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

1

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.

2

Problem Formulation

As part of lifting planning

Focus more on vehicle size

Cannot be regarded as a point

Rolling without slipping

3

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

4

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

5

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

6

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

7

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

8

Low Speed Manoeuvring

An example of A380 (JOS & COS methods)

Extracts from Airplane Characteristics Manual for the A380, (a) JOS method, (b) COC method.

9

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

10

Low Speed Manoeuvring

Following a Straight Line - Jackknifing Position

Jackknife Condition

1 cosln ( , )

2 1 cosc

lt n n

Ζ

0 p p q

11

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.

12

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.

13

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)

14

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

15

Trajectory Planning Framework

Passing Ability Testing

1 2d d

Signed distance:

i i iON OM δ

16

Trajectory Planning Framework

(a) Simulation of the mobile crane turning

around a corner.

(b) Maneuvering of mobile crane in parking

lot.

Local Planner

17

Trajectory Planning Framework

Global Planner

Road Network Node = Milestone

The automatic trajectory planning framework and the generated report. (Courtesy of Li Qing)

18

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)

19

Simulator for Training & Evaluation

The demonstration of the simulator for vehicle driving

20

Future Work

Trajectory Planning in Complex Surroundings

Planning in Dynamic Environment

Trajectory Planning in Environment with PDMS and Point Cloud

Representation

21

Thank You!

22