific
Configuration
Complete specification of every point on a manipulator
set of all possible configurations is the configuration space
For rigid links, it is sufficient to specify the configuration space by the joint angles
State space
Current configuration (joint positions θ) and velocities
Work space
The reachable space the tool can achieve
Reachable workspace
Dextrous workspace
Talk about the number of DOFs in terms of workspace reachability and redundancy. Rigid body has 6DOF
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12. Common configurations: wrists
01_06
Common configurations: wrists
Many manipulators will be a sequential chain of links and joints forming the ‘arm’ with multiple DOFs concentrated at the ‘wrist’
01_06.jpg
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13. Workspace: elbow manipulator
01_10
Workspace: elbow manipulator
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14. Common configurations: Stanford arm (RRP)
01_12
Common configurations: Stanford arm (RRP)
Spherical manipulator (workspace forms a set of concentric spheres)
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15. Common configurations: SCARA (RRP)
01_14
Common configurations: SCARA (RRP)
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16. Common configurations: cylindrical robot (RPP)
01_15
Common configurations: cylindrical robot (RPP)
workspace forms a cylinder
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17. Common configurations: Cartesian robot (PPP)
01_16
Common configurations: Cartesian robot (PPP)
Increased structural rigidity, higher precision
Pick and place operations
01_16.jpg
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18. 01_17 Workspace comparison (a) spherical (b) SCARA (c) cylindrical
(d) Cartesian
01_17.jpg
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19. Parallel manipulators
01_18
Parallel manipulators
some of the links will form a closed chain with ground
Advantages:
Motors can be proximal: less powerful, higher bandwidth, easier to control
Disadvantages:
Generally less motion, kinematics can be challenging
6DOF Stewart platform
01_18.jpg
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20. Simple example: control of a 2DOF planar manipulator
01_19
Move from ‘home’ position and follow the path AB with a constant contact force F all using visual feedback
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21. Coordinate frames & forward kinematics
01_20
Coordinate frames & forward kinematics
Three coordinate frames:
Positions:
Orientation of the tool frame: 1 2 1 2
01_20.jpg
‘0’ is the base frame, ‘2’ is the tool frame. The orientation of the tool frame is the projection of the tool frame onto the base frame (i.e. dot product)
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22. 01_21
Inverse kinematics
Find the joint angles for a desired tool position
Two solutions!: elbow up and elbow down
01_21.jpg
These are simple examples… this becomes more complex for higher DOFs
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23. Velocity kinematics: the Jacobian
01_23
Velocity kinematics: the Jacobian
State space includes velocity
Inverse of Jacobian gives the joint velocities:
This inverse does not exist when q2 = 0 or p, called singular configuration or singularity
01_23.jpg
Give an example of a human arm fully extended
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24. 01_24
Path planning
In general, move tool from position A to position B while avoiding singularities and collisions
This generates a path in the work space which can be used to solve for joint angles as a function of time (usually polynomials)
Many methods: e.g. potential fields
Can apply to mobile agents or a manipulator configuration
01_24.jpg
Potential fields: create a topological map of the environment to account for obstacles (i.e. obstacles would be surrounded by ‘high’ potential fields) and take the path of lowest energy
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25. 01_24
Joint control
Once a path is generated, we can create a desired tool path/velocity
Use inverse kinematics and Jacobian to create desired joint trajectories
desired trajectory
controller
error
system dynamics
01_24.jpg
measured trajectory (w/ sensor noise)
actual trajectory
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26. General multivariable control overview
joint controllers
motor dynamics
manipulator dynamics
desired joint torques
state estimation sensors
estimated configuration
inverse kinematics,
Jacobian
desired trajectory
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27. Sensors and actuators sensors motors/actuators
Motor encoders (internal)
Inertial Measurement Units
Vision (external)
Contact and force sensors
motors/actuators
Electromagnetic
Pneumatic/hydraulic
electroactive
Electrostatic
Piezoelectric
Basic quantities for both:
Bandwidth
Dynamic range
sensitivity
We will form a matrix for both sensors and actuators to describe some common configurations as well as discuss active research in both these areas
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28. Next class…
Homogeneous transforms as the basis for forward and inverse kinematics
Come talk to me if you have questions or concerns!
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