Method for modeling dynamic trajectories of guided, self-propelled moving bodies

• US 10,289,761 B1
• Filed: 12/17/2013
• Issued: 05/14/2019
• Est. Priority Date: 06/12/2013
• Status: Active Grant

• Current Assignee: the united states of america as represented by the secretary of the navy
• Original Assignee: the united states of america as represented by the secretary of the navy
• Inventors: McMahon, Matthew D.
• Primary Examiner(s): Perveen, Rehana
• Assistant Examiner(s): Luu, Cuong V
• Application Number:
  US14/109,136
• Time in Patent Office: 1,974 Days
• Field of Search: 703 2
• CPC Class Codes: G06F 30/15 Vehicle, aircraft or watercraft design
• CPC Class Codes: G06F 30/20 Design optimisation, verification or simulation optimisation, verification or simulation of circuit designs G06F30/30

Abstract

According to exemplary practice of the present invention, the dynamic trajectory of a moving body is incrementally modeled using temporal and spatial relationships between the body and the target that the body pursues. In each time step, the body has starting positional coordinates and ending positional coordinates. The horizontal travel distance is calculated by taking into account the body'"'"'s speed and the body'"'"'s horizontal distance from the target. The vertical travel distance is calculated by taking into account the body trajectory'"'"'s spatial derivative and the body'"'"'s horizontal travel distance. The body'"'"'s time-step-ending positional coordinates thus reflect the change, in accordance with the horizontal travel distance and the vertical travel distance, relative to the body'"'"'s time-step-starting positional coordinates. Each succeeding time step repeats the computations whereby the starting positional coordinates are the ending positional coordinates of the preceding time step.

Claims

1. A computer-implemented method for describing motion of a moving object, the method comprising:

determining a horizontal distance traveled by said guided self-propelled moving object from an initial position of said guided self-propelled moving object, said determining of the horizontal distance traveled including taking into consideration a speed of said guided self-propelled moving object, a horizontal distance between said guided self-propelled moving object and a moving target, and a vertical distance between said guided self-propelled moving object and said moving target, wherein the speed of said guided self-propelled moving object is determined using a speed-dependency interpolation table, said speed-dependency interpolation table describing the speed of said guided self-propelled moving object along a ground range to said moving target versus the ground range to said moving target and an altitude relative to said moving target;

determining a vertical distance traveled by said guided self-propelled moving object from the initial position, said determining of the vertical distance traveled including taking into consideration the horizontal distance traveled and a spatial derivative of a trajectory of said guided self-propelled moving object, wherein the spatial derivative of the trajectory of said guided self-propelled moving object is determined using a spatial-derivative-dependency interpolation table, said spatial-derivative-dependency interpolation table describing the spatial derivative of the trajectory of said guided self-propelled moving object versus the ground range to said moving target and the altitude relative to said moving target;

determining a final position of said guided self-propelled moving object;

incrementally modeling the dynamic trajectory of a guided self-propelled moving object, wherein;

said incrementally modeling the dynamic trajectory of said guided self-propelled moving object is performed using a computer, is based on temporal and spatial relationships between said guided self-propelled moving object and said moving target, and includes dynamically determining a changing shape of a wire with reference to a moving aimpoint in a bead-on-a-wire construct characterizing the dynamic trajectory of said guided self-propelled moving object;

the bead-on-a-wire construct describes a wire and a speed of a moving bead moving along the wire as a function of time;

the moving bead represents said guided self-propelled moving objects;

the moving aimpoint represents said moving target;

the shape of the wire represents an overall shape of the dynamic trajectory of said guided self-propelled moving object;

said dynamically determining the changing shape of the wire includes using a spatial gradient of the shape of the wire.

2. The method of claim 1, wherein:

the horizontal distance traveled is the horizontal distance traveled by said moving object during a time step;

the vertical distance traveled is the vertical distance traveled by said moving object during said time step;

said initial position is at the beginning of said time step;

said final position is at the end of said time step.

3. The method of claim 2, wherein:

said method further comprises performing at least one iteration of said establishing of the initial position, said determining of the horizontal distance traveled, said determining of the vertical distance traveled, and said determining of the final position;

in each said iteration, the initial position is the final position of the previous said iteration;

in each said iteration, the beginning of said time step is the end of said time step of the previous said iteration.

