Professor Amir Hussain, Dr Andrew Abel 1 Division of Computing Science and Mathematics

Cognitive Computation: A Case Study in Cognitive Control of

Autonomous Systems and Some Future DirectionsProfessor Amir Hussain, Dr Andrew Abel

1 Division of Computing Science and Mathematics University of Stirling, Scotland

Work reported here is part of an ongoing UK EPSRC funded project, with: Dr Erfu Yang1 (RF) & Prof Kevin Gurney2 (CI)

2Adaptive Behaviours Research Group (ABRG)

Department of Psychology University of Sheffield, UK

1

The International Joint Conference on Neural Networks (IJCNN)

Dallas, Texas, August 4-9, 2013

• Why Cognitive Computation?

• Why Cognitive Machines?

• Taylor’s Proposal on Cognitive Machines

• Cognitively Inspired Control of Autonomous Systems

• Towards a more generalised cognitive framework

Introduction

Cognitive Signal Image and Control Processing Research (COSIPRA) Laboratory

2

• Cognitive computation

• an emerging discipline linking together neurobiology, cognitive psychology and artificial intelligence;

• Springer’s journal Cognitive Computation publishing biologically inspired theoretical, computational, experimental and integrative accounts of all aspects of natural and artificial cognitive systems.

• Professor John Taylor

• founding Advisory Board Chair of Cognitive Computation;

• proposed on how to create a cognitive machine equipped with multi-modal cognitive capabilities.

• This keynote

• first presents a novel modular cognitive control framework for autonomous systems - potentially realizes the required cognitive action-selection and learning capabilities in Professor Taylor's envisaged cognitive machine.

• Possible future avenues for improving this work in a cognitively inspired manner

Introduction


3

• Promote a more comprehensive and unified understanding of diverse topics

• perception, action, and attention;

• learning and memory;

• decision making and reasoning;

• language processing and communication;

• problem solving and consciousness aspects of cognition.

• Industry, commerce, robotics and many other areas are increasingly calling for the creation of cognitive machines, with ‘cognitive’ powers similar to those of ourselves:

• are able to ‘think’ for themselves;

• reach decisions on actions in a variety of ways;

• are flexible, adaptive and able to learn from both their own previous experience and that of others around them

Why Cognitive Computation?


4

• A multi-disciplinary research challenge

• Understanding our own cognitive powers:

• how they are created and fostered;

• how they can go wrong due to brain malfunction;

• the modelling of the cognitive brain is an important step in developing such understanding.

• Creating autonomous robots and vehicles able to ‘think’ and ‘act’ cognitively and ethically:

• support us in our daily lives.

Why Cognitive Machines?


5

• It was published at J.G. Taylor, “Cognitive computation,” Cogn. Comput, vol.1, pp.4–16 (2009).

• Based on ideas published in many places

• Taylor raised a number of very interesting points in his attempts to construct an artificial being empowered with its own cognitive powers:

• a range of key questions relevant to the creation of such a machine;

• made detailed and methodical attempts to answer these questions;

• providing convincing evidence from national and international research projects he had led over the years.

• Taylor’s proposal is one of very few attempts to construct a global brain theory of cognition and consciousness.

• It is based on a unique multi-modal approach that takes into consideration vision and attention, motor action, language and emotion.

• Conventional studies in cognition and consciousness have mostly focussed on single modalities such as vision.

Taylor’s Proposal on Cognitive Machines


6

• Taylor asked a number of questions

• What is human cognition in general, and how can it be modelled?

• What are the powers of animal cognition, and how can they be modelled?

• How important is language in achieving a cognitive machine, and how might it be developed in such a machine?

• What are the benchmark problems that should be able to be solved by a cognitive machine?

• Does a cognitive machine have to be built in hardware?

• How can hybridisation help in developing truly cognitive machines

• Is consciousness crucial?

• How are the internal mental states of others to be discerned?

