Potential Fields (PF)

The potential field strategy is based on ideas by [89] and [90]. It provides a method by which robots can avoid objects or be attracted to them. It is based on the inverse square law relationship between force and distance and/or Coulomb’s Law of charged particles. It was investigated by Arkin and described in his book ‘Behavior Based Robots’ amongst others [69]. In the Coulomb’s law version of the strategy the force between two objects is calculated as

F =Q1Q2

d2

where Q1is the signed charge on the first object, Q2is the signed charge on the second

object, and d is the distance between them. The advantage of this implementation is that the force can be attractive or repulsive, according to the charge signs allocated to the objects. Potential field strategies have the advantage of being easy to program and because they encode a continuous navigational space through the sensed environment, they provide an infinite set of reactive possibilities. However they also have problems as outlined in [90]. Particularly they are vulnerable to getting stuck in local minima, and cyclic-oscillatory behaviour. Another disadvantage is the time required to calculate the entire potential field. This is overcome in reactive systems by only calculating each fields force contribution at the instantaneous position at which the robot is located. This also allows for potential fields to be used in highly dynamic environments and in a highly parallel implementation.

2.5.2

Neural Networks (NN)

Neural Networks are essentially learning devices, which given our robots might yield interesting strategies. We would need to do this in simulation and then try out the strategy with the robots. There are many neural networks available to use, the following might be of interest to investigate on the Maibot micro robots :- Perceptrons and Multilayer perceptrons, which incorporate feed forward neural networks with hidden layers and pack propagation [91]; Hopfield networks [92], Bidirectional associative memory(BAM) and self-organising neural networks such as Hebbian learning and competitive learning [93].

2.5.3

Fuzzy Systems (FS)

A fuzzy system is a system which handles imprecise data using the principles of fuzzy sets and their associated methods as proposed by Zadeh [1]. Fuzzy inference is a process of mapping from a given input to an output, using fuzzy set theory. Four steps are involved: fuzzification of the input variables, evaluation of the rules, aggregation of the rule outputs and defuzzification of the result. Two fuzzy inference techniques are commonly used.

• Mamdani - good ability to capture expert knowledge in fuzzy rules, but with a high computational overhead.

• Sugeno - a singleton membership function is used. Works well with optimisation and adaptive control, good for non-linear dynamics.

2.5.4

Rule-Based Systems (RB)

A rule based system has five basic components

1. Knowledge base - contains domain knowledge represented as rules 2. Database - set of facts that are used to match against the IF part of rules

3. Inference engine - links rules with facts and provides reasoning for the solution 4. Explanation - Allows queries as to how a conclusion was arrived at, and why a

specific fact is needed. 5. User interface.

They allow natural knowledge representation, uniform structures, separation of knowl- edge from its processing and ability to handle incomplete or uncertain knowledge. The disadvantages include no ability to learn, opaque relationships between rules and ineffi- cient searching.

2.5.5

Reactive Systems (RS)

Reactive systems are tightly coupled perception and action systems, to provide timely responses in dynamic and unstructured environments. Reactive systems can also have planners added to them, the Planner-Reactor Architecture for example [94] and [95].

2.5. Robotic Strategy Methods 65

2.5.6

Other Methods

Genetic Algorithms (GA)

Genetic algorithms (GA) are a class of stochastic search algorithms based on biological evolution. Given a clearly defined problem to be solved and a binary string representation for candidate solutions a basic GA can be represented.

Genetic Programming (GP)

Genetic Programming represents an application of the genetic learning model to generate a computer program that solves the problem. This area of investigation took off in the early 1990’s stimulated by John Kosa [96] and [97].

Hybrib Neuro Fuzzy (HNF)

Neuro-fuzzy systems are neural networks which are functionally equivalent to a fuzzy inference model. The NF system can be trained to generate IF-THEN fuzzy rules and determine the membership functions for the input and output variables. It is easy to incor- porate expert knowledge into the neuro-fuzzy structure. A benefit is that the connectionist structure avoids fuzzy interference and its attendant computational overhead.

Hybrid Neural Expert (HNE)

Neural Expert systems combine a neural network with a rule-based expert system, using domain knowledge in IF-THEN rules as well as sets of numerical data. They are limited by Boolean logic, and attempts to represent continuous input variables can lead to infinite increases in rules.

Adaptive Neuro Fuzzy Inference Systems (ANFIS)

Adaptive Neuro Fuzzy Inference Systems was first proposed by Roger Jang of the Tsing Hua University, in Taiwan. It is very good at generalising and rapidly converging, so can be used in on-line learning. Applications include adaptive control.

Frame-Based Expert Systems (FB)

These are essentially object orientated expert systems, each frame in a class hierarchy being more specialised. Rules often use pattern matching to locate conditions amongst the instance-frames.

Immune Systems (IS)

Detection of foreign agents by pattern recognition. Can neutralise with antidote and iso- lation.

Virus/viral Systems (VS)

Invasion systems which mimic the real agents but carry a different message. Normally malevolent.

