TIME-TO-GO MISSILE GUIDANCE METHOD AND SYSTEM

• US 20100274415A1
• Filed: 03/08/2007
• Published: 10/28/2010
• Est. Priority Date: 12/13/2004
• Status: Active Grant

• Current Assignee: Lockheed Martin Corporation (Martin Marietta Corporation)
• Original Assignee: Lockheed Martin Corporation (Martin Marietta Corporation)
• Inventors: Lam, Vincent C.
• Granted Patent: US 8,378,276 B2
• Time in Patent Office: Days
• US Class Current: 701/3
• CPC Class Codes: F41G 7/2206 using a remote control station
• CPC Class Codes: F41G 7/2246 Active homing systems, i.e. comprising both a transmitter and a receiver
• CPC Class Codes: F41G 7/2286 using radio waves
• CPC Class Codes: F42C 13/04 operated by radio waves

Abstract

A method and apparatus for guiding a vehicle to intercept a target is described. The method iteratively estimates a time-to-go until target intercept and modifies an acceleration command based upon the revised time-to-go estimate. The time-to-go estimate depends upon the position, the velocity, and the actual or real time acceleration of both the vehicle and the target. By more accurately estimating the time-to-go, the method is especially useful for applications employing a warhead designed to detonate in close proximity to the target. The method may also be used in vehicle accident avoidance and vehicle guidance applications.

Claims

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31. A computer readable medium encoded with computer executable code capable of being run on a computer for guiding a vehicle to a target, the computer executable code comprising:

computer executable code for determining a vehicle-to-target position vector r;

computer executable code for determining a net vehicle-to-target velocity v;

computer executable code for determining a net vehicle-to-target acceleration a;

computer executable code for determining the time-to-go τ

according to a first equation;

$\frac{1}{2}<br><br>a·<br><br>a<br><br><br><br>{\mathrm{\tau <br><br>}}^3+\frac{3}{2}<br><br>a·<br><br>v<br><br><br><br>{\mathrm{\tau <br><br>}}^2+\left(a·<br><br>r+v·<br><br>v\right)<br><br>\mathrm{\tau <br><br>}+v·<br><br>r=0;<br><br>$

computer executable code for determining an acceleration command A according to a second equation;

$A=\frac{r}{{\mathrm{\tau <br><br>}}^2}+\frac{v}{\mathrm{\tau <br><br>}}+\frac{1}{2}<br><br>a<br><br>;<br><br>$

and

computer executable code for generating control signals based upon the thus calculated acceleration command A.

32. A computer readable medium in accordance with claim 31, wherein a time-to-go solution to the first equation is approximated by the equation:

$\mathrm{\tau <br><br>}={\left(-\frac{e}{2}+\sqrt{\frac{e^2}{4}+\frac{d^3}{27}}\right)}^{\frac{1}{3}}+{\left(-\frac{e}{2}-\sqrt{\frac{e^2}{4}+\frac{d^3}{27}}\right)}^{\frac{1}{3}}-\stackrel{\_}{v}<br><br>\cos <br><br><br><br>\mathrm{\gamma <br><br>},$

wherein;

d=2( r cos β

+ v²)−

3 v² cos² γ

,

e=2 v³ cos³ γ

−

2 v cos γ

( r cos β

+ v²)+2 v r cos α

,

v=v/a,

cos γ

=a·

v/av,

r=r/a,

cos β

=a·

r/ar,

cos β

=v·

r/vr,

a=|a|, a≠

0,

v=|v|, and

r=|r|.

33. A computer readable medium in accordance with claim 31, wherein a time-to-go solution to the first equation is approximated by the equation:

$\mathrm{\tau <br><br>}=2<br><br>\sqrt{\frac{-d}{3}}<br><br>\cos <br><br>\left\{\frac{1}{3}<br><br>{\cos }^{-1}<br><br>\left(\frac{-e}{2<br><br>\sqrt{-d^3/27}}+\mathrm{\varphi <br><br>}\right)\right\}-\stackrel{\_}{v}<br><br>\cos <br><br><br><br>\mathrm{\gamma <br><br>},$

wherein;

d=2( r cos β

+ v²)−

3 v² cos² γ

,

e=2 v³ cos³ γ

−

2 v cos γ

( r cos β

+ v²)+2 v r cos α

,

φ

=0, 2π

/3, or 4π

/3,

v=v/a,

cos γ

=a·

v/av,

r=r/a,

cos β

=a·

r/ar,

cos α

=v·

r/vr,

a=|a|, a≠

0,

v=|v|, and

r=|r|.

