The idea of placing small mobile robots to move around in a large building to detect potential intruders has been around for some time. However, there are still two major hurdles to overcome: to locate itself in the environment and to make a decision on how to move around safely and effectively at a reasonable computation cost. This paper describes a mathematical model for developing a scheme for an autonomous low cost mobile robot system using visual simultaneous localization and mapping and accelerated particle swarm intelligent path planner. The results indicated that this system could provide a solution for the problem of indoor mobile robot navigation. Advances in computer technology make this technique a cost effective solution for a future home service robot.