Robust String Stability of Vehicle Platoons with Communication

This work investigates longitudinal spacing policies and vehicular communication strategies that can reduce inter-vehicular spacing between the vehicles of automated highway platoons, in the presence of parasitic actuation lags. Currently employed platooning technologies rely on the vehicle’s onboard sensors for information of the neighboring vehicles, due to this they may require large spacing between the vehicles to ensure string stability in the presence of uncertainties, such as parasitic actuation lags. More precisely, they require that the minimum employable time headway (hmin) must be lower bounded by 2τ₀ for string stability, where τ₀ is the maximum parasitic actuation lag. Recent studies have demonstrated that using vehicular communication one may be able to employ smaller spacing between vehicles while ensuring robustness to parasitic lags. However, precise results on the extent of such reduction are sparse in the literature. In this work, platoon string stability is used as a metric to study controllers that require vehicular communication, and find the amount of reduction in spacing such controllers can offer. First, the effects of multiple vehicle look ahead in vehicle platoons that employ a Constant Spacing Policy (CSP) based controller without lead vehicle information in the presence of parasitic lags is studied and string instability of such platoons is demonstrated. A robustly string stable CSP controller that employs information from the leader and the immediate predecessor is considered to determine an upper bound on the allowable parasitic lag; for this CSP controller, a design procedure for the selection of controller gains for a given parasitic lag is also provided. For a string of vehicles adopting a Constant Time Headway Policy (CTHP), it is demonstrated that the minimum employable time headway can be further decreased via vehicular communication in the following manner: (1) if the position, velocity and acceleration of the immediate predecessor vehicle is used, then the ii minimum employable time headway hmin can be reduced to τ₀; (2) if the position and velocity information of r immediately preceding vehicles is used, then hmin can be reduced to 4τ₀/(1 + r); (3) furthermore, if the acceleration of ‘r’ immediately preceding vehicles is used, then hmin can be reduced to 2τ₀/(1 + r); and (4) if the position, velocity and acceleration of the immediate and the r-th predecessors are used, then hmin = 2τ₀/(1 + r). Note that cases (3) and (4) provide the same lower bound on the minimum employable time headway; however, case (4) requires much less communicated information. Representative numerical simulations that are conducted to corroborate the above results are discussed. Vehicle formations employing ring structured communication strategies are also studied in this work and a combinatorial approach for developing ring graphs for vehicle formations is proposed. Stability properties of the platoons with ring graphs, limitations of using ring graphs in platoons, and methods to overcome such limitations are explored. In addition, with ring communication structure, it is possible to devise simple ways to recon- figure the graph when vehicles are added to or removed from the platoon or formation, which is also discussed in this work. Further, experimental results using mobile robots for platooning and two-dimensional formations using ring graphs are discussed