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

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 τ and an explicit delay t d . 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 ξ (in the stable range) give larger values of deceleration for vehicles in the platoon. Optimal operation is attained close to the minimum value of ξ for stability. Small oscillations are found after the main peak in deceleration for ξ in the stable region but near the transition to instability. A theory for predicting the frequency and amplitude of the oscillations is presented.