Minimum Time Headway in Platooning Systems Under the MPF Topology for Different Wireless Communication Scenario

The multiple-predecessor following (MPF) topology is used in vehicle platoons to make it robustly string stable and reduce the minimum employable time headway. It has been demonstrated that communication imperfections such as time delays coming from wireless communications can affect string stability as well as the minimum time headway required to guarantee string stability. Specifically, it was shown that the larger the time delay, the longer the minimum time headway will be. However, by utilizing on-board vehicle sensors, such as radar, lidar and cameras, the distance and speed of nearby vehicles can be measured almost instantaneously, i.e., with almost no delay. Another effective parameter on string stability and minimum time headway is the heterogeneity of the vehicles. Due to the immense complexity of the MPF topology, string stability analysis of this topology in literature has been confined to homogeneous platoons. In this paper, we consider the case of heterogeneous platoons under the MPF topology with the use of the combination of sensors and wireless communications for receiving information. Following that, we find conditions to guarantee the internal and string stability for the heterogeneous case and propose the minimum time headway required to guarantee string stability. Finally, we provide a table, in which we propose the minimum time headway for two other wireless communication scenarios as well: (i) having no communication delay and (ii) having fully-delayed information, i.e., all information, whether it comes from the ego vehicle or its predecessors, is delayed. In addition to exploring the analysis of string stability for the vehicles with more possible connections (vehicles after the $r^{th}$ vehicle, when information from $r$ immediate vehicles is used), we study the string stability conditions (with which we aim at avoiding collisions) and find the minimum time headway for the first few vehicles (vehicle $r$ and all its predecessors). Numerical results clearly show the effectiveness of the proposed lower bounds.