This research explores path integration in mobile robot navigation and path optimization technique using vector calculus. A simulated robot in a simulated environment is used to test the algorithm that is to be developed. The simulated robot is equipped with a sonar sensor and several infrared sensors on its chassis. Mobile robot navigation in an unknown environment is very crucial as It not only has to be concerned about reaching its destination but also to avoid obstacles that may be in the way. This algorithm can effectively allow a mobile robot to navigate an unknown environment without collision into obstacles.

Searching Mechanism is an important technique that is usually used by Search and Rescue team to find people especially victims for natural disasters. In this paper, we propose an exploration algorithm using quadcopter in simulation to discover an unknown area that is based on the expanding circle pattern for searching activities. Expanding circle searching pattern is a circular search procedure that is conducted by a series of distances around a fixed reference point, which can be used for unknown area exploration. The simulation is implemented in a swarm-based environment as it can increase the performance of robots for exploration compared to the non-swarm based environment. Based on the initial simulation result, the swarm-based exploration algorithm with the expanding circle pattern can maximize the searching area covered if compared with only having individual searching robot.