**Abstract**

The autonomous construction of environment maps using mobile robots is a fundamental problem of robotics; this is because virtually all tasks performed by robots need a representation of the working environment to operate. Although many works have addressed this problem known as SLAM, it still remains open; since most of the solutions do not consider a planner that allows the robot to explore autonomously the working environment or the works that consider it, they have developed slow algorithms that do not guarantee a total coverage of the environment or an optimal development of the exploration, which may result in maps of poor quality or definitely not usable given this lack of information. Thus, this work presents a new exploration method based on the random exploration graph (REG), which, unlike its predecessor, defines a systematic analysis of the next positions to be explored eliminating randomness in decision-making and thus minimizing the amount of movements that the robot must make to reach them and the time required to achieve total coverage of the environment. Additionally, a series of tests carried out on the proposed method are presented, and the results obtained in classical variables such as time and distance allow to validate the efficiency of our approach.

**Keywords:** SLAM, integrated exploration, path planning, unknown environments, random exploration graph
