LEGO Mindstorms NXT
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Atmel 32-bit ARM processor
4 inputs/sensors (1, 2, 3, 4)
3 outputs/motors (A, B, C)
256 KB Flash Memory
64 KB RAM
USB 2.0 Communication
4 programmable buttons
100x64 b/w LCD Display
Sensors
 Active:
• Old light and rotation
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Passive
• Touch, sensors for NXT
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Digital
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Motors
 170 RPM
 360 RPM for old motors,
why?
• Ultrasonic
Minds and Computers
3.1
Preview
What five steps would the robot have to take
in order to go forward for 2 rotations?
Spin left
motor
Spin right
motor
Wait until the
motors have spun
two rotations
Stop left
motor
Minds and Computers
Stop right
motor
3.2
Preview
Now lets examine what that would look like in the NXT Educational
Programming Software.
1. Spin left motor
2. Spin right motor
3. Wait for 2 rotations
4. Stop left motor
Minds and Computers
5. Stop right motor
3.3
Preview
While programming your motor blocks, make sure you select the proper
output ports, and set both motors to the same direction and power level.
Minds and Computers
3.4
Preview
Don’t
forget, the comments you include in your program don’t actually have any
effect on what your robot will do.
Comments
simply act as reminders for you when you edit your program. Here, the
“wait for 1440 degrees” won’t do anything because the actual Wait Block is set to
wait for 720 degrees.
Minds and Computers
3.5
Opening Activity
Many things affected how far your robot traveled.
• The number of degrees your Wait For block
is set to wait for
• The size of your tires
Minds and Computers
3.6
Wheels and Distance
In this activity we’re going to program our
robot to move an exact distance.
To do so we must understand a few things
about circles.
START
Minds and Computers
FINISH
3.7
Review
Let’s start with the basics. Answer the
following:
1. What is a radius of a circle?
2. What is a diameter of a circle?
3. What is the formula for the
circumference of a circle?
Minds and Computers
The distance from the
r
center to the outside of
a circle.
The distance, through a
d
circle’s center, from one
edge to another.
Circumference=
diameter * π
3.8
Preview
With our knowledge of circumference, we can start figuring out
how to control the distance our robot goes.
Minds and Computers
3.9
Preview
Finally, be sure to save frequently.
That way, if anything happens to
your computer you don’t have to
start over.
Minds and Computers
3.10
Goals:
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Build better robots
 Minimize mechanical breakdowns
 Build robots that are easy to control
 Encourage good design strategy
 Strive for elegant, clever solutions
Know your materials
 Plastic bricks since 1949 (wooden blocks prior)
 On average, 2100 different parts each year
 Manufacturing tolerance: 1/1000 of an inch
 Number of ways of combining six 8-stud bricks:
102,981,500
 Widely used by scientists and engineers as a rapid
prototyping tool
Minds and Computers
3.11
Connector pegs
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Black pegs are tight-fitting for locking bricks together.
Grey pegs turn smoothly in bricks for making a pivot
Minds and Computers
3.12
Structure
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LEGO bricks are finicky:
 They HATE duct tape.
 They HATE hot glue.
 They HATE super glue.
 They HATE epoxy.
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You should never need adhesives to build reliable LEGO
structures
Minds and Computers
3.13
Drivetrain
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LEGO Gears
40T
8T
16T
24T
Minds and Computers
1T Worm
Bevel
24T
Crown
3.14
Design Strategy
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Incremental design
 Test components parts as you build them
• Drivetrain
• Sensors, sensor mounting
• Structure
Don’t be afraid to redesign
 KISS
Testing
 Don’t wait until you have a final robot to test
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• Interaction of systems
• Work division (work concurrently)
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Develop test methods
Repeatability
Minds and Computers
3.15
Philosophy
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Build for accurate, precise control
 Slow vs. fast?
 Gear backlash
 Stability
 Skidding
Have fun
Be creative, unique
Strive for cool solutions, that work!
Aesthetics: it’s fun to make beautiful robots!
Minds and Computers
3.16
Differential drive
Most common kinematic choice
All of the miniature robots…
Khepera, Braitenberg
- difference in wheels’ speeds
determines its turning angle
VL
VR
Minds and Computers
3.17
Differential drive
Most common kinematic choice
All of the miniature robots…
Khepera, Braitenberg
- difference in wheels’ speeds
determines its turning angle
Questions (forward kinematics)
Given the wheel’s velocities or positions,
what is the robot’s velocity/position ?
VL
VR
Minds and Computers
Are there any inherent system constraints?
3.18
Differential drive
Most common kinematic choice
All of the miniature robots…
Khepera, Braitenberg
- difference in wheels’ speeds
determines its turning angle
Questions (forward kinematics)
Given the wheel’s velocities or positions,
what is the robot’s velocity/position ?
