Determining collision potential as a measure of robustness in vehicular networks

This work defines and quantifies a measure of robustness for vehicular networks with arbitrary physical arrangements and communication structures. The measure quantifies the minimum disturbance energy that is required to cause a collision between any two vehicles in terms of the ℒ
₂
-norm of disturbances distributed throughout the network. The minimum disturbance size that can cause a collision is then defined in terms of the ℒ
₂
to ℒ
_∞
induced norm of an appropriately defined linear system. Closed form expressions and bounds for the proposed robustness measure in terms of effective resistances in the graph underlying the vehicle formation's communication network are provided. We compare the robustness of formations with two control laws, relative position and absolute velocity control, and relative position and relative velocity control. We first consider arbitrary communication graphs, and then consider in detail the special cases of vehicular networks on cycle graphs and path graphs. We present simulations that show how the presence of a leader changes the spacing requirements in different locations along the linear vehicle platoon.