A geometric approach to analysing the effects of time delays on stability of vehicular platoons with ring interconnections

Platooning control of connected and automated vehicles relies on the collected information via onboard sensors and wireless vehicle-to-vehicle communication. However, sensing delay arises from perception and fusion of multiple onboard sensors, and communication delay arises from transmission intermittencies. Two types of time delays may compromise the stability of platoon systems. In this paper, we study the effects of sensing delay and communication delay on stability of the platoons, where multiple vehicles move in a closed roadway. Each vehicle utilizes the delay-based bidirectional asymmetric control to regulate individual longitudinal behaviours, in which nonidentical asymmetry factors between the direct front and back adjacent vehicles are used for the feedback gains of position, velocity, and acceleration information. The platoon system with three weighted Laplacian matrices is decomposed into a finite number of linear spatial modes. Based on a geometric analysis approach for two constant time delays, we obtain the region of stability preservation in the delays plane, as well as the threshold values of sensing delay and communication delay. Numerical calculations show that, in terms of stability margin with respect to time delays, the platoon system tends to have a higher tolerance for sensing delay than for communication delay, especially for small asymmetric level.