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 tau 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 xi (in the stable range) give larger values of deceleration for vehicles in the platoon. Optimal operation is attained close to the minimum value of xi for stability. Small oscillations are found after the main peak in deceleration for xi in the stable region but near the transition to instability. A theory for predicting the frequency and amplitude of the oscillations is presented. (C) 2013 Elsevier B.V. All rights reserved.