mathematical theory of autonomous vehicle (s3223883)

8/8/2019 Mathematical Theory of Autonomous Vehicle (s3223883)

1/28

MATHEMATICAL THEORY OF AUTODRIVER FOR AUTONOMOUS VEHICLES

AUTO 1035 Automotive Major Project

June 16, 2010


2/28

CONTENTS

1. INTRODUCTION

2. VARIOUS TYPES OF AUTONOMOUS VEHICLE

3. WORKING METHODOLOGY

4. FUTURE MODEL

5. SOCIO ECONOMICS IMPACTS

6. CONCLUSION

2010 AUTO1035-Automotive Research Project 1

Mathematical theory of auto driver for autonomous vehicle Anand kiran


3/28

2010 2 AUTO1035-Automotive Research Project2010

Mathematical theory of auto driver for autonomous vehicles Anand kiran

Auto driver or auto pilot

system is a smart system that

guides the vehicle by itself

without any human

assistance.

Auto driver system reduces

the driving stress for the

driver by following the

desirable path by changingthe steering angles

automatically.

INTRODUCTION


4/28

2010 3

VARIOUS TYPES OF AUTONOMOUS

VEHICLES

AUTO1035-Automotive Research Project2010


FULLY AUTOMATED SYSTEMS

ENCHANCEMENT OF

INFRASTRUCTURE

ASSISSTANT SYSTEMS


5/28

Fully autonomous systems requires a car to drive itself to a pre-set target

using unmodified infrastructure.

These vehicles require a high level software that identifies and classifies

objects that are provided by generic sensor systems such as LIDAR,

RADAR,GPS/INS,

The input is recorded from the sensors in a variety of formats and external

information to build an ontological structure.

This model is effective than the remaining.

FULLY AUTOMATED SYSTEMS




6/28

This system of autonomous model works only on developed infrastructure

such as specified lanes or specified areas.

This system is a combination of autonomous vehicles and central supervisory

system.

The central system plans routes and autonomously guides and plans thevehicles from A to B (pre-determined targets) and also guides the traffic in

required zones.

ENCHANCEMENT OF INFRASTRUCTURE




7/28

This system involves minor human involvement.

Potential fully autonomous systems are not created so far these systems can

be seen as incremental stepping stones in that direction.

Few examples of the systems are

1. Cruise control

2.Avoidance strategy

ASSISTED SYSTEMS




8/28

we develop an algorithm to guide and control a vehicle on path

autonomously .

Assuming that path is mathematical determined by equations.

Vehicle can follow the given path only if it turns about the centre of

curvature of the path at a correct distance equal to paths radius of curvature.

WORKING METHODOLOGY




9/28

BASIC TERMINOLOGY



FIG 1: A POSITIVE AWS STEERING VEHICLE IN LEFT TURN

Fig 1: A Positive AWS steering vehicle in left turn


10/28

System uses Ackerman steering condition

The front and rear tracks are Wf and Wr.

The steering angles of the front inner and outer wheels are if and of .

Ris the kinematic radius of rotation of a vehicle.

O is the curvature centre .

C is the centre of mass of the car .

lis the called the wheel base it the distance between the front and rear axle .

c1 and c 2 are the longitudinal distance from O




11/28

We introduce a smart algorithm to allow the wheels to change the mode of

steering depending upon the position and orientation of the vehicle and to

adjust the steer angles for various purposes.

A smart steering system is introduced called active steering system or

steering system by wire .This steering system provides a negative steering at

low speeds and positive steering at high speeds .

We analyse the system consider that car is moving on a given road with a

function Y=f(X)in a global coordinate frame G. The vehicle frame B

attached at the car centre of mass .

Assuming that the z and Z axes are parallel to each other Assuming that the orientation angle between G and B ( x and X axes).

Xc and Yc indicates the coordinates of road curvature in curvature centre Cc.

AUTO DRIVER ALGORITHM




12/28



Fig 2: illustration of the car that is moving on road at point that Cc is centre of curvature


13/28

RAIDUS OF THE CURVATURE OF ROAD AT GIVEN POINT

DETERMINING THE BODY AND GLOBAL COORDINATES AT THAT

POINT

FINDING THE KINEMATIC CHARACTERSTICS

STEER ANGLES OF THE VEHICLE




14/28

ideal motion of the vehicle on elliptic road with road radius of curvature is

plotted.