4. The method of claim 3, wherein each said time step has the same duration.

5. The method of claim 1 comprising:

providing said speed-dependency interpolation table;

providing said spatial-derivative-dependency interpolation table;

establishing said initial position of said guided self-propelled moving object.

17. The method of claim 1, wherein said incrementally modeling the dynamic trajectory of said guided self-propelled moving object includes using a computer display for representing the dynamic trajectory of said guided self-propelled moving object.

6. An apparatus comprising a computer having computer code characterized by computer program logic for enabling said computer to describe motion of a guided and self-propelled moving object, said computer code being executable by said computer so that, in accordance with said computer program logic, said computer performs acts including:

determining a horizontal distance traveled by said moving object from an initial position of said moving object, said determination of the horizontal distance traveled being based on a speed of said moving object, a horizontal distance between said object and a moving target, and a vertical distance between said moving object and said moving target, wherein the speed of said moving object is determined using a speed-dependency interpolation table, said speed-dependency interpolation table describing the speed of said moving object along a ground range to said moving target versus the ground range to said moving target and an altitude relative to said moving target;

determining a vertical distance traveled by said moving object from the initial position of said moving object, said determination of the vertical distance traveled being based on the horizontal distance traveled by said moving object and a spatial derivative of a trajectory of said moving object, wherein the spatial derivative of the trajectory of said moving object is determined using a spatial-derivative-dependency interpolation table, said spatial-derivative-dependency interpolation table describing the spatial derivative of the trajectory of said moving object versus the ground range to said moving target and the altitude relative to said moving target;

determining a final position of said moving object;

incrementally modeling the dynamic trajectory of said moving object, wherein said incrementally modeling the dynamic trajectory of said moving object is based on temporal and spatial relationships between said moving object and said moving target, wherein said incrementally modeling the dynamic trajectory of said moving object includes dynamically determining a changing shape of a wire with reference to a moving aimpoint in a bead-on-a-wire construct characterizing the dynamic trajectory of said moving object, the bead-on-a-wire construct describing a wire and a speed of a moving bead moving along the wire as a function of time, the moving bead representing said moving object, the moving aimpoint representing said moving target, the shape of the wire representing an overall shape of the dynamic trajectory of said moving object, wherein said dynamically determining the changing shape of the wire includes using a spatial gradient of the shape of the wire.

7. The apparatus of claim 6, wherein:

the horizontal distance traveled is the horizontal distance traveled by said moving object during a time step;

the vertical distance traveled is the vertical distance traveled by said moving object during said time step;

said initial position is at the beginning of said time step;

said final position is at the end of said time step.

8. The apparatus of claim 7, wherein:

said computer performs acts further including performing at least one iteration of said establishment of the initial position, said determination of the horizontal distance traveled, said determination of the vertical distance traveled, and said determination of the final position;

in each said iteration, the initial position is the final position of the previous said iteration;

in each said iteration, the beginning of said time step is the end of said time step of the previous said iteration.

9. The apparatus of claim 7, wherein said computer performs acts including:

providing said speed-dependency interpolation table;

providing said spatial-derivative-dependency interpolation table;

establishing said initial position of said moving object.

10. The apparatus of claim 8, wherein each said time step has the same duration.

18. The apparatus of claim 6, wherein said incrementally modeling the dynamic trajectory of said moving object includes using a computer display for representing the dynamic trajectory of said moving object.

11. A computer program product for modeling the dynamic trajectory of a moving body, the computer program product comprising a non-transitory computer-readable storage medium having computer-readable program code portions stored therein for execution by a computer, the computer-readable program code portions including:

a first executable program code portion, for providing a speed-dependency interpolation table;

a second executable program code portion, for providing a spatial-derivative-dependency interpolation table;

a third executable program code portion, for establishing a time step, a first horizontal position coordinate, and a first vertical position coordinate, wherein the first horizontal position coordinate and the first vertical position coordinate define a position of a moving body at the beginning of the time step, said moving body being a guided and self-propelled moving body;

a fourth executable program code portion, for computing a speed-dependency relationship, the speed-dependency relationship describing a relationship between a speed of said moving body and at least two independent variables, wherein said at least two independent variables include a horizontal distance between said moving body and a moving target, and a vertical distance between said moving body and said moving target, wherein the speed of said moving body is determined using said speed-dependency interpolation table, said speed-dependency interpolation table describing the speed of said moving body along a ground range to said moving target versus a ground range to said moving target and an altitude relative to said moving target;

