Introduction to Robotics

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Introduction to Robotics

• Amitabha Mukerjee
• IIT Kanpur, India

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What is a Robot?

• Robot properties
• Flexibility in Motion
• Mobile robots

daksh ROV de-mining robot 20
commissioned in Indian army 2011. 100
more on order built by RD Engineers,
Pune daksh platform derived gun mounted
robot (GMR)
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Want your personal robot?

Roomba vacuum Cleaning robot By i-robot Price
rs. 15-30K
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How to vacuum a space?

Roomba vacuum Cleaning robot By i-robot Price
rs. 30K
https//www.youtube.com/watch?vdweVBqei9LA
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Models of Robot Motion

Circular robot
W
World Frame(Workspace frame)
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Models of Robot Motion

DEFINITION degrees of freedom number
of parameters needed to fix the robot frame
R in the world frame W
R
NOTE Given robot frame R, every point on the
robot is known
Robot frame
y
(x,y) configuration (vector q)
y
W
x
x
given configuration q for a certain pose of the
robot, the set of points on the robot is a
function of the configuration say R(q)
World Frame(Workspace frame)
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Non-Circular Robot
DEFINITION degrees of freedom number
of parameters needed to fix the robot frame
R in the world frame W How many
parameters needed to fix the robot frame if it
can only translate? How many if it can rotate
as well?
W
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Full 3D motion Piano movers problem
General 3D motion How many parameters needed to
fix the pose? Can a design be assembled? Test
based on CAD models
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Research mobile robot

Turtlebot Based on i-robot (roomba)
platform (with kinect RGB-D sensor) ROS
(open-source) software Price 75K
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Articulated robots
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What is a Robot?

• Robots properties
• Flexibility in Motion
• Mobile robots
• Articulated robots

SCARA 4-axis arm (4 degrees-of-freedom) by
Systemantics Bangalore
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Industrial Robot

• Robots involve
• Flexibility in Motion
• Mobile robots
• Articulated robots
• Industrial robot

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Industrial Robots
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How to program a welding robot?
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What is a Robot?

• Robot properties
• Flexibility in Motion
• Mobile robots
• Articulated robots
• Industrial robot
• Surgicalrobots

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Surgical Robot Lumbar biopsy
inserted needle position
needle path as planned on CAT scan
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Modeling Articulated Robots
Kinematic chain Pose of Link n depends on the
poses of Links 1...(n-1) Transformation between
frame of link (n-1) and link n, depends on a
single motion parameter, say ?n Exercise What
are the coordinates of the orgin of the
end-effector center?
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Modeling Articulated Robots
workspace
configuration space
?2
?1
Exercise Sketch the robot pose for the
configuration 0, -90
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Modeling Articulated Robots
Forward kinematics Mapping from
configuration q to robot pose, i.e.
R(q) Usually, R() is the product of a sequence
of transformations from frame i to frame
i1. Note Must be very systematic in how frames
are attached to each link Inverse kinematics a.
Given robot pose, find q Or b. Given
end-effector pose, find q Q. Is the answer in
(b) unique?
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Modeling Articulated Robots
workspace
configuration space
?2
?1
What is the robot configuration q for the
end-effector position (-L1,L2)?
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Research humanoid robot
Aldebaran Nao Grasping an offered ball
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Sensor-Guided motion planning
1. detect ball using colour
image captured by nao HSV
binarized contour detected
2. estimate distance of ball (depth) from image
size 3. Inverse kinematics to grasp ball
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What is a Robot?

• Robots properties
• Flexibility in Motion
• Mobile robots
• Articulated robots
• Digital actors

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Mobility isnt everything
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What is a Robot?

• Robots properties
• Flexibility in Motion
• Mobile robots
• Articulated robots
• Digital actors
• ? Dentists cradle?
• ? Washing machine?
• Intentionality

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What is a Robot?
Bohori/Venkatesh/Singh/Mukerjee2005
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What is a Robot?

