An extended model for pairwise conflict resolution in air traffic management

A conflict resolution model for aircraft traversing planar intersecting trajectories is developed and solved. The model incorporates the flight dynamics of each aircraft. Three types of optimal conflict avoidance manoeuvres are examined. The first is the minimum-time safe deviation to a designated objective and the second and third are the minimum-time safe deviation to and from a designated ground track. These objectives lead to singular optimal control problems where the control variable constraint is defined in terms of the maximum allowable turn rate |u(t)| ⩽ uM, 0 ⩽ t ⩽ tf, for the aircraft executing the avoidance manoeuvre and the non-autonomous state variable constraint is defined in terms of the radius rp of the protected zone about the potentially conflicting aircraft. A fast, accurate procedure is derived for computing the optimal steering program which requires the solution of a coupled differential–algebraic system of equations to determine the control law on any boundary arc of an extremal trajectory. An example pairwise trajectory conflict is analysed in detail. The incorporation of variable airspeed v(t) and an acceleration/deceleration control u2(t) is also discussed.