Introduction to Mobile Robotics Wheeled...
Transcript of Introduction to Mobile Robotics Wheeled...
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Wheeled Locomotion
Introduction to Mobile Robotics
Wolfram Burgard, Michael Ruhnke, Bastian
Steder
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Locomotion of Wheeled Robots
Locomotion (Oxford Dict.): Power of motion from place to place
Differential drive (AmigoBot, Pioneer 2-DX) Car drive (Ackerman steering) Synchronous drive (B21) XR4000 Mecanum wheels
y
ro ll
z m o tio n
x
y
we also allow wheels to rotate around the z axis
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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
R
ICC w
(x,y)
y
l/2
q x
v l
v r
w(R+ l / 2) = vr
w(R- l / 2) = vl
R =l
2
(vl + vr)
(vr - vl)
w =vr - vl
l
v =vr + vl
2
]cos,sin[ICC qq RyRx
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Differential Drive: Forward Kinematics
ICC
R
P(t)
P(t+dt)
t
y
x
tt
tt
y
x
y
x
y
x
wdq
wdwd
wdwd
q
ICC
ICC
ICC
ICC
100
0)cos()sin(
0)sin()cos(
'
'
'
')'()(
')]'(sin[)'()(
')]'(cos[)'()(
0
0
0
t
t
t
dttt
dtttvty
dtttvtx
wq
q
q
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Differential Drive: Forward Kinematics
ICC
R
P(t)
P(t+dt)
t
y
x
tt
tt
y
x
y
x
y
x
wdq
wdwd
wdwd
q
ICC
ICC
ICC
ICC
100
0)cos()sin(
0)sin()cos(
'
'
'
')]'()'([1
)(
')]'(sin[)]'()'([2
1)(
')]'(cos[)]'()'([2
1)(
0
0
0
t
lr
t
lr
t
lr
dttvtvl
t
dtttvtvty
dtttvtvtx
q
q
q
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tan
]cos,sin[ICC
dR
RyRx
Ackermann Drive
R
ICC
(x,y)
y
l/2
q x
v l
v r l
vv
vv
vvlR
vlR
vlR
lr
lr
rl
l
r
w
w
w
)(
)(
2
)2/(
)2/(w
d
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Synchronous Drive
q
y
x
v(t)
w( ) t
')'()(
')]'(sin[)'()(
')]'(cos[)'()(
0
0
0
t
t
t
dttt
dtttvty
dtttvtx
wq
q
q
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XR4000 Drive
q
y
x
vi(t)
wi(t)
')'()(
')]'(sin[)'()(
')]'(cos[)'()(
0
0
0
t
t
t
dttt
dtttvty
dtttvtx
wq
q
q
ICC
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Mecanum Wheels
4
4
4
4
3210
3210
3210
3210
/)vvvv(v
/)vvvv(v
/)vvvv(v
/)vvvv(v
error
x
y
q
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The Kuka OmniRob Platform
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Example: KUKA youBot
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Tracked Vehicles
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Other Robots: OmniTread
[courtesy by Johann Borenstein]
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Non-Holonomic Constraints
Non-holonomic constraints limit the possible incremental movements within the configuration space of the robot.
Robots with differential drive or synchro-drive move on a circular trajectory and cannot move sideways.
XR-4000 or Mecanum-wheeled robots can move sideways (they have no non-holonomic constraints).
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Holonomic vs. Non-Holonomic
Non-holonomic constraints reduce the control space with respect to the current configuration
E.g., moving sideways is impossible.
Holonomic constraints reduce the configuration space.
E.g., a train on tracks (not all positions and orientations are possible)
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Drives with Non-Holonomic Constraints
Synchro-drive
Differential drive
Ackermann drive
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Drives without Non-Holonomic Constraints
XR4000 drive
Mecanum wheels
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Dead Reckoning and Odometry
Estimating the motion based on the issued controls/wheel encoder readings
Integrated over time
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Summary
Introduced different types of drives for wheeled robots
Math to describe the motion of the basic drives given the speed of the wheels
Non-holonomic constraints
Odometry and dead reckoning