34. A computer readable medium in accordance with claim 31, wherein a time-to-go solution to the first equation is approximated by the equation:

τ

=(r₀/v₀)f(N, α

₀),

wherein;

r₀ is an initial vehicle-to-target distance,

v₀ is an initial net vehicle-to-target speed,

$\cos <br><br><br><br>{\mathrm{\alpha <br><br>}}_0=\frac{{\stackrel{.}{r}}_0}{v_0},$

and

N is a proportional navigation constant.

35. A computer readable medium in accordance with claim 34, wherein f(N, α

₀) is approximated by;

$f<br><br>\left(N,{\mathrm{\alpha <br><br>}}_0\right)=\sec <br><br><br><br>{\mathrm{\alpha <br><br>}}_0<br><br>{\int <br><br>}_0^1<br><br>\frac{<br><br>\stackrel{\_}{r}}{\sqrt{1+\frac{{\tan }^2<br><br>{\mathrm{\alpha <br><br>}}_0}{N-1}<br><br>\left({\stackrel{\_}{r}}^{2<br><br><br><br>N-2}-1\right)}},<br><br>\mathrm{and}<br><br><br><br>\stackrel{\_}{r}=\frac{r}{r_0}.$

36. A computer readable medium in accordance with claim 34, wherein f(N, α

₀) is approximated by;

f(N, α

₀)≈

[1+p₁(N)α

₀+p₂(N)α

₀²+p₃(N)α

₀³+p₄(N)α

₀⁴+p₅(N)α

₀⁵], and p₁(N), p₂(N), p₃(N), p₄(N), and p₅(N) are polynomials of N.

37. A computer readable medium in accordance with claim 34, wherein f(N, α

₀) is approximated by;

$f<br><br>\left(N,{\mathrm{\alpha <br><br>}}_0\right)\approx <br><br>\sec <br><br><br><br>{\mathrm{\alpha <br><br>}}_0<br><br>{\left\{1-\frac{{\tan }^2<br><br>{\mathrm{\alpha <br><br>}}_0}{N-1}\right\}}^{-\frac{1}{2}}<br><br>\left\{1-\frac{{\tan }^2<br><br>{\mathrm{\alpha <br><br>}}_0}{2<br><br>\left(2<br><br><br><br>N-1\right)<br><br>\left[\begin{array}{c}\left(N-1\right)-\\ {\tan }^2<br><br>{\mathrm{\alpha <br><br>}}_0\end{array}\right]}\right\}.$

38. A computer readable medium in accordance with claim 37, wherein τ

tan² α

₀<

(N−

1)/2.

39. A computer readable medium in accordance with claim 34, wherein N>

2.

40. A computer readable recording medium in accordance with claim 34.

89. The computer readable medium of claim 40, wherein N is one of 3, 4, and 5.

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48. A computer readable medium including computer executable code capable of being run on a computer for guiding a vehicle to avoid an obstacle, the computer executable code comprising:

computer executable code for determining a vehicle-to-obstacle position vector r;

computer executable code for determining a net vehicle-to-obstacle velocity v;

computer executable code for determining a net vehicle-to-obstacle acceleration a;

computer executable code for determining the time-to-go τ

between a current vehicle position and an obstacle position according to a first equation;

$\frac{1}{2}<br><br>a·<br><br>a<br><br><br><br>{\mathrm{\tau <br><br>}}^3+\frac{3}{2}<br><br>a·<br><br>v<br><br><br><br>{\mathrm{\tau <br><br>}}^2+\left(a·<br><br>r+v·<br><br>v\right)<br><br>\mathrm{\tau <br><br>}+v·<br><br>r=0;<br><br>$

computer executable code for determining an offset vector ψ

to avoid an obstacle;

computer executable code for determining an acceleration command A according to a second equation;

$A=\frac{r}{{\mathrm{\tau <br><br>}}^2}+\frac{v}{\mathrm{\tau <br><br>}}+\frac{1}{2}<br><br>a+\mathrm{\psi <br><br>};<br><br>$

and

computer executable code for generating a guidance signal based upon the thus determined acceleration command A.

49. A computer readable medium in accordance with claim 48, wherein the guidance signal is at least one of an audible warning and a visual warning.

50. A computer readable medium in accordance with claim 48, wherein the guidance signal is a braking command.

51. A method, comprising:

estimating a time-to-go from a vehicle to a target; and

adjusting the estimated time-to-go for the actual acceleration of the target.

52. The method of claim 51, wherein:

estimating the time-to-go includes determining a zero-effort-miss estimate; and

adjusting for the actual acceleration results in zero-effort-miss with acceleration compensation guidance estimate.

