Autonomous vehicle platoons are a promising solution to road safety, efficient road utilization, emission reduction, among other problems facing today's transportation industry. However, consistently maintaining the desired inter-vehicle distance is one of the major problems facing autonomous vehicle platoons. In this study, we propose a proportional-integral-derivative (PID)-based cost-efficient algorithm to control the longitudinal inter-vehicle distance between successive members of an autonomous vehicle platoon. In our approach, calculations of the control algorithm are decentralized, and the data used in the control algorithm is obtained using one sensor per platoon member making the algorithm cost-efficient both computationally and financially. The proposed algorithm was implemented using the Robot Operating System (ROS) and applied to 3D vehicle models in simulations designed to mimic the natural environment in order to demonstrate and evaluate the suitability of the proposed algorithm for demanding and applicable scenarios. We performed meticulous simulations using the ROS framework in conjunction with the gazebo platform. In the proposed approach, the desired inter-vehicle distance between platoon members was successfully kept with a maximum absolute error of 5 m under any given scenario at any given time while maintaining platoon formation and ensuring that no collisions occur among platoon members.