Linearized longitudinal dynamics of an automatic car-following system are analyzed to determine the minimum headway required to avoid collisions. The linear controller with multiple control factors that satisfies all of the system constraints and has a minimum stopping distance is given. The constraints are stability, no oscillations, and the control forces remaining within a specified physical limitation of the vehicle. Numerical results show that a linear controller that satisfies all of the system constraints requires a large headway in order to avoid collisions when subject to extreme initial conditions. The results indicate the need for a nonlinear controller if collisions are to be avoided with proposed small headways. (Author/publisher).
Abstract