VL
VR
Are there any inherent system constraints?
1) Specify system measurements
2) Determine the point (the radius) around
which the robot is turning.
3) Determine the speed at which the robot is
turning to obtain the robot velocity.
Minds and Computers
4) Integrate to find position.
3.19
Differential drive
1) Specify system measurements
- consider possible coordinate systems
y
VL
l
q
x
VR
Minds and Computers
(assume
a wheel radius of 1)
3.20
Differential drive
1) Specify system measurements
- consider possible coordinate systems
y
2) Determine the point (the radius) around
which the robot is turning.
VL
l
q
x
VR
Minds and Computers
(assume
a wheel radius of 1)
3.21
Differential drive
1) Specify system measurements
- consider possible coordinate systems
y
VL
l
x
q
2) Determine the point (the radius) around
which the robot is turning.
- to minimize wheel slippage, this point
(the ICC) must lie at the intersection of
the wheels’ axles
- each wheel must be traveling at the
same angular velocity
VR
ICC
Minds and Computers
(assume
a wheel radius of 1)
“instantaneous center of curvature”
3.22
Differential drive
1) Specify system measurements
- consider possible coordinate systems
y
w
VL
l
x
q
2) Determine the point (the radius) around
which the robot is turning.
- to minimize wheel slippage, this point
(the ICC) must lie at the intersection of
the wheels’ axles
- each wheel must be traveling at the
same angular velocity around the ICC
VR
ICC
Minds and Computers
(assume
a wheel radius of 1)
“instantaneous center of curvature”
3.23
Differential drive
1) Specify system measurements
- consider possible coordinate systems
y
2) Determine the point (the radius) around
which the robot is turning.
- each wheel must be traveling at the
same angular velocity around the ICC
w
VL
x
l
3) Determine the robot’s speed around
the ICC and its linear velocity
VR
ICC
R
robot’s turning radius
w(R+l/2) = VL
w(R- l/2) = VR
(assume a wheel radius of 1)
Minds and Computers
3.24
Differential drive
1) Specify system measurements
- consider possible coordinate systems
y
2) Determine the point (the radius) around
which the robot is turning.
- each wheel must be traveling at the
same angular velocity around the ICC
w
VL
x
l
3) Determine the robot’s speed around
the ICC and then linear velocity
VR
ICC
w(R+d) = VL
R
w(R-d) = VR
robot’s turning radius
Thus,
Minds and Computers
(assume
a wheel radius of 1)
w = ( VR - VL ) / l
R = l ( VR + VL ) / ( VR - VL )
3.25
Differential drive
1) Specify system measurements
- consider possible coordinate systems
y
2) Determine the point (the radius) around
which the robot is turning.
- each wheel must be traveling at the
same angular velocity around the ICC
w
VL
x
l
3) Determine the robot’s speed around
the ICC and then linear velocity
VR
ICC
w(R+d) = VL
R
w(R-d) = VR
robot’s turning radius
Thus,
w = ( VR - VL ) / l
R = l ( VR + VL ) / 2( VR - VL )
3.26
Minds and Computers
So, the robot’s velocity is
V = wR = ( VR + VL ) / 2
Differential drive
4) Integrate to obtain position
y
Vx = V(t) cos(q(t))
w(t)
Vy = V(t) sin(q(t))
VL
x
l
VR
ICC
R(t)
robot’s turning radius
with
w = ( VR - VL ) / l
WhatMinds
has and
to Computers
happen to change the ICC ?
R = l( VR + VL ) / ( VR - VL )
3.27
V = wR = ( VR + VL ) / 2
Differential drive
4) Integrate to obtain position
y
Vx = V(t) cos(q(t))
w(t)
Thus,
VL
x(t) =
x
l
Vy = V(t) sin(q(t))
y(t) =
q(t) =
VR
∫ V(t) cos(q(t)) dt
∫ V(t) sin(q(t)) dt
∫ w(t) dt
ICC
R(t)
robot’s turning radius
with
w = ( VR - VL ) / l
Minds and Computers
R = l ( VR + VL ) / 2( VR - VL )
3.28
V = wR = ( VR + VL ) / 2
Differential drive
4) Integrate to obtain position
y
Vx = V(t) cos(q(t))
w(t)
Thus,
VL
x(t) =
x
l
Vy = V(t) sin(q(t))
y(t) =
q(t) =
VR
∫ V(t) cos(q(t)) dt
∫ V(t) sin(q(t)) dt
∫ w(t) dt
ICC
Kinematics
R(t)
robot’s turning radius
with
w = ( VR - VL ) /l
What has to happen to change the ICC ?
Minds and Computers
R = l ( VR + VL ) / 2( VR - VL )
3.29
V = wR = ( VR + VL ) / 2