Multiple aircraft deconflicted path planning with weather avoidance constraints

A nonlinear model predictive control based algorithm is presented for aircraft motion planning that will apply to converging flows of aircraft going through convective weather in the en route airspace. Two approaches for computing the objective function are explored and compared. The first involves a quadratic objective function while the second derives the objective function from the solution to the Hamilton-Jacobi equation, a nonlinear partial differential equation. For given static convective weather conditions and aircraft destinations, 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. In both cases, the optimal control sequence is computed over a fixed horizon by minimizing the aircraft objective function, subject to aircraft separation constraints, bounds on aircraft turning rates and convective weather avoidance constraints. This algorithm results in a set of locally optimal trajectories for the aircraft considered.