53. The method of claim 51, wherein:

estimating the time-to-go includes determining a true proportional navigation estimate; and

adjusting for the actual acceleration results in an augmented proportional navigation estimate.

54. The method of claim 51, further comprising acquiring the information from which the time-to-go is estimated.

55. The method of claim 54, wherein acquiring the information includes acquiring the vehicle-to-target vector, the vehicle-to-target velocity, and the vehicle-to-target acceleration.

56. The method of claim 54, wherein acquiring the information includes determining the information from a RADAR return signal or an optical return signal.

57. The method of claim 54, wherein acquiring the information includes receiving information from an external source.

58. The method of claim 54, wherein acquiring the information includes accessing at least a portion of the information from a memory.

59. The method of claim 51, further comprising modifying the course of the vehicle responsive to the acceleration adjusted estimated time-to-go.

60. The method of claim 59, wherein modifying the course of the vehicle includes modifying the course so that the vehicle intercepts the target.

61. The method of claim 59, wherein modifying the course of the vehicle includes modifying the course so that the vehicle avoids colliding with the target.

62. The method of claim 61, wherein modifying the course includes applying a minimum margin offset.

63. The method of claim 61, wherein modifying the course includes maintaining a safe distance relative to surrounding vehicles.

64. The method of claim 61, wherein modifying the course includes maintaining an intercept course.

65. The method of claim 51, wherein the target is an obstacle.

66. A computer readable medium encoded with a instructions that, when executed by a processor, perform a method, the method comprising:

estimating a time-to-go from a vehicle to a target; and

adjusting the estimated time-to-go for the actual acceleration of the target.

67. The computer readable medium of claim 66, wherein, in the method:

estimating the time-to-go includes determining a zero-effort-miss estimate; and

adjusting for the actual acceleration results in zero-effort-miss with acceleration compensation guidance estimate.

68. The computer readable medium of claim 66, wherein, in the method:

estimating the time-to-go includes determining a true proportional navigation estimate; and

adjusting for the actual acceleration results in an augmented proportional navigation estimate.

69. The computer readable medium of claim 66, wherein the method further comprises modifying the course of the vehicle responsive to the acceleration adjusted estimated time-to-go.

70. The computer readable medium of claim 69, wherein modifying the course of the vehicle in the method includes modifying the course so that the vehicle intercepts the target.

71. The computer readable medium of claim 69, wherein modifying the course of the vehicle in the method includes modifying the course so that the vehicle avoids colliding with the target.

72. The computer readable medium of claim 69, wherein modifying the course in the method includes applying a minimum margin offset.

73. The computer readable medium of claim 69, wherein modifying the course in the method includes maintaining a safe distance relative to surrounding vehicles.

74. The computer readable medium of claim 69, wherein modifying the course in the method includes maintaining an intercept course.

75. The computer readable medium of claim 66, wherein the target is an obstacle.

76. An apparatus, comprising:

a processor;

software that, when executed by the processor, performs a method comprising;

estimating a time-to-go from a vehicle to a target;

adjusting the estimated time-to-go for the actual acceleration of the target; and

iterating the estimating and adjusting over time.

77. The apparatus of claim 76, wherein, in the method:

estimating the time-to-go includes determining a zero-effort-miss estimate; and

adjusting for the actual acceleration results in zero-effort-miss with acceleration compensation guidance estimate.

78. The apparatus of claim 76, wherein, in the method:

estimating the time-to-go includes determining a true proportional navigation estimate; and

adjusting for the actual acceleration results in an augmented proportional navigation estimate.

79. The apparatus of claim 76, wherein the method further comprises modifying the course of the vehicle responsive to the acceleration adjusted estimated time-to-go.

80. The apparatus of claim 79, wherein modifying the course of the vehicle in the method includes modifying the course so that the vehicle intercepts the target.

81. The apparatus of claim 79, wherein modifying the course of the vehicle in the method includes modifying the course so that the vehicle avoids colliding with the target.

82. The apparatus of claim 79, wherein modifying the course in the method includes applying a minimum margin offset.

83. The apparatus of claim 79, wherein modifying the course in the method includes maintaining a safe distance relative to surrounding vehicles.

84. The apparatus of claim 79, wherein modifying the course in the method includes maintaining an intercept course.

85. The apparatus of claim 76, wherein the target is an obstacle.

86. The apparatus of claim 76, further comprising an on-board RADAR sensor and in which the method further comprises acquiring data through the RADAR sensor on which the estimating and adjusting are performed.

87. The apparatus of claim 76, wherein the method further comprises acquiring data on which the estimating and adjusting are performed from an external source.

88. The apparatus of claim 76, wherein the method further comprises acquiring data on which the estimating and adjusting are performed from an on-board memory.