Optimal coordinated maneuvers for three dimensional aircraft conflict resolution

Abstract

In this paper, we study the problem of designing optimal coordinated maneuvers for multiple aircraft conflict resolution. We propose an energy function to select among all the conflict-free maneuvers the optimal one. The introduced cost function incorporates a priority mechanism that favors those maneuvers where aircraft with lower priority assume more responsibility in resolving the predicted conflicts. The energy-minimizing resolution maneuvers may involve changes of heading and speed, as well as of altitude. However, vertical maneuvers are penalized with respect to horizontal ones for the sake of passenger comfort. A geometric construction and a numerical algorithm for computing the optimal resolution maneuvers are given in the two aircraft case. As for the multiaircraft case, an approximation scheme is proposed to compute a suboptimal two-legged solution. Extensive examples are presented to illustrate the effectiveness of the proposed algorithms.

Trajectory optimization in convex underapproximations of safe regions

“…In this formulation of the problem, it is assumed that the intent of the aircraft involved in a conflict scenario is known perfectly, either to a centralized controller, or through the exchange of information through data link between aircraft. In centralized schemes, the central planner chooses the control input of all agents in the conflict scenario to satisfy safety constraints and minimize a global optimality criterion [4], [5].…”

Parallelisation of Sequential Monte Carlo for real-time control in air traffic management

“…There are many existing multi-aircraft trajectory optimi sation methods, most focus purely on cruise-like conditions where trajectories can be approximated in two dimensions or movement in the third dimension is highly penalised for passenger comfort [2]- [4]. Methods such as mixed integer linear progranuning (MILP) require a linearisation of the problem and are too slow on centralised problems with large numbers of vehicles due to the number of binary variables [5].…”

Optimal circular 3-arced with constant speed coordinated maneuvers for planar multi aircraft conflict resolution

“…In this case explicit mathematical solution becomes available [6]. An extension of this method for three dimensional encounters for two aircraft was presented in [3]. This method has not been extended for multiple aircraft encounters.…”

“…Assuming, each aircraft has a cost function which is defined by integration of square of its speed over the specified maneuver time interval. It has been shown that the least energy for a single aircraft is the constant-speed motion along the line segment from its starting to its destination position [3]. If an aircraft is forced to move along some fixed curve other than a line segment, then the parameterization of the curve with the least energy is the one with constant speed, and the minimal energy is proportional to the square of the curve length.…”

“…imposes shorter travel distance, less speed variation, less fuel consumption and more passenger comfort, which are important in the ATM context [3].…”