A NOVEL POTENTIAL FIELD ALGORITHM AND AN

INTELLIGENT MULTI-CLASSIFIER FOR THE AUTOMATED

CONTROL AND GUIDANCE SYSTEM (ACOS)

Thomas Statheros, Gareth Howells, Pierre Lorrentz

Department of Electronics,University of Kent, Canterbury, Kent, U.K.

Klaus McDonald-Maier

School of Computer Science and Electronic Engineering, University of Essex, Colchester, U.K.

Keywords: Autonomous Intelligent Guidance, Potential Field Algorithms, Weightless Neural Systems.

Abstract: The ACOS project seeks to improve and develop novel robot guidance and control systems integrating

Novel Potential Field autonomous navigation techniques, multi-classifier design with direct hardware

implementation. The project development brings together a number of complementary technologies to form

an overall enhanced system. The work is aimed at guidance and collision avoidance control systems for

applications in air, land and water based vehicles for passengers and freight. Specifically, the paper

addresses the generic nature of the previously presented novel Potential Field Algorithm based on the

combination of the associated rule based mathematical algorithm and the concept of potential field. The

generic nature of the algorithm allows it to be efficient, not only when applied to multi-autonomous robots,

but also when applied to collision avoidance between a single autonomous agent and an obstacle displaying

random velocity. In addition, the mathematical complexity, which is inherent when a large number of

autonomous vehicles and dynamic obstacles are present, is reduced via the incorporation of an intelligent

weightless multi-classifier system which is also presented.

1 INTRODUCTION

This paper presents additional novel algorithms,

methods and technologies adapted by the ACOS

automated guidance system (Statheros, 2006) for

collision free autonomous navigation, not only in a

single autonomous manner, as initially presented in

(Statheros et. al., 2006), but also for multi-

autonomous vehicles in the presence of independent

dynamic obstacles.. The technologies employed fall

into three major categories: Novel Potential Field

autonomous navigation techniques, multi-classifier

design and direct hardware implementation. This

paper presents an overview, further development and

ideas regarding the integration of these technologies

within the ACOS system. The paper presents the

novel features of the Potential Field methodology

described in (Statheros 2007), and also the new

concept of Trajectory Equilibrium State (TES)

between a potential field autonomous vehicle and a

dynamic obstacle. In addition, we propose the

combination of the multi-classifier with the novel

potential field algorithm in a new hybrid navigation

system. This is followed by a description of the

multi-classifier framework employed by ACOS

which utilises weightless neural network technology

allowing a rapid adaptable learning environment and

facilitating efficient direct hardware implementation.

The multi-classifier additionally possesses the

desirable properties of 1) a capacity to implicitly

adapt to the relative discriminant abilities of its

component classifiers and 2) be able to accept both

absolute and probability based classifications from

its component classifiers.

337

Statheros T., Howells G., Lorrentz P. and McDonald-Maier K.

A NOVEL POTENTIAL FIELD ALGORITHM AND AN INTELLIGENT MULTI-CLASSIFIER FOR THE AUTOMATED CONTROL AND GUIDANCE SYSTEM (ACOS).

DOI: 10.5220/0002171203370342

In Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2009), page

ISBN: 978-989-8111-99-9

2 NOVEL POTENTIAL FIELD

METHOD FOR

MULTI-AUTONOMOUS

VEHICLE NAVIGATION

A major part of ACOS work for autonomous

navigation is based on novel potential field

algorithmic methodology improving both single and

multi-autonomous vehicle navigation (Statheros

2007). The generic concept of “artificial potential

fields” originates from (Khatib, 1985). This study

introduces the potential field method (PFM) for real-

time obstacle avoidance for both manipulators and

mobile robots. In later years PFM quickly gained

popularity for autonomous vehicle navigation

because of its elegance and simplicity. A Widely

used PFM for mobile robot real-time obstacle

avoidance is termed Virtual Force Field (VFF)

(Borenstein, 1989, 1990). The VFF method has also

been utilised in complex hybrid systems for air, land

and water based autonomous navigation. A number

of VFF algorithms specialised in water based

navigation are briefly explained in (Statheros, 2008).