a fifth executable program code portion, for providing a spatial-derivative-dependency relationship, wherein the spatial-derivative-dependency relationship describes a relationship between a spatial derivative of a trajectory of said moving body and said at least two independent variables, wherein the spatial derivative of the trajectory of said moving body is determined using said spatial-derivative-dependency interpolation table, said spatial-derivative-dependency interpolation table describing the spatial derivative of the trajectory of said moving object versus the ground range to said moving target and the altitude relative to said moving target;

a sixth executable program code portion, for computing a horizontal speed component of said moving body, wherein the computation of the horizontal speed component includes using the speed-dependency relationship;

a seventh executable program code portion, for computing a horizontal travel distance of said moving body, wherein the computation of the horizontal travel distance includes using the horizontal speed component;

an eighth executable program code portion, for computing a spatial derivative of said moving body, wherein the computation of the spatial derivative includes using the spatial-derivative-dependency relationship;

a ninth executable program code portion, for computing a vertical travel distance of said moving body, wherein the computation of the vertical travel distance includes using the horizontal travel distance and the spatial derivative;

a tenth executable program code portion, for computing a second horizontal position coordinate and a second vertical position coordinate, the second horizontal position coordinate and the second vertical position coordinate defining a position of said moving body at the end of the time step, wherein the computation of the second horizontal position coordinate and the second vertical position coordinate includes using the computed horizontal travel distance and the computed vertical travel distance;

an eleventh executable program code portion, for incrementally modeling the dynamic trajectory of said moving body, wherein said incrementally modeling the dynamic trajectory of said moving body is based on temporal and spatial relationships between said moving body and said moving target, wherein said incrementally modeling the dynamic trajectory of said moving body includes computing a dynamically changing shape of a wire with reference to a moving aimpoint in a bead-on-a-wire construct characterizing the dynamic trajectory of said moving body, the bead-on-a-wire construct describing a wire and a speed of a moving bead moving along the wire as a function of time, the moving bead representing said moving body, the moving aimpoint representing said moving target, the shape of the wire representing an overall shape of the dynamic trajectory of said moving body, wherein said computing the changing shape of the wire includes using a spatial gradient of the shape of the wire.

12. The computer program product of claim 11, wherein:

the duration of the time step is Δ

t;

the beginning time of the time step is t;

the ending time of the time step is t+Δ

t;

the first horizontal position coordinate is x;

the first vertical position coordinate is a;

the second horizontal position coordinate is x+Δ

x;

the second vertical position coordinate is a+Δ

a;

the horizontal speed component is v_x;

the spatial derivative is da/dx;

the horizontal travel distance is Δ

x;

the vertical travel distance is Δ

a;

the computation of the horizontal travel distance is in accordance with the equation Δ

x=v_xΔ

t;

the computation of the vertical travel distance is in accordance with the equation

13. The computer program product of claim 12, wherein:

the computer-readable program code portions further include a twelfth executable program code portion, for bringing about at least one iteration of the computations of the computer-readable program code portions including said sixth executable program code portion, said seventh executable program code portion, said eighth executable program code portion, said ninth executable program code portion, and said tenth executable program code portion;

in each said iteration;

said first horizontal position coordinate is said second horizontal position coordinate of the previous said time step;

said first vertical position coordinate is said second vertical position coordinate of the previous said time step;

the beginning time of said time step is the ending time of the previous said time step.

14. The computer program product of claim 13, wherein each said time step has the same duration Δ

t.

15. The computer program product of claim 11, wherein:

the computer-readable program code portions further include a twelfth executable program code portion, for bringing about at least one iteration of the computations of the computer-readable program code portions including said sixth executable program code portion, said seventh executable program code portion, said eighth executable program code portion, said ninth executable program code portion, and said tenth executable program code portion;

in each said iteration;

said first horizontal position coordinate is said second horizontal position coordinate of the previous said time step;

said first vertical position coordinate is said second vertical position coordinate of the previous said time step;

the beginning time of said time step is the ending time of the previous said time step.

16. The computer program product of claim 15, wherein each said time step has the same duration.

19. The computer program product of claim 11, wherein said incrementally modeling the dynamic trajectory of said moving body includes using a computer display for representing the dynamic trajectory of said moving body.