• Discussed notion of attention control



7

• This approach to attention control relevant to our interests

• Will link to a case study that uses this as a basis for a new approach to autonomous vehicle control

• Initially focus on control and decision making

• Ongoing work!



8

Cognitive Control of Autonomous Systems

A Case Study

9

Two problem domains

Planetary rovers (SciSys) Smart cars (Google)

10

• Urban driving in smart cars

• constantly changing trajectories

• moderated speed in urban areas

• ‘sentinel’ awareness of high pedestrian density

• Planetary rovers

• real-time trajectory planning for feasible path to follow on

• Autonomous navigation

• Intelligent motion control with most optimal controller

• Active and smart obstacle avoidance

• ‘cognitive’ awareness of complex environments

Challenges in each domain


11

The problem we tackle:from partially specified trajectories to

cognitive control

12

X(t0)

X(t1)

X(t2)Construct P(t) subject to smoothness and time constraints

Path following with error correctionTake account of obstacles and challenges

13

X(t0)

X(t1)

X(t2)Construct P(t) subject to smoothness and time constraints

Vehicle with given dynamics and kinematicsDrives along P(t)

The problem we tackle:from partially specified trajectories to

cognitive control

• Historically

• Hard switching

• One controller selected at any one time

• Issue is ‘bumpiness’ when switching between controllers

• Our goal

• ‘Bumpless’ control

• Soft switching

• Select a subset of all controllers

• Mix controller decisions together

• Smoother output

Multiple controller methods

14 Cognitive Signal Image and Control Processing Research (COSIPRA) Laboratory

Existing hard switching control

15

supervisor

Plant Model

scontroller 1

controller n

yu

w

s

bank of candidate controllers

measured

output

control signal

disturbance/ noiseswitching

signal

Key ideas:1. Build a bank of alternative controllers2. Switch among them online based on switching condition

+_

r(t) e(t)

reference input

Compare with the problem of action selection in animals

Fight, flight or feeding, but not “do nothing”


The animal solution is centred on a set of sub-cortical brain nuclei – the basal ganglia, which act as a central ‘switch’ or selector

Can we leverage the biological solutions for use in AVC?

Basal ganglia in brain

The biology: Disinhibition gating and action channels(compare with modular control)

Motor resources

Ctx1: action1

BG

Thalamus

Predisposing conditions

Ctx2: action2

BG

Thalamus


Modular control : Challenges

• Meeting multiple performance criteria

– Stability

– Convergence

– Tackling problems of ‘chattering’

– Anti-windup and ‘Bumpless’ switching

– Real-time operation


Three-stage modular framework: a bio-inspired approach


Motion planning(`goal selection’)

Kinematics-based motion control

(basal ganglia, feedback controllers, soft switching)

(`action selection’)

Dynamics-based vehicle control

(engine, drivetrain,etc )(`action realization’)

Measurements(sensors, GPS, cameras ,etc)(`sensing and perception’)

Selectedpoints on atarget path

'Planned trajectory'

dv

d

Actual trajectory

Actual velocty

Target velocity andsteering angle

Using the biomimetic BG model in a control environment

4-wheel rover – Kinematics-based motion control and planning

20

Three-stage modular framework: case study

21










dv

d

Actual trajectory

Actual velocty



“Actual trajectory”

Kinematics-based motion control and planning

Cognitive Signal Image Processing and Control Systems Research (COSIPRA) Laboratory

• The motion control of autonomous vehicles is mostly based on the vehicle’s kinematics model

• Usually assumed that the vehicle’s internal dynamics can immediately satisfy the velocity/steering angle requests from the kinematics-based motion control

• This study:

– BG-based kinematic motion controllers are used for motion planning and control

– Perfect dynamics assumed

22



23

Controller

Controller Autonomous Vehicle

xe

xv

dx

Referenceinput Error

+

Output

+-

FuzzyLogic

Basal Ganglia(BG)

