Designing stable finite state machine behaviours using phase plane analysis and variable structure control

This paper discusses how phase plane analysis can be used to describe the overall behaviour of single and multiple autonomous robotic vehicles with finite state machine rules. The importance of this result is that we can begin to design provably asymptotically stable group behaviours from a set of simple control laws and appropriate switching points with decentralized variable structure control. The ability to prove asymptotically stable group behaviour is especially important for applications such as locating military targets or land mines.