Exploration of unknown environments is one of the tasks that mobile robots should perform in different practical situations, such as dangerous or difficult-to-access environments. In spite of its importance, this problem is still not solved and many applications use remote control instead of autonomy. This work presents a complete framework for autonomous exploration inspired on the Rapidly-exploring Random Tree method. The proposed algorithm randomly selects obstacle-free goal positions for continuous exploration and mapping of the real space in which the robot moves. These goals are used to drive the robot using a PID controller. The environmental map is presented as a visible matrix and is generated using grid mapping techniques and scale transformations. Experimental results show the application of the proposed framework using a differential mobile robot with an onboard Kinect sensor.