Multiple Aircraft Deconflicted Path Planning with Weather Avoidance Constraints

Jessica Pannequin, Alexandre Bayen, Ian Mitchell, Hoam Chung and Shankar Sastry.

Article submitted to the 2007 AIAA Guidance, Navigation and Control Conference. PDF

Abstract

We present a model predictive control based algorithm for aircraft motion planning that will apply to converging flows of aircraft going through convective weather in the en route airspace. The cost function associated with the model predictive control optimization problem is obtained by solving the Hamilton-Jacobi equation, a non-linear partial differential equation. For a given wind profile, convective weather conditions and aircraft destination, the solution to the Hamilton-Jacobi equation provides a value function that corresponds to the minimum travel time from any point in the NAS to the specified destination. The optimal control sequence is then computed over a fixed horizon by minimizing the aircraft cost function, subject to aircraft separation constraints and bounds on aircraft turning rates. This algorithm results in aircraft trajectories corresponding to a locally optimal solution of the optimization program involving the set of aircraft considered.

Movies

	Trajectories generated by the algorithm of section III with a quadratic objective function for 16 aircraft with no weather avoidance. (1 unit=1km). The larger circles correspond to the aircraft destinations while the smaller circles located at the current position of each aircraft refers to the protected zone around an aircraft, which must not be entered by another aircraft.
	Trajectories generated by the algorithm of section III with a quadratic objective function for 20 aircraft with convective weather avoidance. In this simulation, the bound around convective weather regions is tight. As a result, aircraft can fly next to severe convective weather cells. The larger circles correspond to the aircraft destinations while the smaller circles located at the current position of each aircraft refers to the protected zone around an aircraft, which must not be entered by another aircraft.
	Trajectories generated by the algorithm of section III with a quadratic objective function for 20 aircraft with convective weather avoidance. In this simulation, the bound around convective weather regions is conservative. As a result, aircraft fly at a greater distance from severe convective cells than in the previous simulation. The larger circles correspond to the aircraft destinations while the smaller circles located at the current position of each aircraft refers to the protected zone around an aircraft, which must not be entered by another aircraft.
	Trajectories generated by the algorithm of section III for 4 aircraft with an objective function derived from the HJ PDE with convective weather avoidance. The larger circles correspond to the aircraft destinations while the smaller circles located at the current position of each aircraft refers to the protected zone around an aircraft, which must not be entered by another aircraft.