Trajectory Planning and 3D Simulation for Long...
Transcript of Trajectory Planning and 3D Simulation for Long...
Trajectory Planning and 3D Simulation
for Long Vehicles
CHEN YONG- School of Mechanical & Aerospace Engineering
- Institute for Media Innovation
Supervisors:
Assoc Prof. Cai Yiyu- Institute for Media Innovation
- School of Mechanical & Aerospace Engineering
Prof. Daniel Thalmann- Institute for Media Innovation
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Introduction
Wheeled Mobile Robots
(a)
(c)
(b)
(a) Three-wheeled tortoise (1948)
(b) Mars exploration rover (2004)
(c) Google driverless car (2012)
vx
ωz
vx
ωz
vy ωz
vx
vx
ωz
v
ωz
(a) (b) (c)
(d) (e)
(a) Skid-steering (b) Ackermann (c) Omnidirectional (d) Corner steering (e) All-wheel steering.
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Problem Formulation
As part of lifting planning
Focus more on vehicle size
Cannot be regarded as a point
Rolling without slipping
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Related Work
Robot Motion Planning
Method Pros Cons
Cell Decomposition Easy, clear Sometimes hard to partition spaces
Trajectory maybe unsmooth
Control Based Online, robust Many restrictions on the trajectory
Potential Fields Online, intuitive May fail due to local minima
Hard to construct potential function
Sampling-based Fast, effective Cannot recognize impossible query
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Related Work
Differential Constraints
Front-wheel-drive
Rear-wheel-drive
ϑ
y
ϕ
x
l
v1f
v1r
1
2
cos cos 0
sin cos 0
(1/ )sin 0
0 1
f
x
vyq
vl
1
2
cos 0
sin 0
(1/ ) tan 0
0 1
r
x
vyq
vl
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Related Work
Swept Path Analysis Commercial software:
AutoTurn, AutoPath,
AutoTrack
TURN.LSP
Work with AutoCAD
Assumption
For each step: front and rear wheels
travels in a circular motion.
P0Q0
Q1
P1
O
P0
P1
Q1
Q0
β
β
MS1
S2
l
l
α
1
1
1
sin 2 sin
sintan
2cos
S l
l
S
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Proposed Method
Adopt a bicycle model for long vehicle
Analyze straight line & circular arc motion
Combine swept path analysis and sampling-based planning
P
Q
θ
φ
Simplification of a four-wheel vehicle model
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Geometric Modeling
Distance = wheelbase
The tangent at point Q should pass through the
point P
OP OQ l
2
1
l q p p q p q
P
Q
l
2 2
2 1 1 1 2 1 2 1 1 1 1 2 1 1 1 2 1 2 2 12
2 2
2 1 1 1 2 1 1 1 2 1 2 2 1 1 1 1 2 1 2 12
12
12
x x x x x x x x x y y x y y x y y x y yl
y x y x x y x x y x x y x y y y y y y yl
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Low Speed Manoeuvring
An example of A380 (JOS & COS methods)
Extracts from Airplane Characteristics Manual for the A380, (a) JOS method, (b) COC method.
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Low Speed Manoeuvring
Following a Straight Line
2
2
2
2
2
cos 1 cos 1
cos 1 cos 1
2 sin
1 cos cos 1
t
l
t
l
t
l
t
l
l e
t
e
l ey t
e
x t
2
2 22
2 2 22
1
1
x t xl
y t x yl
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Low Speed Manoeuvring
Following a Straight Line - Jackknifing Position
Jackknife Condition
1 cosln ( , )
2 1 cosc
lt n n
Ζ
0 p p q
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Low Speed Manoeuvring
Following a Circular Arc
l < r
2 2
2 2 2 2 2 22
2 2
2 2 2 2 2 22
1sin cos sin cos cos
1sin cos sin sin cos
x r t x r t t x t x y r t yl
y r r t x r t t y t x y t yl
2 2
Q Pr r l
Complete shapes of trajectories when α = π/6 and 5π/6.
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Low Speed Manoeuvring
Following a Circular Arc
l = r
Vehicles satisfying the assumptions can follow a circular arc with its front wheels and keep the position of q
unchanged.
Each curve with a singular point outside Cp except for the special case of α = π where the trajectory of q
degenerates into a point.
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Low Speed Manoeuvring
Following a Circular Arc
l > r
r < l < 2r (r = 0.8)
l = 2r (r = 0.5)
l > 2r (r = 0.4)
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Trajectory Planning Framework
An example of LTM1200
A
B D
C
8545 mmQP
E F2370 mm800
mm
1056
.5 m
m
1275
mm
1275
mm
l
b
a
QE
l m q R p q
cos sin,
sin coswhere
R
The trajectory of any point M can be calculated based on the position of Q
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Trajectory Planning Framework
Passing Ability Testing
1 2d d
Signed distance:
i i iON OM δ
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Trajectory Planning Framework
(a) Simulation of the mobile crane turning
around a corner.
(b) Maneuvering of mobile crane in parking
lot.
Local Planner
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Trajectory Planning Framework
Global Planner
Road Network Node = Milestone
The automatic trajectory planning framework and the generated report. (Courtesy of Li Qing)
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Simulator for Training & EvaluationV
eh
icle
sS
cen
es
Plant
INPUT
Driving Simulator
PROCESSING CONTROLS
Roads
Obstacles
Buildings
Cranes
Trailers
Trucks
Forklifts
3D Models
Naming Conventions
Object Hierarchies
Su
perst
ru
ctu
res
Vis
ua
liza
tion
Scene Graph
Precipitations
Stereo Display
Rendering
Luffing
Hoisting
Swinging
Telescoping Su
perst
ru
ctu
res
Ch
ass
is
Forwarding
Steering
Braking
Reversing
Luffing
Hoisting
Swinging
Telescoping
Software
PhysX
OpenSceneGraph
Hardware
Joysticks & Steering
Wheel
Mouse & Keyboard
(a) Design scheme of the driving simulator
(b) PhysX scene including different vehicles
(a) (b)
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Simulator for Training & Evaluation
The demonstration of the simulator for vehicle driving
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Future Work
Trajectory Planning in Complex Surroundings
Planning in Dynamic Environment
Trajectory Planning in Environment with PDMS and Point Cloud
Representation
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Thank You!
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