This paper describes the implementation of a miniature open-source and cost-effective SLAM-robot, utilizing a novel occupancy-grid SLAM algorithm based on the concept of random-finite-sets (RFS). This robotic platform is remotely controlled to move and scan unknown environments using a differential drive system algorithm, sending instantaneous position feedback to the remote operator. The mobile robot utilizes a LIDAR-Lite 2 laser range finder to map the environment while simultaneously estimating its position and orientation within the map. Even though there are many mobile robots that implement this behavior, the main advantage in this proposed robotic platform is modeling of LIDAR measurements at each scan as a RFS. This model provides robustness against the random count of received returns, due to false and missed detections, allowing the use of an inexpensive LIDAR sensor and commercial off the shelf hardware.