Gating

Salience Selection strengthx

Gating function

1xv

1xs

1xC

2xC

3xC

Controller

2xs

3xs

2xv

xg1x

2x

xs

3x

1xg

2xg

3xg

uxy

3xv

Controller

Controller ye yvdy +

+-

1yv

1yC

2yC

3yC

Controller

2yv

3yv

FuzzyLogic

Basal Ganglia(BG)

Gating

Salience Selection strength

yGating function

1ys

2ys

3ys

yg

1y

2y

ys3y

1yg

2yg

3yg

1( )( ( ))x v x “actual”trajectoryTwo trajectory

Components(input from motion planner)

Feedbacklinearisation

Kinematicsto path

Controllers are all Pole placement-based

Action surface for fuzzy salience model


Simulation Results

25

A. Circular Trajectory Tracking Control


(a) States in the circular tracking with BG-based switching and a single feedback linearization motion controller under noises

(b) x − y trajectory comparison for BG-based switching and a single feedback linearization motion controller under noise


C. General Path Tracking – double lane change and roundabout


26

x-y trajectory under BG-based switching and a single feedback linearization motion controller under noises



4-wheel rover – B-Spline path planning and three-stage motion control with integrated kinematics and dynamics

27

Smooth path planning with B-splines

28

The dimension of the knot vector: 24; The number of control points: 18; The degree of splines: 5


Control points and smooth path planned with B-spline method


0 20 40 60 80 100 1200

1

2

3

4

5

6

General Path Tracking – double lane change and roundabout


29

Comparison of BG-based soft switching control and single-fixed controller with noises


0 20 40 60 80 100 1200.5

1

1.5

2

2.5

3

3.5

4

x(m)

y(m

)

Single fixed

BG switching

desired


30

Comparison of Control Performance (MSE: Mean Squared Error)


Performance

BG without noise

BG with noise

Single without noise

Single with noise

MSE in x

0.0044 0.0046 0.0565 0.0652

MSE in y

0.0000016832 0.00090293 0.000014852 0.0020

MSE in x-y

0.0031 0.0033 0.04 0.0461

Summary


• BG-based controller selection is bumpless ‘soft-switching’ because it combines outputs of multiple controllers– We have some evidence that this also helps avoid

windup & chattering

• BG will allow adaptive control by varying internal parameters which are now better understood from our neurobiological models

• Based on model of biological decision making• Attention switching using salience• Ongoing work

31

Autonomous Control Specific Future Work


• Test against traditional switched controller designs with same controllers

• Adaptive online operations– learn salience weights to BG controller – Dynamic allocation of controllers

• Use of more realistic models

• Real experimental test beds

32

Cognitive Future Work


• Incorporating vision– Better able to react to world– Use of multiple modalities

• Dual process control….– Automatic behaviour mode– Process known differently from unknown– Learning over time, becomes automatic– Mimics processing in the brain

33


Cognitive Computation…

…towards a multimodal framework

34

More Cognitive Computation?


• This is a specific case study– Inspired by work of John Taylor

• Cognitive Computation is very wide ranging field of research

– Can be applied in many different contexts

– Means different things to different people

• Presentation tomorrow– Discuss cognitive computation in more depth

– Application in more fields

• Want to consider a more general cognitive framework

35

Sentic Computing


• Sentiment Analysis

• Common sense computing

• Read emotion and tone from text

• Traditional approaches inadequate– Machine Learning

– Keyword counting

– May identify topic, but not sentiment

• Concept based approach– Can assign emotions to concepts

– Relate similar concepts together

36

AffectNet Graph


37

AffectiveSpace


E. Cambria and A. Hussain. Sentic Computing: Techniques, Tools, and Applications. Dordrecht, Netherlands: Springer, ISBN: 978-94-007-5069-2 (2012)

38

Sentic Computing


• Sentic Activation

• Consider conscious and unconscious level processing

• The two interact

• Can be used for sentiment analysis

• Emotion detection

39

Multimodal Speech Processing


• Traditional hearing aids focus on single modality

• This is not the whole story!