However, Artificial potential field based

algorithms experience local minima traps, which

cause autonomous vehicle’s trajectory deadlocks

and/or oscillations (Koren 1991). This problem can

be resolved by PFM in integration with intelligent

methods and/or mathematical navigational

algorithms.

In recent years potential field algorithms have

also gained popularity in the field of multi-

autonomous navigation (Pradhan 2006, Masoud

2007). In (Statheros 2007) a novel multi-

autonomous navigation algorithm enables a simple

VFF algorithm to navigate local multi-autonomous

independent vehicles exceptionally efficient in terms

of trajectory length, trajectory smoothness and time

of arrival. This approach uses a novel rule-based

mathematical algorithm and the newly defined

concept of trajectory equilibrium state (TES).

2.1 VFF Trajectory Equilibrium State

In a multi-mobile robot environment where the

robots are guided by the VFF method, in which the

virtual repulsive force is described in (Statheros

2007), we can observe the Trajectory Equilibrium

State (TES) as shown in Figure 1. Here, we observe

that the robot trajectories cross at point C to reach

their target destinations in straight line trajectories.

However, with VFF, the trajectory diversion leads to

autonomous navigational deadlock and both robots

stop at points D and E without reaching their target

destinations T1 and T2. We can define the distance

DE as

Saturation

D , the minimum distance they may

have between them. The robots will only stop

without reaching their target destination in Absolute

TES. Where equation (2) is not fully satisfied but

equation (1) is satisfied, we define the state as Close

TES.

Saturation Efficiency

DDD

≤

< (1)

CBC

and

VV= (2)

In equation 1,

Efficiency

D is the minimum distance

between the two robots so the non-linear effect of

the equation 1 is not apparent. Where V1 is the

speed of mobile robot 1 and V2 is the speed of

mobile robot 2.

As stated above, the TES causes trajectory

inefficiencies such as long and curved power

consuming trajectories for all the guided robots. In

the most extreme case, absolute TES, both robots

divert from their target destination and the distance

between them decreases to the point where the

resultant force vectors are equal to zero. The

Absolute TES has been identified utilizing two

mobile robots in (Statheros 2007).

Figure 1: Two mobile robots at Absolute Trajectory

Equilibrium State (TES).

2.2 TES Detection and Avoidance

The TES detection and avoidance algorithm predicts

and prevents Absolute and Close TES. This

algorithm maintains close to straight line efficient

trajectories for the robots in cases of possible

collision by adjusting separately their speeds. The

performance of this algorithm is demonstrated in

Figure 2.

ICINCO 2009 - 6th International Conference on Informatics in Control, Automation and Robotics

338

Figure 2: Two mobile robots close-optimum trajectories

due to TES Detection and Avoidance algorithm in case of

Absolute TES.

The above has introduced the concept of guiding

independently multi-autonomous robots or vehicles

with identical algorithmic principle with exceptional

efficiency. However, in this paper, we have

identified that the above algorithm is more generic

in nature, as it may also be applied to dynamic

obstacles. For example, in Figure 3, a collision

scenario is presented between a dynamic obstacle

and a standard potential field guided robot. In this

case, we can consider a new concept of TES

between a potential field robot and a dynamic

obstacle. This TES forces the potential field guided

robot to divert from its target destination and follow

the inefficient trajectory shown in figure 3. The TES

detection and avoidance algorithm can also be

applied in this case. The algorithm incorporates a

velocity variation of the autonomous guided robot

based on the potential field algorithm dynamics. The

effectiveness of the algorithm is displayed in Figure

4, where the autonomous vehicle follows a near

optimum straight line trajectory.

Figure 3: Standard Potential Field robot with dynamic

obstacle.

Figure 4: The effect of TES Detection and Avoidance

algorithm when a Potential Field robot is in TES with a

dynamic obstacle.

The processing requirements of the above

algorithm increase in a presence of a large number

of autonomous vehicles and/or dynamic obstacles.