• Robots involve
• Flexibility in Motion
• Dentists cradle?
• Washing machine?
• Intentionality
• Measure not default probability distribution
• e.g. Turn-taking (contingent behaviour)
• Goal intrinsic or extrinsic

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Humans and Robots
madhur ambastha cs665 2002
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Robot Motion Planning

• Amitabha Mukerjee
• IIT Kanpur, India

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Nature of Configuration Spaces
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Robot Model

• Boolean predicates / Model theory inadequate
• Model must be grounded andaccessible (e.g. in
  perception)
• Metaphor extends basic concepts through
  similarity

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Models of Robot Motion

DEFINITION degrees of freedom number
of parameters needed to fix the robot frame
R in the world frame W
R
NOTE Given robot frame R, every point on the
robot is known
Robot frame
y
(x,y) configuration (vector q)
y
W
x
x
given configuration q for a certain pose of the
robot, the set of points on the robot is a
function of the configuration say R(q)
World Frame(Workspace frame)
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Robot Motion Planning

goal
Valid paths will lie among those where the robot
does not hit the obstacle How to characterize
the set of q for which the robot does not hit
the obstacle B?
start
(xG,yG)
(xS,yS)
the set of configurations q where R(q) n B
Ø constitute the free space Qfree i.e. Qfree
q R(q) n B Ø
Obstacle B
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Robot Motion Planning
find path P from qS to qG s.t. for all q ? P,
R(q) n B Ø ? generate paths and check each
point on every path? Would it be easier to
identify Qfree first?
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Robot Motion Planning

QB
Q
QB q R(q) n B ? Ø
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Motion Planning in C-space
path
configurations are points in C-space path P is
a line if P n QB Ø, then path is in Qfree
goal q
start q
QB
Q
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Robot Motion Planning

goal
start
path
CB
configuration space C
workspace W
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Non-circular mobile robots
Triangle - translational
edges of C-obstacle are parallel to obstacle and
robot edges...
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Non-circular mobile robots
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Configuration Space Analysis

• Basic steps (holds for ANY kind of robot)
• determine degrees of freedom (DOF)
• assign a set of configuration parameters q
• e.g. for mobile robots, fix a frame on the robot
• identify the mapping R Q ?W, i.e. R(q) is the
  set of points occupied by the robot in pose q
• For any q and given obstacle B, can determine if
  R(q) n B Ø. ? can identify Qfree
• Main benefit The search can be done for a point
• However, computation of C-spaces is not needed in
  practice it is primarily a conceptual tool.

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Articulated Robot C-space
How many parameters needed to fix the robot pose
? What may be one assignment for the
configuration parameters?
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Articulated Robot C-spaceTopology is not
Euclidean
Topology of C-space torus (S1 x S1)
Choset, H etal 2007, Principles of robot motion
Theory, algorithms, and implementations, chapter 3
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Mapping obstacles
Point obstacle in workspace
Obstacle in Configuration Space
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Map from C-space to W

• Given the configuration q, determine the volume
  occupied by the robot in W
• For multi-link manipulators, spatial pose of link
  (n1) depends on links 1..n.
• Main benefit The search can be done for a point
• However, computation of C-spaces is not needed in
  practice it is primarily a conceptual tool.

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Finding shortest paths Visibility Graph methods
restrict to supporting and separating
tangents Complexity Direct visibility
test O(n3) Plane sweep algorithm O(n2logn)
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Finding shortest paths Generalized Voronoi
Graphs
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Roadmaps
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Beyond Geometry

• Real robots have limitations on acceleration
  owing to torque / inertia ? Dynamics
• Learning to plan motions?
• - Babies learn to move arms
• - Learn low-dimensional representations of
  motion
• Grasping / Assembly Motions along obstacle
  boundary-

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Articulated Robot C-space
Path in workspace Path in Configuration Space
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Articulated Robot C-space
Topology of C-space torus (S1 x S1)
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Articulated Robot C-space
Topology of C-space torus (S1 x S1)
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Articulated Robot C-space
Topology of C-space torus (S1 x S1)