• Perception, attention switching

• Multimodality

• McGurk effect

• Lip reading used in noisy environments– More extensively by those with hearing problems

• Visual information used, but only when appropriate

• Conscious and unconscious processing– Speech often works on prediction

40

Multimodal Speech Processing


• A different direction for listening devices and hearing aids

• Consider how people actually hear

• Lip reading as part of speech filtering

• Cognitively inspired nuanced use of visual information

41

General Cognitive Framework


• Taylor discussed the creation of a cognitive being– Language

– Consciousness

– Decision making

– Memory

– Emotional coding

• Aim is to consider a more general purpose approach– Basal Ganglia inspired decision making

– Concept based emotion analysis

– Multimodal speech interpretation capabilities

– Dual level processing

• Can they be combined into a multimodal framework?

42



• Multimodality– More environmentally aware

– Additional sensors to feed into a vehicle control system

– Vision, sound, weather conditions etc.

• Communication– Communicate with those in the car and outside

– Speech recognition and generation

– Sentiment analysis from passengers

– Able to learn and adapt to wishes of those in car

• Adjust behaviour to suit conditions and emotions

• Multimodal social and cognitive agents

43

Sentic Blending: Scalable Multimodal Fusion for the Continuous Interpretation of Semantics and Sentics


• A general and scalable methodology termed sentic blending, for interpreting the conceptual and affective information associated with natural language through different modalities:

• enables the continuous interpretation of semantics and sentics (i.e., the conceptual and affective information associated with natural language);

• based on the integration of an affective common-sense knowledge base with any multimodal cognitive signal image and control processing module.

• operates in a multidimensional space that enables the generation of a continuous stream characterizing user’s semantic and sentic progress over time - despite the outputs of the unimodal categorical modules having very different time-scales and output labels.

• Uses decision fusion

44

A sample schema of continuous multimodal fusion through sentic blending


An application example: SenticNet Engine


Ensemble streams obtained when applying sentic blending to the SenticNet engine (left) and the facial expression analyser (right), without ‘sentic kinematics’ filtering.



Ensemble stream obtained when applying sentic blending to the proposed conversation, with (right) and without (left) using ‘sentic kinematics’ filtering.

Performance Comparison

48

Confusion matrix obtained combining the five classifiers. Success rates for neutral, joy, and surprise are very high, but disgust, anger, and fear tend to be confused

Confusion matrix obtained after human assessment. Success ratios considerably increase, meaning that the adopted classification strategy is consistent with human classification.



• Considers the emotional states of others

• Considers aspects of human cognition

• Considers the issue of language

• Considers benchmark problems– Convincing communication

• Could be extended to include vehicle and language control– Driving, extremely challenging problem

– Dual level processing

– Cognitively inspired use of different modalities

• Dual layer processing is unifying

49

Acknowledgements


• Everyone who helped to organise this conference!

• All of the COSIPRA Lab

– http://cosipra.cs.stir.ac.uk

– Dr Erfu Yang, Prof Leslie Smith, Dr Erik Cambria

50

http://cosipra.cs.stir.ac.uk/


• Thanks for listening!

• Questions?

51

Appendix

52

Two Modes of Biological Action Selection: Automatic/Habitual and Controlled/Executive Processing - I

In psychological literature, modes of behavioural control refer to automatic (or habitual) & controlled (or executive) processing respectively with their joint use constituting a dual-process theory of behaviour

Controlled processing is under the subject’s direct and active control, is slow, and requires serial attention to component stimuli or sub-tasks. In contrast, automatic control is less effortful, less prone to interference from simultaneous tasks, is driven largely by the current stimulus and does not necessarily give rise to conscious awareness

Dual-process theory also supposes a dynamic transfer of control under learning.

The development of automatic processing has close similarities with the notion of stimulus-response (S-R) learning, or habit learning.

Controlled processing may be likened to goal-directed behaviour in animals.


Two Modes of Biological Action Selection: Automatic/Habitual and Controlled/Executive Processing - II

Habits are supported in closed-loop circuits through BG associated with sensorimotor cortical areas.