Path Planning (PP)

These include both deliberative(planning) and reactive strategies. These can also include potential field strategies

Deliberative Systems (DS)

Deliberative or Planning Systems use symbolic knowledge and reasoning to generate a strategy. Extremely well adapted for manufacturing tasks.

2.5.

Robotic

Strategy

Methods

67

Table 2.3: Number of Hits in Google for Robot Soccer Strategies

Method PF NN GA GP HNF HNE ANFIS FS RB FB IS VS PP DS RS

Title 62 584 125 85 52 0 1 230 32 3 27 0 650 0 1 Body 2900 18300 5540 2460 304 18 244 7240 1570 287 859 9 15700 124 872 Soccer 235 626 0 288 8 0 17 726 70 16 28 0 602 21 78 FIRA 18 50 20 15 3 0 0 90 4 3 16 0 62 0 2 robocup 171 466 224 249 5 0 14 588 69 9 16 0 447 23 74 robosoccer 3 14 7 12 0 0 0 26 2 0 1 0 24 0 3 mirosot 29 24 10 14 0 0 0 69 3 1 0 0 65 0 4

Where:- PF - Potential Fields, NN - Neural Networks, GA - Genetic Algorithms, GP - Genetic Programming HNF - Hybrib Neuro Fuzzy HNE - Hybrid Neural Expert, ANFIS - Adaptive Neuro Fuzzy Inference Systems FS - Fuzzy Systems, RB - Rule-Based Systems

2.6

PID Control

The most used feed back controller design in current use, is probably the PID controller. PID is the commonly used acronym for this controller standing for Proportional-Integral- Derivative. Alternative names included a three term controller referring to the number of components that make up the controller. The controller operates in a sense-think-act cycle.

Repeat

sense the current state

reduce difference between current state and required state Until

current state = required state

At time t, If y(t) is the current state and r(t) is the required state, then the error e(t) = r(t) - y(t). At time t, the current error is the Proportional component, the sum of the errors up to time t is the Integral component and the rate of change of the error is the Differential component.

The control action at time t CA(t), is then simply the weighted sum of the three com- ponents.

CA(t) = KPe(t) + KI

R

e(t)dt + KD_dtde(t)

The required closed loop dynamics of the controller is then achieved by adjusting the

three parameters KP, KI and KD. This is often done iteratively by the tuning process and

without specific knowledge of a plant model. There are many instances where all three parameters are not needed to control a process. The appropriate parameters can be set to zero in order to create PI, PD, P or I controllers. The PI controller is very common since the I component removes steady state error and the D component is sensitive to noisy measurements. The effects of the parameters within the controller are as follows.

The Proportional term KPe(t) is usually the dominant term of the controller. A high

proportional gain results in a large change in the output of a given error. If the gain is too high then the system can become unstable. Too low and the response time to changes become unacceptably slow. Stability can often be achieved by using the proportional term only. However the system will not settle at the setpoint. To achieve the setpoint

2.7. Robot Football 69 the Integral term KI

R

e(t)dt is required. The integral term contributes proportionally both to the magnitude and the duration of the error, being the sum of errors over time. The integral term accelerates the process towards the setpoint and eliminates any steady state errors. However the drawback is that it can cause overshoot to occur generating opposite error and drive the process away from the setpoint. If the system is too dynamic then the output oscillates about the setpoint and hits the control limits of the device. Reset is often used in controllers to prevent Integral windup. This is when the Integral term exceeds a given value, then the Integral term is reset to zero. The contribution of the Derivative term, KD_dtde(t), is proportional to the rate of change of the error over time. It is calculated as KD(e(t0) − e(t−1)) for unit time. The effect of the Derivative term is to slow the rate of change of the error, known as damping. It acts to reduce any overshoot effects caused by the Integral term and is most effective when the process is close to the setpoint. However it amplifies noisy signals and can cause instability to occur in the system. This problem is usually solved by having a filter on the input and adjusting the controller parameters accordingly. PID controllers are the most established class of controllers however they cannot properly control non-linear systems or systems that have multiple inputs and outputs. There are many reference books describing PID controllers and methods to tune them, as given in [98], [99], [100] and [101].

2.7

Robot Football

As stated previously in Chapter 1, one of the major motivations in getting involved with this research was the presence of a robot football facility in the University of Nottingham’s robot laboratory. There are two major organisations that govern the playing of competi- tion robot football. The first is FIRA [102], to which the University of Nottingham (UoN) is affiliated, and the other is The RoboCup Federation [103]. Each organisation has different rules governing the configuration of the game, but share a common goal in developing, promoting and advertising the use of robots. The UoN is unable to com- pete under RoboCup Federation rules due to use of BlueTooth wireless communications, which is banned by that organisation. There are no restrictions on the software deployed on the robots. Except where stated this literature review refers to the FIRA organisation

and mirosot middle league rules.

Robot football is a problem that combines strategy, cooperation and control among a team of robots. The highly dynamic nature of robot football makes it so difficult to

solve, especially as the robots are capable of speeds in excess of 3msec−1. During a robot

football game robots frequently collide with each other, often at high speed. Although in the rules this is a foul, it is usually only called when it occurs in the penalty area. Also it is permitted to push another team member subject to occupation rules. The UoN robot football team is described in [104].