Nonlinear dynamics of autonomous vehicles with limits on acceleration

The stability of autonomous vehicle platoons with limits on acceleration and deceleration is determined. If the leading-vehicle acceleration remains within the limits, all vehicles in the platoon remain within the limits when the relative-velocity feedback coefficient is equal to the headway time constant. Furthermore, if the sensitivity alpha is greater than the relative-velocity feedback coefficient k, no collisions occur. String stability for small perturbations is assumed and the initial condition is taken as the equilibrium state. Other values of k and alpha that give stability with no collisions are found from simulations. For vehicles with non-negligible mechanical response, simulations indicate that the acceleration-feedback-control gain might have to be dynamically adjusted to obtain optimal performance as the response time changes with engine speed. Stability is demonstrated for some perturbations that cause initial acceleration or deceleration greater than the limits, yet do not cause collisions.