The pre-frontal-cortex (PFC) serves as an ‘executive' or supervisory role in enabling controlled processing. PFC also forms loops through BG. The ‘supervisory' PFC works to modulate or bias the action selection of the automatic (sensorimotor) processing system.

Controlled processing dominates in the early acquisition of new skills which subsequently, when well-practiced, are carried out using automatic processing.

As in dual-process theory, it is supposed that goal-directed (non-habitual) behaviours governed by PFC can transfer into habits in sensorimotor loops by learning therein under the influence of the PFC loops


nonholonomic constraints

with the inputs chosen as

The State Constraint:

: Cartesian location

: steering angle: heading angle

If the steering angle is selected as one control input, then the kinematics model can be further simplified as:

Kinematics Vehicle model for Motion Control and Planning:

55

imposes the physical constraint, -the steering angle delta is contrained within a desired (state) range (to enable a smooth time invariantcontrol solution)

Yang, Hussain, and Gurney. (BICS 2013) to appear.

Advanced Motion Controller Method: I/O Feedback Linearization Controller Design Process

56

Original NonlinearSystem

Linear Controller Design, e.g.LQR, zero-pole placement

Dynamic Extension(if needed)

AugmentedSystem after Extension

Push Back

State-space Linearization

Erfu Yang, Amir Hussain, and Kevin Gurney. A basal ganglia inspired soft switching approach to the motion control of a car-like autonomous vehicle. The 2013 International Conference on Brain Inspired Cognitive Systems (BICS 2013),June 9-11, 2013, Beijing, China, to appear.

Fuzzy logic rules for BG-Based soft switching motion control


58

Path/Trajectory Planning:Consider two sixth-order polynomials of time t and their derivatives

the initial and final boundary points are:

59

Thus, solving the following equations

60

If T=30, the resulting solution is

Generic Solution

Dynamics vehicle model used (for car-like rover)

Eric N Moret. Dynamic Modeling and Control of a Car-Like Robot. Thesis, Virginia Polytechnic Institute and State University,2003.


Gain-Scheduling vs BG control

Cognitive Signal Image and Control Processing Research Laboratory

Another important idea formed in this project thus far is to utilize the reference signal as a priori knowledge of the control system under consideration to aid the realization of automatic (habitual) mode behaviour.

This shares some similarity with traditional gain-scheduling solution in which a family of controllers such as PI or PID related to the control reference signal and desired output are designed (Zhao et al, ).

An engine control model for autonomous vehicle has been employed initially to illustrate this traditional gain-scheduling approach.

u

-K-

rad/sto rpm

Teng

Tload

N

VehicleDynamics

Throttle Ang.

Engine Speed, N

Air charge

Throttle & Manifold

Air charge

N

Air Charge

Induction to Power Stroke Delay

EngineSpeed(rpm)

Load

Drag Torque

Air Charge

N

Torque

Combustion

1

Throttle perturbation Speed

uu

62

Gain-Scheduling vs. Reference-based habits?

Cognitive Signal Image and Control Processing Research Laboratory

11 PI controllers are demonstrated.

So, the action (controller) selection in the ‘automatic mode’ can be realized by mapping the reference signal (desired engine speed in the case) to the controllers’ parameters (gains).

In our proposed BG-based soft switching approach, this action selection can be realised in a more natural way, which will be demonstrated further in the vehicle’s cognitive cruise control - NEXT

0 0.5 1 1.5 2 2.5-0.2

0

0.2

0.4

0.6

0.8

1

1.2

From: engineol/Sum To: Out(1)

Step Response

Time (seconds)

Am

plitu

de

2000 2200 2400 2600 2800 3000 3200 3400 3600 3800 40000.004

0.006

0.008

0.01

0.012

0.014

0.016

Speed (rpm)

Gain-Scheduling Proportional and Integral Gains

Kp

Ki

63

Appendix B

Sentic blending

64

Aimed at extending the modular cognitive framework to incorporate additional modalities

by integrating vision, language and emotion;

for enabling multi-modal social cognitive and affective behavioural capabilities in autonomous agents.

