Aircraft Guidance Based on Partial Differential Equation for Miss Distance

摘要

A guidance, navigation and control (GNC) system guides an aircraft based on a special partial differential equation (PDE). The system does not depend on a predetermined desired flight path. To overcome effects of unpredictable wind speed and direction, systems and methods effectively repeatedly determine the worst landing the wind can cause and issue flight control commands that minimize among these worst outcomes. A function C that satisfies the PDE calculates smallest miss distance a guidance system can bring about by appropriately steering an aircraft, given the aircraft's current heading, current location relative to a target and current remaining amount of time to fly. The system repeatedly determines at least a component of a current gradient of the function C. A value of the gradient component is used to select an appropriate flight control command, such as turn left or turn right.

主权项

1. A method for automatically guiding an aircraft toward a target, the aircraft having a maximum turn rate, the method comprising:
(a) receiving signals indicating current location, current altitude and current heading of the aircraft; (b) from the signals indicating the current location of the aircraft, automatically calculating current coordinates of the aircraft, relative to location of the target; (c) from the signals indicating the current altitude of the aircraft, automatically estimating current remaining amount of time of flight of the aircraft; (d) automatically determining at least one component of a current gradient of function C, wherein C satisfies a partial differential equation and a boundary condition, and C represents miss distance as a function of at least the current heading of the aircraft, the current coordinates of the aircraft, relative to the location of the target, and the current remaining amount of time of flight of the aircraft; (e) automatically comparing the at least one component of the current gradient to at least one of a first predetermined value and a second predetermined value; (f) if the at least one component of the current gradient is found by the comparing to be less than the first predetermined value, automatically sending a first signal commanding a turn of the aircraft in a first direction; (g) if the at least one component of the current gradient is found by the comparing to be greater than the second predetermined value, automatically sending a second signal commanding a turn of the aircraft in a second direction opposite the first direction; and (h) repeating (a)-(g) until the current remaining amount of time of flight of the aircraft is less than a third predetermined value.