Formal Modeling of Navigation System of Autonomous Mobile Robots using Graphs, Automata and Z

In recent years, interest has been developed for the problem of mobile robot navigation system because of its applications in various disciplines. The software development of mobile robot navigation is a complex phenomena and it is passed through different stages of design. It can be modeled either for autonomous, usually, in an unknown environment or for controlled robots in a known environment. Finite automata and graph theory have proved to be useful tools in modeling the robot navigation system through discrete environment, for example, building with rooms, doors, stairs and passageways. In this research, we have used an integration of graph theory, automata and Z notation. In finite automata, an automatic movement of robot is described in which the states are represented by nodes (rooms) and transitions (passageways, stairs and doors) by directed edges. In the mobile robot navigation system, a robot travels from a start state to a specified final state. Graphs are used to model and analyze the paths from start state to the final state. Using Z/Eves, it is investigated and analyzed the entire formal specification.