A general and scalable methodology termed sentic blending, for interpreting the conceptual and affective information associated with natural language through different modalities:

enables the continuous interpretation of semantics and sentics (i.e., the conceptual and affective information associated with natural language);

based on the integration of an affective common-sense knowledge base with any multimodal cognitive signal image and control processing module.

operates in a multidimensional space that enables the generation of a continuous stream characterizing user’s semantic and sentic progress over time - despite the outputs of the unimodal categorical modules having very different time-scales and output labels.

Sentic Blending: Scalable Multimodal Fusion for the Continuous Interpretation of Semantics and Sentics


65

A sample schema of continuous multimodal fusion through sentic blending




Ensemble streams obtained when applying sentic blending to the SenticNet engine (left) and the facial expression analyser (right), without ‘sentic kinematics’ filtering.



Ensemble stream obtained when applying sentic blending to the proposed conversation, with (right) and without (left) using ‘sentic kinematics’ filtering.

Performance Comparison

69

Confusion matrix obtained combining the five classifiers. Success rates for neutral, joy, and surprise are very high, but disgust, anger, and fear tend to be confused

Confusion matrix obtained after human assessment. Success ratios considerably increase, meaning that the adopted classification strategy is consistent with human classification.

Appendix C

Attention control

70

Taylor’s Attention Control

Ballistic Attention Control System

71

GoalModuleGoal

Module

ATTNSignal

Creator

ATTNSignal

Creator

Input ModuleInput Module

ATTNSignal

Creator

ATTNSignal

Creator

Input Module

Input Module

ATTNCopy

Module

ATTNCopy

Module

BufferMemory

BufferMemory

Attention copy of Attention Control The corollary discharge of attention model (CODAM) for consciousness

GoalsGoals AttentionControllerAttentionController CortexCortex

WM cdWM cdObjects/FeaturesObjects/FeaturesMonitorMonitor

Wm input Wm input

• One promising approach to AVC is to break the task into sub-tasks, each valid over a restricted range of conditions, and to switch between them when required, based on sensory and internally generated signals.

• Historically achieved using several approaches such as

• PID+Gain scheduling (Ahmad 09)

• Sliding mode control

• Dynamic feedback linearisation (Oriolo 02; Kulkarn,NASA JPL )

• Fuzzy logic+PID+multiple models (Iagnemma 99, MIT; Narendra, Yale; Hussain & Gurney et al. 08,09, Stirling)

• Neural approaches (Shumeet 96, Kawato & Wolpert, 2001)

• Decision-theoretic control (Zilberstei,02)

Multiple controller methods


Appendix D - A biological interlude

Basal ganglia and action selection

73

BG Functional Model

Z1 Z2 Z3


(Gurney et al. 2001)

S1 S2 S3

FeedforwardOff-centre, on-surroundnetwork

Vector inputs: effective salience


• Effective salience s (scalar), with input vector x, and channel weight vector w, is given by s = f(w, x)

• s = f(w, x) may be simple dot product or arbitrary nonlinear function

Appendix E - Using the biomimetic BG model in a

control environment4-wheel rover – Kinematics-based

motion control and planning

76

Three-stage modular framework: case study

77










dv

d

Actual trajectory

Actual velocty



“Actual trajectory”



• The motion control of autonomous vehicles is mostly based on the vehicle’s kinematics model

• Usually assumed that the vehicle’s internal dynamics can immediately satisfy the velocity/steering angle requests from the kinematics-based motion control

• This study:

– BG-based kinematic motion controllers are used for motion planning and control

– Perfect dynamics assumed

78



79

Controller

Controller Autonomous Vehicle

xe

xv

dx

Referenceinput Error

+

Output

+-

FuzzyLogic

Basal Ganglia(BG)

