Aircraft guidance based on partial differential equation for miss distance

• US 9,684,309 B2
• Filed: 01/06/2016
• Issued: 06/20/2017
• Est. Priority Date: 03/12/2015
• Status: Active Grant

• Current Assignee: Charles Stark Draper Laboratory Incorporated
• Original Assignee: Charles Stark Draper Laboratory Incorporated
• Inventors: Carter, David W., Rasmussen, Scott A.
• Primary Examiner(s): NGUYEN, TAN QUANG
• Application Number:
  US14/989,033
• Publication Number:
  US 20160266582A1
• Time in Patent Office: 531 Days
• Field of Search: 701 3, 701408
• CPC Class Codes: G01C 23/00 Combined instruments indicating more than one navigational value, e.g. for aircraft; Combined measuring devices for measuring two or more variables of movement, e.g. distance, speed or acceleration
• CPC Class Codes: G05D 1/0676 specially adapted for landing
• CPC Class Codes: G05D 1/105 specially adapted for unpowered flight, e.g. glider, parachuting, forced landing parachutes per se B64D17/00
• CPC Class Codes: G05D 1/12 Target-seeking control

Abstract

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.

Claims

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.

2. A method according to claim 1, wherein:

the aircraft is characterized by an amount by which its airspeed can be changed while maintaining flight; and

C takes into account the amount by which the aircraft airspeed can be changed.

3. A method according to claim 1, wherein C satisfies a Hamilton-Jacobi partial differential equation.

4. A method according to claim 3, wherein:

the method automatically guides the aircraft through wind;

C satisfies a partial differential equation of the form;

5. A method according to claim 4, wherein determining the at least one component of the current gradient comprises calculating a projection of the current gradient along a direction that is orthogonal to a direction from the aircraft to the target.

6. A method according to claim 5, wherein determining the at least one component of the current gradient of C comprises calculating a difference between

7. A method according to claim 4, wherein:

the aircraft is characterized by an amount (δ

v_max) by which nominal airspeed of the aircraft can be changed while maintaining flight; and

C satisfies a partial differential equation of the form;

8. A method according to claim 7, further comprising:

automatically comparing

9. A method according to claim 8, wherein automatically determining the at least one component of the current gradient of C comprises:

selecting a table from a plurality of tables, wherein the plurality of tables stores pre-calculated values of partial derivatives of C for a plurality of nominal aircraft airspeeds, a plurality of maximum turn rates and a plurality of uncertainties of speed of the wind, wherein the selecting is based on the nominal aircraft airspeed, the maximum turn rate of the aircraft and uncertainty of speed of the wind; and

accessing the selected table according to the current coordinates and the current remaining amount of time of flight of the aircraft, wherein the table stores pre-calculated values of the partial derivatives of C for a plurality of current coordinates and a plurality of remaining amounts of time of flight of the aircraft.

10. A method according to claim 1, wherein automatically determining the at least one component of the current gradient of C comprises accessing a table according to the current coordinates and the current remaining amount of time of flight of the aircraft, wherein the table stores pre-calculated values of partial derivatives of C for a plurality of current coordinates and a plurality of remaining amounts of time of flight of the aircraft.

11. A method according to claim 10, wherein:

the method automatically guides the aircraft through wind; and

accessing the table comprises selecting a table of a plurality of tables, wherein the plurality of tables stores pre-calculated values of partial derivatives of C for a plurality of aircraft airspeeds, a plurality of maximum turn rates and a plurality of uncertainties of speed of the wind, wherein the selecting is based on the aircraft airspeed, the maximum turn rate of the aircraft and uncertainty of speed of the wind.

12. A method according to claim 1, wherein automatically determining the at least one component of the current gradient of C comprises accessing a table according to the current coordinates and the current remaining amount of time of flight of the aircraft, wherein the table stores pre-calculated partial derivatives of C for a plurality of current coordinates and a plurality of remaining amounts of time of flight of the aircraft.

13. A method according to claim 1, wherein automatically determining the at least one component of the current gradient of C comprises, after each time receiving the signals indicating a then-current location of the aircraft, calculating a partial derivative of C according to then-current coordinates and then-current remaining amount of time of flight of the aircraft.

14. A method according to claim 1, further comprising:

estimating displacement of the aircraft due to wind; and

adjusting the current coordinates of the aircraft by the estimated displacement of the aircraft, thereby automatically determining adjusted current coordinates of the aircraft.

15. A method according to claim 14, wherein estimating the displacement of the aircraft due to the wind comprises:

estimating velocity of the wind as a function of altitude; and

calculating;

16. A method according to claim 15, wherein estimating the velocity of the wind comprises accessing a table according to the altitude of the aircraft, wherein the table stores a plurality of velocities of the wind for a corresponding plurality of altitudes.

17. A method according to claim 14, further comprising rotating the adjusted current coordinates of the aircraft, thereby automatically determining rotated adjusted current coordinates of the aircraft, such that an axis of the rotated adjusted current coordinates of the aircraft points in a direction of horizontal current flight of the aircraft.

18. A method according to claim 17, wherein:

C satisfies a partial differential equation of the form;

19. A method according to claim 17, wherein adjusting the current coordinates of the aircraft by the estimated displacement due to the wind and rotating the adjusted current coordinates of the aircraft comprise calculating:

x=+(r_N+Δ

r_N)cos ψ

+(r_E+Δ

r_E)sin ψ

, and

y=−

(r_N+Δ

r_N)sin ψ

+(r_E+Δ

r_E)cos ψ

, where;

ψ

represents the current heading of the aircraft.

20. A system for automatically guiding an aircraft toward a target, the aircraft having a maximum turn rate, the system comprising:

a coordinates calculator receiving signals indicating current location of the aircraft and automatically generating signals indicating current coordinates of the aircraft, relative to location of the target;

a flight time estimator receiving signals indicating current altitude of the aircraft and automatically generating signals indicating estimated current remaining amount of time of flight of the aircraft;

a gradient component calculator coupled to the coordinates calculator and to the flight time estimator and automatically generating signals indicating at least one component of a current gradient of function C, where C satisfies a partial differential equation and a boundary condition, and C represents miss distance as a function of at least current heading of the aircraft, the current coordinates of the aircraft, relative to the target, and the current remaining amount of time of flight of the aircraft;

a first comparator coupled to the gradient component calculator and comparing the at least one component of the current gradient of C to at least one of a first predetermined value and a second predetermined value;

a first signal generator coupled to the first comparator and generating a first signal commanding a turn of the aircraft in a first direction if the at least one component of the current gradient is found by the first comparator to be less than the first predetermined value; and

a second signal generator coupled to the first comparator and generating a second signal commanding a turn of the aircraft in a second direction different than the first direction if the at least one component of the current gradient is found by the first comparator to be greater than the second predetermined value;

wherein

the coordinates calculator, the flight time estimator, the gradient component calculator, the first comparator, the first signal generator and the second signal generator operate repeatedly until the current remaining amount of time of flight of the aircraft is less than a third predetermined value.

21. A non-transitory computer-readable medium encoded with instructions that, when executed by a processor, establish processes for performing a computer-implemented method of providing automatic guidance of an aircraft toward a target, the aircraft having a maximum turn rate, the processes 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.