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The idea of placing small mobile robots to move around in a large building for potential intruders detection has been aroused for some time. However it is still facing two major hurdles: not to lose its ground truth and to make a decision on how to move around safely and effectively within reasonable computation cost. This paper describes a mathematical model for a development of a scheme for an autonomous low cost mobile robot system using visual SLAM (simultaneous localisation and mapping) and Particle Swarm Intelligent path planner. The result showed that this system could provide a solution for the problem in indoor mobile robot navigation. The advancements of the computer technology make this technique as a cost effective solution for a future home service robot.