We can reduce its processing load by focusing the

algorithm onto a group of similarly behaving

dynamic vehicles and/or obstacles that are

recognised by an intelligent multi-classifier, which

we present in the next section. This is possible due

to the patterns of location, direction, speed and

potential field algorithm dynamics, which are

generated from the autonomous vehicles and/or

dynamic obstacle in the same local navigation

environment).

3 THE INTELLIGENT

FAST-LEARNING

MULTI-CLASSIFIER SYSTEM

Modern intelligent Robotic Guidance systems are

being employed in practical application domains

where the required performance level often exceeds

that achievable from a single guidance paradigm

typically because the complexity of the problem is

such that too many potential outcomes are present,

equivalent to the number of pattern classes when the

system is viewed as a pattern recognition problem.

To address this issue, current systems often

concurrently employ a number of distinct classifiers,

where the component classifiers are trained on a

subset of situation which the robotic system may

encounter in practice. Therefore, the component

classifiers will possess the ability to distinguish well

between certain situations but will be unable to offer

the same distinguishing pattern classification

performance over the entire range of scenarios

A NOVEL POTENTIAL FIELD ALGORITHM AND AN INTELLIGENT MULTI-CLASSIFIER FOR THE

AUTOMATED CONTROL AND GUIDANCE SYSTEM (ACOS)

339

specific to the problem domain because they are

unaware of all possible situations. In such

circumstances, engineering a solution to a practical

problem is reduced to a selection process of

available classifiers where the combination of the

classifiers chosen is able to distinguish the entire set

of pattern classes present within the problem

domain. A combiner classifier is required in addition

which is trained on the outputs of the component, or

base, classifiers and makes an overall decision.

The ACOS system utilises an intelligent multi-

classifier combiner system which is able to

automatically assimilate outputs of component

system classifiers which are inaccurate due to their

restricted training knowledge and produce a single

classification for a given classification instance The

system possesses the following significant

properties:-

• All base classifiers and the combiner classifier

follow a generic architecture based on the

Probabilistic Convergent Network (PCN)

(Howells 2000, Lorrentz 2007).

• The significance of the classification decision of

a given classifier is varied according to the likely

pattern classes under consideration. Therefore, a

classifier which possesses good knowledge of the

scenario in question is able to provide a strong

weighted decision which is utilised by the

combiner network. Conversely, when an

unfamiliar scenario is encountered, a low

weighted incorrect decision is produced due to

the unfamiliarity of the classifier with the true

scenario.

• The multi-classifier system possesses fast

learning properties so that the significance of

class distinguishing properties are immediately

accepted by the system

• The system is problem domain independent and

may be adapted to a large number of automated

navigation based scenarios.

• The system uses simple logic operations to guide

its decision making process and it is thus suitable

for fast direct hardware based implementation

As stated, the proposed technique employs a type

of weightless artificial neural system known as the

Probabilistic Convergent Network (PCN) to

assimilate the classification potential of each of the

component classifiers employed in a given situation.

The PCN network architecture (Howells 2000,

Lorrentz 2007). is designed to provide an extended

recognition information base to the user whilst

retaining the training and performance potential

achieved with previous Weightless architectures

(Austin 1998). An example PCN architecture is

illustrated in Figure 5.

Figure 5: PCN Network Architecture.

The following are significant points regarding the

architecture:-

• The neurons comprising the network are

arranged in x × y matrices or layers where x and

y are the dimensions of the input sensor data

under consideration.

• Each element within the sensor data is therefore

associated with a corresponding neuron within

each layer.

• The layers comprising the network are arranged

in two groups, termed the Pre group and the

Main group. A Merge layer exists after each

group whose function is to combine the outputs

of the constituent layers of the group. The

connectivity of the neurons comprising a Merge

layer is equal to the number of layers within the

group to which it pertains.

• The merged output of the Main Group is fed

back, unmodified, to the inputs of each layer

comprising the group.

• The number of layers within each group may be

varied depending on the recognition performance

required from the network.

• The constituent layers of a group differ in the

selection of sensor data elements attached to the

inputs of their constituent neurons (termed the

connectivity pattern).

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340

• Neurons within a given layer possess the same

connectivity pattern relative to their position

within the matrix.

