MECH / ELEN 337 - Robotic - Santa Clara University

MECH / ELEN 337 - Robotics I
Course Introduction
Dr. Christopher Kitts, Associate Professor
Departments of Mechanical & Electrical Engineering
Director, Robotic Systems Laboratory
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MECH/ELEN 337, Fall 2006, © C. Kitts

Class Overview
Introduction
Administrative & Logistics Issues
Overview of Robotics at Santa Clara University
Overview of MECH/ELEN 337 & 338 Course Topics
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MECH/ELEN 337, Fall 2006, © C. Kitts

Administrative & Logistics Issues
Course Web Site
Syllabus
Schedule
Textbook
Homework Policy
Matlab / Simulink
Course Communication
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MECH/ELEN 337, Fall 2006, © C. Kitts

Robotics at Santa Clara University - Courses
Undergraduate Courses
– Mechatronics
– Introduction to Robotics
– Senior Design Program
Graduate Courses
– Robotics I, II and III (Robotic Manipulation) [MECH/ELEN 337/8/9]
– Modeling & Control of Telerobotic Systems (4 units)[ MECH/ELEN 311]
– Mobile Robots (coming soon)
– Advanced Mechatronics [MECH/ELEN 207/208/209/310]
– Systems Courses: Ocean Engineering, Space System Engineering
– Capstone, Thesis, Dissertation Programs
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MECH/ELEN 337, Fall 2006, © C. Kitts

Robotics at Santa Clara University - Programs
Academic Programs
– Certificate Program
Mechatronic Systems Engineering , MECH
– Masters Degree Depth Areas
Robotics and Mechatronic Systems, MECH and ELEN
Research Opportunities
– Cluster Space Control or Mobile Multi-Robot Systems
Based on techniques learned in MECH/ELEN 337/338
10 Masters theses in past 2 years months, and 6 more in progress
– Multi-Robot Collaboration
– Model-Based Anomaly Management
– Teleoperation and Autonomy
– Composable Mission Design
– Robotic/Mechatronic Device Design
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MECH/ELEN 337, Fall 2006, © C. Kitts

SCU Robotic Systems Laboratory
Activities: Student-based development of robotic systems, devices, technologies
Collaboration with scientists to integrate instruments & technologies
Execution of field missions to conduct science & validate systems
Expertise: System design, controls, tele-operation, automation, systems of systems, etc
Student-based program: Design & operation, engineering development, mission management
Initiatives: Multi-robot collaboration, diagnostics, environmental sensing, disaster response, etc.
Current Field Robotics
--------------------------Land – Sea – Air – Space-------------------------------
----------- Sponsors & Partners------------
Gov: NSF, NASA, DoD, NOAA,USGS…
Ind: Lockheed, CSA, Mitsubishi, BMW…
Univ: Stanford, Wash U, UT Austin…
Non-Profit: CSGC, MBARI, IEEE, MTS…
--Field Operation for Real-World Missions-- --------------- Real Mission Data Products---------------
- Applications-
Geology
Biology
Land Mngmnt
Remote Sensing
Archeology
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MECH/ELEN 337, Fall 2006, © C. Kitts

Overview of MECH/ELEN 337/338 - General
What this course IS:
– A specific focus on serial chain manipulators
– In depth concentration on kinematics, dynamics
and control architectures
– Analysis, simulation and limited exposure to a few
real manipulators
– Difficult and time-consuming
What this course IS NOT
– A course on mobile robots
– A course on mechatronics
– A control law design course
– A hands-on, team-based set of exercises
– Fun and easy
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MECH/ELEN 337, Fall 2006, © C. Kitts

Overview of MECH/ELEN 337/338 - General
Why I LOVE this course
– Rigorous and interdisciplinary
Motivates very appropriate use of state space
Outstanding application to exploit Matlab/Simulink
– Academically grounded + directly applicable
– Brings linear algebra topics to life
Linear transforms, matrix math, null space,
Jacobian, singularity, etc.
– Joint Space vs Cartesian Space
Kinematic points of view
Low-level vs high-level descriptions
– Control Architectures
Conceptualization of control
Trade-offs in implementation
– Many concepts applicable beyond manipulators
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MECH/ELEN 337, Fall 2006, © C. Kitts

