A swarm is defined as a large and independent collection of heterogeneous or homogeneous agents operating in a common environment and seemingly acting in a coherent and coordinated manner. Swarm architectures promote decentralisation and self-organisation which often leads to emergent behaviour. The emergent behaviour of the swarm results from the interactions of the swarm with its environment (or fellow agents), but not as a direct result of design. The creation of artificially simulated swarms or practical robot swarms has become an interesting topic of research in the last decade. Even though many studies have been undertaken using a practical approach to swarm construction, there are still many problems need to be addressed. Such problems include the problem of how to control very simple agents to form patterns; the problem of how an attractor will affect flocking behaviour; and the problem of bridging formation of multiple agents in connecting multiple locations. The central goal of this thesis is to develop early novel theories and algorithms to support swarm robots in. pattern formation tasks. To achieve this, appropriate tools for understanding how to model, design and control individual units have to be developed. This thesis consists of three independent pieces of research work that address the problem of pattern formation of robot swarms in both a centralised and a decentralised way.The first research contribution proposes algorithms of line formation and cluster formation in a decentralised way for relatively simple homogenous agents with very little memory, limited sensing capabilities and processing power. This research utilises the Finite State Machine approach.In the second research contribution, by extending Wilensky's (1999) work on flocking, three different movement models are modelled by changing the maximum viewing angle each agent possesses during the course of changing its direction. An object which releases an artificial potential field is then introduced in the centre of the arena and the behaviours of the collective movement model are studied.The third research contribution studies the complex formation of agents in a task that requires a formation of agents between two locations. This novel research proposes the use Of L-Systems that are evolved using genetic algorithms so that more complex pattern formations can be represented and achieved. Agents will need to have the ability to interpret short strings of rules that form the basic DNA of the formation
