Optimality and oscillations near the edge of stability in the dynamics of autonomous vehicle platoons

• The mechanical response of autonomous vehicles strongly affects platoon dynamics.
• For perturbations to decay the fastest, the optimal acceleration feedback gain is near the edge of stability.
• Unique oscillations due to mechanical response occur for gain close to the transition to instability.
• The conventional definition of string stability needs additional constraints for acceptable performance.

A model that includes the mechanical response of a vehicle to a demanded change in acceleration is analyzed to determine the string stability of a platoon of autonomous vehicles. The response is characterized by a first-order time constant ττ and an explicit delay tdtd. The minimum value of the acceleration feedback control gain is found from calculations of the velocity of vehicles following a lead vehicle that decelerates sharply from high speed to low speed. Larger values of ξξ (in the stable range) give larger values of deceleration for vehicles in the platoon. Optimal operation is attained close to the minimum value of ξξ for stability. Small oscillations are found after the main peak in deceleration for ξξ in the stable region but near the transition to instability. A theory for predicting the frequency and amplitude of the oscillations is presented.