Frequent inspections are essential for false ceilings to maintain the service infrastructures, such as mechanical, electrical, and plumbing, and the structure of false ceilings. Human-labor-based conventional inspection procedures for false ceilings suffer many shortcomings, including safety concerns. Thus, robot-aided solutions are demanded for false ceiling inspections similar to other building maintenance services. However, less work has been conducted on developing robot-aided solutions for false ceiling inspections. This paper proposes a novel design for a robot intended for false ceiling inspections named Falcon. The compact size and the tracked wheel design of the robot allow it to traverse obstacles such as runners and lighting fixtures. The robot’s ability to autonomously follow the perimeter of a false ceiling can improve the productivity of the inspection process since the heading of the robot often changes due to the nature of the terrain, and continuous heading correction is an overhead for a teleoperator. Therefore, a Perimeter-Following Controller (PFC) based on fuzzy logic was integrated into the robot. Experimental results obtained by deploying a prototype of the robot design to a false ceiling testbed confirmed the effectiveness of the proposed PFC in perimeter following and the robot’s features, such as the ability to traverse on runners and fixtures in a false ceiling.