Transcript CS225B Robot Programming Laboratory

Locomotion of Wheeled Robots
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3 wheels are sufficient and guarantee stability
Differential drive (TurtleBot)
Car drive (Ackerman steering)
Synchronous drive (B21)
Omni-drive: Mecanum wheels, PR2
[Many slides come from www.probabilistic-robotics.org and Steffen Gutmann]
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Instantaneous Center of Curvature
ICC
• For rolling motion to occur, each wheel has to
move along its y-axis
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Differential Drive
Two driven wheels
One passive (castor) wheel
TurtleBot, Erratic, Pioneers…
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Differential Drive Kinematics
ICC  [ x  R sin  , y  R cos ]
ICC

 ( R  l / 2)  vr
 ( R  l / 2)  vl
vl
l (vl  vr )
2 (vr  vl )
vr  vl

l
vr  vl
v
2
R

R
(x,y)
y
vr
l/2
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x
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Differential Drive: Forward Kinematics
ICC


x
'
cos(
t
)
sin(
t
)0
x

ICC
x
IC
x














y
'

sin(
t
)
cos(
t
)
0
y

ICC
y

IC
y




 






'
0 1


0



t


 
R
Compare to PR (5.9), p 127
P(t+t)
For changing velocities, integrate
over small dt.
P(t)
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Odometry
Integrating relative position information
➔ Need
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to deal with incremental errors
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Ackerman Drive
One driven wheel
Two passive wheels
Similar to front-driven cars
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Synchronous Drive
• All wheels are actuated
synchronously by one
motor
➔Defines robot speed
• All wheels are steered
synchronously by 2nd motor
➔Sets robot's heading
• Orientation of robot frame
is always the same
➔Not possible to control
orientation of robot
frame
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Active Casters
Rollin’ Justin (DLR)
PR2 (Willow Garage)
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Mecanum Wheels
vx (v0 v1v2 v3)/4
Kuka Omni-Drive
vy (v0 v1v2 v3)/4
v (v0 v1v2 v3)/4
verror
(v0 v1v2 v3)/4
y
v1
v1
v0
v1
v0
v2
v3
v2
forward
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v0
v2
x
left
v3
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turn
v3
Motion planning is the ability for an agent to compute its own motions in order to
achieve certain goals. All autonomous robots and digital actors should eventually have
this ability
[Latombe]
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Robot Motion Planning
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Goal of Motion Planning
Compute motion strategies, e.g.:
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Geometric paths
Time-parameterized trajectories
Sequence of sensor-based motion commands
To achieve high-level goals, e.g.:
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Go into a room without colliding with obstacles
Assemble/disassemble a car
Explore and build map of our department
Find an object (a person, the soccer ball, etc.)
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Mobile Robot Navigation
Path planning and obstacle avoidance
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No clear distinction, but usually:
Path-planning
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low-frequency, time-intensive search method for global finding of a path to a goal
Examples: road maps, cell decomposition
Obstacle avoidance
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fast, reactive method with local time and space horizon
Examples: Vector field histogram, dynamic window approach
“Gray area”
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Fast methods for finding path to goal which can fail if environment contains “local minima”
Example: potential field method
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Path Planning
Global vs. Local Path Planning
Configuration Space
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Each configuration is a point in the
space
Obstacles are regions of the space
A freespace path represents valid
motion
Hard – PSPACE hard
Local Methods
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Potential field
Fuzzy rules
Motor schemas
Vector Field Histogram
Local Methods => Global Method?
Borenstein VFH
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Vector Field Histogram [Borenstein and Koren]
Potential field method
• Workspace obstacles
• Obstacle probabilities
from Cartesian histogram
• Polar histogram of good
directions
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Vector Field Histogram [Borenstein and Koren]
Potential field method
• Workspace obstacles
• Obstacle probabilities
from Cartesian histogram
• Polar histogram of good
directions
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Vector Field Histogram [Borenstein and Koren]
Issues
• Width of robot, safety margin
• Cost function for handling tradeoffs: safety,
progress, etc.
• Trajectory and dynamics
• Oscillation
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Tool: Configuration Space
Articulated object (4DoF)
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C-Space (2D cut)
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Configuration Space of a Disc
Workspace W
Configuration space C
path
y
x
Configuration = coordinates (x,y) of robot’s center
Configuration space C = {(x,y)}
Free space F = subset of collision-free configurations
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Workspace
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Configuration Space
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Discretization
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Dynamic Window Method [Fox et al.]
R  v /
vc  av dt  v  vc  av dt
c  a dt    c  a dt
Evaluating constant curvature path in
configuration space
Window of values based on one-step
acceleration
When will the robot crash?
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Dynamic Window Method [Fox et al.]
R  v /
vc  av dt  v  vc  av dt
c  a dt    c  a dt
Admissible trajectories: braking
before collision
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Dynamic Window Method [Fox et al.]
Heading: achieve the goal
Distance: avoid obstacles
Velocity: do it fast
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Dynamic Window Method [Fox et al.]
DWA Issues
• Computation
• Evaluation function tuning: small openings
• Longer paths / lower acceleration
• Oscillation
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