Fig 3: the radius of curvature R for an ideal motion on elliptic road




15/28

The vehicle dynamics plays a prominent role in determining the vehiclestability. In order to achieve high accuracy in this system we introduced

POSITION ERROR

The distance between the actual centre of rotation and the curvature centre

Fig 4 : represents the position error

VEHICLE DYANMICS




16/28

ORIENTATION ERROR

The orientation error denotes the angle error of the system

Fig 9 : angles involved in the vehicle motion ( indicates the orientation error)

)




17/28

By incorporating position error and orientation error with adjusted steer angles

we would achieve the following results

Fig 10: adjusted front steer angles as the function of speed

RESULTS




18/28



Fig 11: Adjusted rear steer angles as a function of speed


19/28



Fig 12: kinematic turning radius a function of speed


20/28

This model is created with an idea to combine the mathematical algorithm

with sophisticated hardware technology to develop a highly accurate andresponsive autonomous vehicle.

Fig 13 : basic block diagram of the system

EXPERIMENTAL MODEL




21/28

THE ARCHITECTURE:

The architecture model consists of main stages

fig 14 : model flow of data into the vehicle

Environmental sensing: sensors that are mounted on the vehicle gives outputs and

those are used to modal the environment (roads, lanes).

Planning: once environmental modal is confirmed, planning stage develops various

strategies, suitable scenario is chosen

Coordination: finally the output data will be coordinated to the power train

Decision control : the feedback errors are given to control task and final output is

given in terms of motion vector i.e. Acceleration and steering with respect to

environment.




22/28

HARDWARE REQUIREMENTS

LIDAR, RADAR, GPS/INS, FLIR.

The framework will accept inputs from sensors in a variety of formats and

external information sources such as satellite, Wi-Fi and DSRC to built the

environmental model.

Both high-level(ultra sonic) and low-level(infrared) sensor fusion techniques

will be incorporated. Computer with Pentium 4 processor at 2.8 GHz and windows Xp

professional dedicated to image sensing and to run dynamic algorithms.

Camera with high resolution of 750(width)*400(height) pixels are needed.




23/28

PLACEMENT OF HARDWARE ON A VEHICLE

Fig 15 : Placement of hardware on the vehicle




24/28

Three stages in the working model

PREDICTION: Prediction is based on the navigation system (GPS) will deliver both

the globalcoordinateandlocalcoordinate of position of vehicle on the map

environment. Prediction helps in localisation of the vehicle on the street map. The

latest navigation system capable of delivering more precise information about the

road curvature etc.

PERCEPTION: By using the information given out from the prediction we can

recognize the upcomingcurvesandintersectionscan be predicted from a long

distance ahead of the vehicle.

FUSION: Both the prediction and perception models are fused together to develop a

probalistic environment model. This model contains theposition andyawrate of the

vehicle relative to the lane. The width of the each lane and the curvature by means of

a curve radius. The obstacles are represented mainly by their positions relative to the

vehicle , their size and motion vector modelling the speed relative to the vehicle.

The entire data obtained during this process is integrated to power train controller to

operate the vehicle.

WORKING PROCEDURE FOR EXPERIMENTAL

MODEL




25/28

1.SAFETY: These autonomous systems fall under intelligent vehicle controlsystem helps in reduction of accidents ,especially during lane change and

turn at intersections etc.

2. IMPACTS ON TRAFFIC: Cars in the mere future would be able to

seamlessly merge into moving traffic and exit into traffic with ease. With

reduction of traffic there is a chance in the fuel of economy.

Speed can be eventually increased because there is no chance of human

errors.

Parking assistants with system is made is easy .especially parking problems

in urban scenarios will be reduced subsequently.

SOCIO- ECONOMIC IMPACTS




26/28

This experimental model is implementation of an idea which has a scope ofdevelopment in the future. This entire model is made to run on an ideal

scenario. With minor modification in the hardware we can test this system

in a wide range of environments such as heavy traffic scenario with traffic

lights, pesdestrian walking on the road and can be used to whilst in the urban

scenarios. Keeping the socio economic impacts in the mind people should trust the

working ability of the autonomous systems and they should encourage these

systems for further development.

CONCLUSION




27/28


28/28

QUESTIONS



mathematical theory of autonomous vehicle (s3223883)

Documents