Overview of MECH/ELEN 337/338 - Topics
Introduction to Serial Chain Manipulators (Craig, Chp 1)
– The typical “industrial robot”
– One end fixed (generally to the floor)
– Serial chain of:
joints (DOFs)
links (with some geometry)
– Actuators typically drive joints
– Tool typically at the endpoint (end-effector)
Mathematical Framework (Craig, Chp 2)
– Representations of translation and rotation
– Use of reference frames
– Use of matrix transform to represent frames – “homogeneous transform”
– Manipulation of homogeneous transforms
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MECH/ELEN 337, Fall 2006, © C. Kitts

Overview of MECH/ELEN 337/338 - Topics
Kinematics
– Motion without regard to forces
– Assume links are rigid and joints are revolute or prismatic
– Degrees of Freedom (DOF) - # of independent position variables
– Joint space vs Cartesian space representations
“Forward” Kinematics (Criag, Chp 3)
– “given joint positions, get position/orientation of end-effector”
“Inverse” Kinematics (Craig, Chp 4)
– “given position/orientation of end-effector, find all possible sets of joint angles”
– Challenges:
(x,y)
Nonlinear – so, difficult to compute or determine
Potential for multiple solutions
?
Potential for no solutions
?
?
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MECH/ELEN 337, Fall 2006, © C. Kitts

Overview of MECH/ELEN 337/338 - Topics
Jacobians (Craig, Chp 5)
– Multi-dimensional derivative
⎛ c1
⎞
⎛ g1(
r1
, r2
, L,
rmn)
⎞
⎜ ⎟
⎜
⎟
r ⎜ c ⎟ r
2
⎜ g2
( r1,
r2
, L,
r )
G
mn ⎟
C = ⎜ ⎟ = KIN(
R)
=
M
⎜ M ⎟
⎜ ⎟
⎜
⎟
⎜ ⎟
⎜
⎟
⎝cmn
⎠
⎝ gmn(
r1
, r2
, L,
rmn)
⎠
– The Jacobian relates joint velocities to endpoint velocities:
– We often want to do the inverse:
⎛ ∂g1
⎜
⎛ c&
⎞
⎜ ∂r
1
1
⎜ ⎟
⎜ ∂
⎜ c&
⎟ r g2
2 G G &r
C = = = ⎜
⎜ ⎟ J ( R)
R ∂r
M
1 ⎜
⎜ ⎟
⎜ ⎟
⎜ M
⎝c&
mn ⎠
⎜ ∂gmn
⎜
⎝ ∂r1
⎞
⎟
⎟⎛
r&
1 ⎞
⎟
⎜ ⎟
⎜ r&
⎟
⎟
⎟
⎜ M ⎟
⎟
⎜ ⎟
⎜ ⎟
⎟⎝r&
mn ⎠
⎟
⎠
Problem: singularities - J not invertible for some sets of joint angle values
Physically: at a workspace boundary or have some sort of interior joint lock-up
Conceptually: manipulator has lost a DOF
– It turns out that the Jacobian also relates joint torques to endpoint forces
∂g1
∂r2
∂g2
∂r2
M
∂g
∂r
mn
L
L
O
L
∂g
∂r
∂g
∂r
M
∂g
∂r
&r
mn
2
2
&r
Θ =
J
r r
( ) V
−1
Θ
2
r
V
1
mn
mn
mn
=
r &r
J ( Θ)
Θ
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MECH/ELEN 337, Fall 2006, © C. Kitts

Overview of MECH/ELEN 337/338 - Topics
Dynamics (Craig, Chp 6)
– Study of how forces cause motions to occur
– Forward dynamics – “given forces/torques, determine motions”
– Inverse dynamics – “given desired motions, determine forces/torques
Trajectory Generation (Craig, Chp 7)
– Determine the instantaneous, desired position/velocity for each DOF given a
simple description of the trajectory to be followed (time-ordered waypoints)
Feedback Control (Criag, Chp 9-11)
– “given desired motions and a measure of the current state, determine and apply
the necessary forces/torques”
– Linear control vs non-linear control
– Joint space control vs Cartesian space control
– Position control vs force control vs hybrid control
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MECH/ELEN 337, Fall 2006, © C. Kitts