Gating

Salience Selection strengthx

Gating function

1xv

1xs

1xC

2xC

3xC

Controller

2xs

3xs

2xv

xg1x

2x

xs

3x

1xg

2xg

3xg

uxy

3xv

Controller

Controller ye yvdy +

+-

1yv

1yC

2yC

3yC

Controller

2yv

3yv

FuzzyLogic

Basal Ganglia(BG)

Gating

Salience Selection strength

yGating function

1ys

2ys

3ys

yg

1y

2y

ys3y

1yg

2yg

3yg

1( )( ( ))x v x “actual”trajectoryTwo trajectory

Components(input from motion planner)

Feedbacklinearisation

Kinematicsto path

Controllers are all Pole placement-based

• Each controller has different parameters• One salience, one controller• 300 controllers• Sub tasks – following path

80

• Input signals (x,y) separated• Each input fed into all controllers

– Each controller is different– Outputs a recommended action

• Signal and error also fed into fuzzy logic– Determines salience, – urgency, based on error and reference

• Apply to basal ganglia model– Selection strength of each controller

• Gating function to normalise– Between 0 and 1

• Gating function output applied to each controller– Acts as a weight, could be zero

• Outputs summed• Recoupled to determine output• See BICS 2013 paper

81

Action surface for fuzzy salience model


• Each one represents a different salience output

• Essentially, each one reacts differently

83

Simulation Results

84

A. Circular Trajectory Tracking Control


(a) States in the circular tracking with BG-based switching and a single feedback linearization motion controller under noises



• Currently only single controller• Testing against hard controller currently

85

B. Lane Change


86

(a) States under BG-based switching and a single feedback linearization motion controller under noises


0 5 10 15 20 25 300

0.5

1

1.5

2

2.5

Time (s)

x(m

)

Single fixed

BG switching

desired

0 5 10 15 20 25 300

0.5

1

1.5

2

2.5

Time (s)

y(m

)

Single fixed

BG switching

desired

0 5 10 15 20 25 30-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Time (s)

Single fixed

BG switching

0 5 10 15 20 25 30-1.5

-1

-0.5

0

0.5

1

1.5

Time (s)

Single fixed

BG switching

-0.5 0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

x(m)

y(m

)

Single fixed

BG switching

desired


0 5 10 15 20 25 300

0.5

1

1.5

2

2.5

Time (s)

x(m

)

Single fixed

BG switching

desired

0 5 10 15 20 25 300

0.5

1

1.5

2

2.5

Time (s)

y(m

)

Single fixed

BG switching

desired

0 5 10 15 20 25 30-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Time (s)

Single fixed

BG switching

0 5 10 15 20 25 30-1.5

-1

-0.5

0

0.5

1

1.5

Time (s)

Single fixed

BG switching

C. General Path Tracking – double lane change and roundabout


87

x-y trajectory under BG-based switching and a single feedback linearization motion controller under noises



4-wheel rover – B-Spline path planning and three-stage motion control with integrated kinematics and dynamics

88

• B spline generates smoother path

89

Smooth path planning with B-splines

90

The dimension of the knot vector: 24; The number of control points: 18; The degree of splines: 5


Control points and smooth path planned with B-spline method


0 20 40 60 80 100 1200

1

2

3

4

5

6

What is spline?What is the knot vector, control parameter, controlling?

91

General Path Tracking – double lane change and roundabout


92

Comparison of BG-based soft switching control and single-fixed controller with noises


0 20 40 60 80 100 1200.5

1

1.5

2

2.5

3

3.5

4

x(m)

y(m

)

Single fixed

BG switching

desired


93

Comparison of Control Performance (MSE: Mean Squared Error)


Performance

BG without noise

BG with noise

Single without noise

Single with noise

MSE in x

0.0044 0.0046 0.0565 0.0652

MSE in y

0.0000016832 0.00090293 0.000014852 0.0020

MSE in x-y

0.0031 0.0033 0.04 0.0461

Professor Amir Hussain, Dr Andrew Abel 1 Division of Computing Science and Mathematics

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Transcript of Professor Amir Hussain, Dr Andrew Abel 1 Division of Computing Science and Mathematics