The PCN architecture utilises highly efficient

training and recognition algorithms which are

detailed in (Lorrentz 2007). These allow the network

to produce weighted decisions on their output giving

a confidence level associated with the decision.

Specifically:-

• Symbols within the PCN architecture are taken

from an extended compound set.

• A given symbol is designed to contain a

component for each of the possible pattern

classes on which the network has been trained.

• Each component itself is constructed from a pre-

determined number of sub-symbols. This number

represents the number of divisions available for

each pattern class where each divisional symbol

represents a probability approximation that the

given sample pattern belongs to the given pattern

class.

The neurons comprising the network differ

between the Pre and Main groups. The Pre group

neurons take their inputs from the binary sensor

values comprising the network input data. The

contents of the memory locations of the neurons are

taken from the extended compound set of symbols

described above. The main group neurons take their

inputs and memory contents from the compound set

of symbols.

Due to the weightless nature of PCN it lends

itself to straightforward hardware implementation

that requires mainly standard memory to realise the

network structure and some limited arithmetic

resources. An enhanced version of the PCN

architecture has been prototyped and forms a

hardware fabric the for the systems implementation

(Lorrentz 2008).

The ACOS system consists of several base PCN

base classifiers based on separate scenarios which a

robot may encounter. It is infeasible to train a single

PCN classifier with a large number of scenarios due

to the exponential increase in memory required as

each neuron memory will increase in size for each

new scenario. The PCN architecture naturally lends

itself to employment as an intelligent multi-classifier

however. To achieve this end, the output

classifications of the selection of base classifiers

employed, form the input to a given combiner PCN

classifier. The outputs of the combiner PCN will

then represent a weighed classification for the

problem at hand based on the combined wisdom of

the component classifiers as illustrated in Figure 6.

Figure 6: Schematic of the PCN based Multi-Classifier.

As stated, in order to employ the PCN

architecture as a basis for a multi-classifier system, it

is necessary to combine the outputs of the

component classifiers to form a single input which

may be considered as a classification image for the

particular problem in question. The general strategy

requires the following steps to be taken:-

• Outputs of component classifiers are interpreted

as binary numbers, either indicting a single

preferred pattern class or representing a

combination of classed with associated

probabilities.

• The combiner PCN overloads the meanings of

the outputs of the component classifier in order

to address the memory scale issue associated

with the requirement that it be able to distinguish

between a large number of component decisions.

So, for example, the meaning of class decision 1

for base classifier 1 will differ from the same

output for classifier 2. However, the combiner

PCN sees a compound input pattern which

essentially represents a compressed

representation of all possible decision scenarios

with associated weightings and is able to

efficiently reach a conclusion.

• Suitable training examples must be compiled

which will allow the PCN system to distinguish

between the various scenarios. To this effect it is

a supervised learning environment.

Examples of classifications may now be

A NOVEL POTENTIAL FIELD ALGORITHM AND AN INTELLIGENT MULTI-CLASSIFIER FOR THE

AUTOMATED CONTROL AND GUIDANCE SYSTEM (ACOS)

341

presented to the PCN architecture according to the

training algorithm in (Howells 2000, Lorrentz 2007).

The system effectively relies of the fact that if a base

classifier encounters a situation with which it is

familiar (i.e. it has encountered in training), it will

produce a decision with high confidence.

Conversely, if a base classifier encounters a scenario

with which it is not familiar, it will produce a

classification from one of the scenarios which it is

familiar but with low confidence. i.e. it will produce

an erroneous but low weighted result. The combiner

PCN is able to sift these decisions and produce the

desired decisions based on their confidence rating.

4 CONCLUSIONS

The ACOS project has been successful in producing

an integrated, automated, robotic guidance system

which is highly flexible and capable of fast

autonomous learning. It has achieved its primary

aim of providing state-of-the-art knowledge on

autonomous navigation techniques and technologies

as well as a novel autonomous navigation techniques

architecture which constitutes design and

implementation suitable for industrial exploitation.

ACKNOWLEDGEMENTS

This research is supported by the European Union

ERDF Interreg IIIa scheme under the ACOS Grant.

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